******************************************************************************* ******************************************************************************* ********** *********** ********** "Establishment of *********** ********** the Direct Numerical Simulation Data Bases of *********** ********** Turbulent Transport Phenomena" *********** ********** *********** ********** Co-operative Research *********** ********** No. 02302043 *********** ********** *********** ********** Supported by the Ministry of Education, *********** ********** Science and Culture *********** ********** *********** ********** 1990 - 1992 *********** ********** *********** ********** *********** ********** *********** ********** *********** ********** N. Kasagi (PI) *********** ********** K. Horiuti, Y. Miyake, T. Miyauchi, Y. Nagano *********** ********** *********** ******************************************************************************* ******************************************************************************* ******************************************************************************* ******************************************************************************* ********** << CAUTION >> *********** ********** *********** ********** All rights are reserved by the computors of each data *********** ********** base. No part of the data described herein may be *********** ********** represented or otherwise used in any form without fully *********** ********** referring to this data base and the literature cited at *********** ********** the end of the data base. The original data base will *********** ********** be revised without notice, whenever necessary. *********** ********** *********** ******************************************************************************* ******************************************************************************* =================== this data base begins from this line ====================== Test Case: Fully Developed Thermal Field in a 2-D Turbulent Channel Flow Code Number: CH122_PG.WL2 Date of Release: April 16, 1991, May 1, 1993 Date of Revision: Computors: Y. Ohtsubo and N. Kasagi Department of Mechanical Engineering The University of Tokyo Bunkyo-ku, Tokyo 113 Nomenclature alfa = thermal diffusivity alfa_t = eddy diffusivity for heat delta = channel half width k_x, k_z = streamwise and spanwise wave numbers nu = kinematic viscocity nu_t = eddy diffusivity for momentum omega_y = vorticity component in the y-direction Pr = Prandtl number Pr_t = turbulent Prandtl number R(ab) = correlation coefficient between a and b Re_tau = Reynolds number based on u_tau, delta and nu Uc = channel center mean velocity u, v, w = streamwise, wall-normal and spanwise velocity fluctuations u_mean = mean temperature u_tau = friction velocity u_i = i-th component of velocity fluctuation u+, v+, w+ = u/u_tau, v/u_tau, w/u_tau t = temperature fluctuation t_mean = mean temperature t_tau = friction temperature t+ = t/t_tau x,y,z =streamwise, wall-normal, spanwise directions y+ = y*u_tau/nu 1. Description of Flow Field The flow field simulated is a fully developed two-dimensional turbulent flow between two parallel walls. The iso-flux condition is imposed on the walls so that the local mean temperature linearly increases in the streamwise direction. Hence, temperature is re-defined as the difference from the wall temperature, and both flow and thermal fields are homogeneous in the streamwise and spanwise directions; the turbulence statistics are dependent only upon the distance from the wall. The data presented here are non- dimensionalized by the wall variables, i.e., u_tau, nu and t_tau. The flow condition is specified by the mean pressure gradient imposed (or the friction velocity) and the distance between the walls (channel height). 2. Numerical Method Governing equations: a forth-order equation for v, second-order equation for omega_y, the continuity equation for flow field and the energy equation for thermal field. Discretization method: spectral method = 128 x 128 Fourier series in the x- and z-directions, and Chebyshev polynomials up to the order 97 in the y- direction (Chebyshev-tau method). Aliasing treatment: nonlinear terms computed with collocation grids 1.5 times finer in each direction. Grid spacing: 18.4 and 7.36 viscous units in the x- and z-directions and 0.08 to 4.9 viscous units in the y-direction. Time integration: second order Adams-Bashforth for the nonlinear terms and Crank-Nicolson for the diffusion terms. Size of computational box: 5*pi*delta x 2*delta x 2*pi*delta. Initial conditions: u', v' and u_mean given by the previous numerical results (see, Flow Case CH12__PG.WL1). t_mean given by Kader's correlation eq. and t' given by uniform low values in spectral space. Criterion for stationary state: identified by balance of the mean energy equation and also by stationary behavior of second, third and forth moments of temperature fluctuations. Error in continuity equation: not applicable Length of time integration for ensemble averaging: about 13.6*delta/u_tau (2040 nu/u_tau**2) after the fully developed state is reached. Computer: HITAC-S820/80 at the Computer Center of the University of Tokyo. Computation time: 5.3 sec CPU time per one time step. 3. Flow Conditions Re_tau = delta*u_tau/nu = 150 Re_bulk = 2*delta*Um/nu = 4580 Pr = 0.025 4. Numerical Data 4.1 Turbulence statistics j y+ t_mean/t_tau 1 1.000000e-40 -2.140121e-15 2 3.569590e-02 8.950923e-04 3 1.427670e-01 3.579737e-03 4 3.211620e-01 8.052638e-03 5 5.707950e-01 1.431172e-02 6 8.915490e-01 2.235325e-02 7 1.283270e+00 3.217245e-02 8 1.745770e+00 4.376308e-02 9 2.278840e+00 5.711630e-02 10 2.882210e+00 7.222106e-02 11 3.555600e+00 8.906348e-02 12 4.298690e+00 1.076254e-01 13 5.111130e+00 1.278854e-01 14 5.992520e+00 1.498170e-01 15 6.942460e+00 1.733871e-01 16 7.960480e+00 1.985587e-01 17 9.046110e+00 2.252881e-01 18 1.019880e+01 2.535251e-01 19 1.141810e+01 2.832136e-01 20 1.270330e+01 3.142906e-01 21 1.405380e+01 3.466886e-01 22 1.546910e+01 3.803335e-01 23 1.694840e+01 4.151482e-01 24 1.849100e+01 4.510497e-01 25 2.009620e+01 4.879533e-01 26 2.176320e+01 5.257729e-01 27 2.349130e+01 5.644183e-01 28 2.527960e+01 6.038014e-01 29 2.712720e+01 6.438332e-01 30 2.903330e+01 6.844248e-01 31 3.099700e+01 7.254887e-01 32 3.301730e+01 7.669399e-01 33 3.509330e+01 8.086939e-01 34 3.722400e+01 8.506682e-01 35 3.940840e+01 8.927839e-01 36 4.164540e+01 9.349621e-01 37 4.393400e+01 9.771259e-01 38 4.627300e+01 1.019204e+00 39 4.866150e+01 1.061116e+00 40 5.109810e+01 1.102799e+00 41 5.358190e+01 1.144175e+00 42 5.611150e+01 1.185181e+00 43 5.868580e+01 1.225740e+00 44 6.130360e+01 1.265796e+00 45 6.396350e+01 1.305272e+00 46 6.666450e+01 1.344105e+00 47 6.940510e+01 1.382238e+00 48 7.218400e+01 1.419588e+00 49 7.500000e+01 1.456109e+00 50 7.785170e+01 1.491729e+00 51 8.073770e+01 1.526391e+00 52 8.365670e+01 1.560026e+00 53 8.660730e+01 1.592571e+00 54 8.958800e+01 1.623974e+00 55 9.259750e+01 1.654173e+00 56 9.563430e+01 1.683113e+00 57 9.869700e+01 1.710737e+00 58 1.017840e+02 1.736981e+00 59 1.048940e+02 1.761806e+00 60 1.080260e+02 1.785161e+00 61 1.111770e+02 1.806991e+00 62 1.143470e+02 1.827254e+00 63 1.175340e+02 1.845907e+00 64 1.207360e+02 1.862908e+00 65 1.239530e+02 1.878222e+00 66 1.271810e+02 1.891811e+00 67 1.304210e+02 1.903653e+00 68 1.336700e+02 1.913719e+00 69 1.369270e+02 1.921979e+00 70 1.401900e+02 1.928422e+00 71 1.434570e+02 1.933033e+00 72 1.467280e+02 1.935796e+00 73 1.500000e+02 1.936711e+00 j y+ t_rms/t_tau 1 1.000000e-40 1.092053e-15 2 3.569590e-02 1.251645e-04 3 1.427670e-01 5.006020e-04 4 3.211620e-01 1.126153e-03 5 5.707950e-01 2.001593e-03 6 8.915490e-01 3.126645e-03 7 1.283270e+00 4.501049e-03 8 1.745770e+00 6.124493e-03 9 2.278840e+00 7.996541e-03 10 2.882210e+00 1.011650e-02 11 3.555600e+00 1.248311e-02 12 4.298690e+00 1.509437e-02 13 5.111130e+00 1.794711e-02 14 5.992520e+00 2.103646e-02 15 6.942460e+00 2.435582e-02 16 7.960480e+00 2.789624e-02 17 9.046110e+00 3.164621e-02 18 1.019880e+01 3.559142e-02 19 1.141810e+01 3.971467e-02 20 1.270330e+01 4.399592e-02 21 1.405380e+01 4.841215e-02 22 1.546910e+01 5.293803e-02 23 1.694840e+01 5.754609e-02 24 1.849100e+01 6.220723e-02 25 2.009620e+01 6.689137e-02 26 2.176320e+01 7.156792e-02 27 2.349130e+01 7.620640e-02 28 2.527960e+01 8.077694e-02 29 2.712720e+01 8.525070e-02 30 2.903330e+01 8.960016e-02 31 3.099700e+01 9.379939e-02 32 3.301730e+01 9.782443e-02 33 3.509330e+01 1.016530e-01 34 3.722400e+01 1.052650e-01 35 3.940840e+01 1.086427e-01 36 4.164540e+01 1.117691e-01 37 4.393400e+01 1.146307e-01 38 4.627300e+01 1.172149e-01 39 4.866150e+01 1.195106e-01 40 5.109810e+01 1.215092e-01 41 5.358190e+01 1.232029e-01 42 5.611150e+01 1.245867e-01 43 5.868580e+01 1.256563e-01 44 6.130360e+01 1.264085e-01 45 6.396350e+01 1.268438e-01 46 6.666450e+01 1.269621e-01 47 6.940510e+01 1.267671e-01 48 7.218400e+01 1.262624e-01 49 7.500000e+01 1.254535e-01 50 7.785170e+01 1.243481e-01 51 8.073770e+01 1.229541e-01 52 8.365670e+01 1.212814e-01 53 8.660730e+01 1.193408e-01 54 8.958800e+01 1.171465e-01 55 9.259750e+01 1.147121e-01 56 9.563430e+01 1.120562e-01 57 9.869700e+01 1.091975e-01 58 1.017840e+02 1.061594e-01 59 1.048940e+02 1.029663e-01 60 1.080260e+02 9.964787e-02 61 1.111770e+02 9.623543e-02 62 1.143470e+02 9.276493e-02 63 1.175340e+02 8.927641e-02 64 1.207360e+02 8.581466e-02 65 1.239530e+02 8.242946e-02 66 1.271810e+02 7.917627e-02 67 1.304210e+02 7.611604e-02 68 1.336700e+02 7.331419e-02 69 1.369270e+02 7.083921e-02 70 1.401900e+02 6.875965e-02 71 1.434570e+02 6.713989e-02 72 1.467280e+02 6.603500e-02 73 1.500000e+02 6.548494e-02 j y+ S(t) 1 1.000000e-40 -1.000000e-40 2 3.569590e-02 4.760502e-01 3 1.427670e-01 4.760568e-01 4 3.211620e-01 4.760621e-01 5 5.707950e-01 4.760778e-01 6 8.915490e-01 4.760995e-01 7 1.283270e+00 4.760999e-01 8 1.745770e+00 4.760349e-01 9 2.278840e+00 4.758396e-01 10 2.882210e+00 4.754191e-01 11 3.555600e+00 4.746598e-01 12 4.298690e+00 4.734358e-01 13 5.111130e+00 4.716113e-01 14 5.992520e+00 4.690463e-01 15 6.942460e+00 4.656076e-01 16 7.960480e+00 4.611625e-01 17 9.046110e+00 4.555889e-01 18 1.019880e+01 4.487781e-01 19 1.141810e+01 4.406378e-01 20 1.270330e+01 4.310985e-01 21 1.405380e+01 4.201212e-01 22 1.546910e+01 4.076992e-01 23 1.694840e+01 3.938591e-01 24 1.849100e+01 3.786598e-01 25 2.009620e+01 3.621858e-01 26 2.176320e+01 3.445424e-01 27 2.349130e+01 3.258483e-01 28 2.527960e+01 3.062282e-01 29 2.712720e+01 2.858073e-01 30 2.903330e+01 2.647086e-01 31 3.099700e+01 2.430479e-01 32 3.301730e+01 2.209304e-01 33 3.509330e+01 1.984530e-01 34 3.722400e+01 1.756981e-01 35 3.940840e+01 1.527353e-01 36 4.164540e+01 1.296215e-01 37 4.393400e+01 1.063990e-01 38 4.627300e+01 8.309591e-02 39 4.866150e+01 5.972499e-02 40 5.109810e+01 3.628539e-02 41 5.358190e+01 1.276522e-02 42 5.611150e+01 -1.085504e-02 43 5.868580e+01 -3.459840e-02 44 6.130360e+01 -5.848753e-02 45 6.396350e+01 -8.254068e-02 46 6.666450e+01 -1.067694e-01 47 6.940510e+01 -1.311775e-01 48 7.218400e+01 -1.557544e-01 49 7.500000e+01 -1.804740e-01 50 7.785170e+01 -2.052965e-01 51 8.073770e+01 -2.301665e-01 52 8.365670e+01 -2.550167e-01 53 8.660730e+01 -2.797649e-01 54 8.958800e+01 -3.043068e-01 55 9.259750e+01 -3.285028e-01 56 9.563430e+01 -3.521656e-01 57 9.869700e+01 -3.750450e-01 58 1.017840e+02 -3.968090e-01 59 1.048940e+02 -4.170261e-01 60 1.080260e+02 -4.351407e-01 61 1.111770e+02 -4.504549e-01 62 1.143470e+02 -4.621160e-01 63 1.175340e+02 -4.691284e-01 64 1.207360e+02 -4.704063e-01 65 1.239530e+02 -4.648760e-01 66 1.271810e+02 -4.516684e-01 67 1.304210e+02 -4.304046e-01 68 1.336700e+02 -4.015780e-01 69 1.369270e+02 -3.669544e-01 70 1.401900e+02 -3.298377e-01 71 1.434570e+02 -2.949435e-01 72 1.467280e+02 -2.676716e-01 73 1.500000e+02 -2.527978e-01 j y+ F(t) 1 1.000000e-40 1.000000e-40 2 3.569590e-02 3.184134e+00 3 1.427670e-01 3.184201e+00 4 3.211620e-01 3.184238e+00 5 5.707950e-01 3.184273e+00 6 8.915490e-01 3.184325e+00 7 1.283270e+00 3.184316e+00 8 1.745770e+00 3.184127e+00 9 2.278840e+00 3.183581e+00 10 2.882210e+00 3.182435e+00 11 3.555600e+00 3.180404e+00 12 4.298690e+00 3.177184e+00 13 5.111130e+00 3.172447e+00 14 5.992520e+00 3.165884e+00 15 6.942460e+00 3.157206e+00 16 7.960480e+00 3.146168e+00 17 9.046110e+00 3.132568e+00 18 1.019880e+01 3.116302e+00 19 1.141810e+01 3.097345e+00 20 1.270330e+01 3.075808e+00 21 1.405380e+01 3.051897e+00 22 1.546910e+01 3.025948e+00 23 1.694840e+01 2.998371e+00 24 1.849100e+01 2.969664e+00 25 2.009620e+01 2.940340e+00 26 2.176320e+01 2.910918e+00 27 2.349130e+01 2.881890e+00 28 2.527960e+01 2.853701e+00 29 2.712720e+01 2.826741e+00 30 2.903330e+01 2.801332e+00 31 3.099700e+01 2.777721e+00 32 3.301730e+01 2.756119e+00 33 3.509330e+01 2.736661e+00 34 3.722400e+01 2.719453e+00 35 3.940840e+01 2.704550e+00 36 4.164540e+01 2.691985e+00 37 4.393400e+01 2.681762e+00 38 4.627300e+01 2.673871e+00 39 4.866150e+01 2.668279e+00 40 5.109810e+01 2.664947e+00 41 5.358190e+01 2.663832e+00 42 5.611150e+01 2.664879e+00 43 5.868580e+01 2.668066e+00 44 6.130360e+01 2.673365e+00 45 6.396350e+01 2.680786e+00 46 6.666450e+01 2.690341e+00 47 6.940510e+01 2.702070e+00 48 7.218400e+01 2.716004e+00 49 7.500000e+01 2.732186e+00 50 7.785170e+01 2.750650e+00 51 8.073770e+01 2.771444e+00 52 8.365670e+01 2.794602e+00 53 8.660730e+01 2.820141e+00 54 8.958800e+01 2.848054e+00 55 9.259750e+01 2.878289e+00 56 9.563430e+01 2.910734e+00 57 9.869700e+01 2.945194e+00 58 1.017840e+02 2.981360e+00 59 1.048940e+02 3.018730e+00 60 1.080260e+02 3.056548e+00 61 1.111770e+02 3.093694e+00 62 1.143470e+02 3.128639e+00 63 1.175340e+02 3.159359e+00 64 1.207360e+02 3.183374e+00 65 1.239530e+02 3.197851e+00 66 1.271810e+02 3.199933e+00 67 1.304210e+02 3.187353e+00 68 1.336700e+02 3.159375e+00 69 1.369270e+02 3.117953e+00 70 1.401900e+02 3.068676e+00 71 1.434570e+02 3.020769e+00 72 1.467280e+02 2.985389e+00 73 1.500000e+02 2.972241e+00 j y+ /(u_rms*t_rms) 1 1.000000e-40 1.138512e-30 3.798366e-02 2 3.569590e-02 6.177718e-07 3.831238e-01 3 1.427670e-01 9.936838e-06 3.854967e-01 4 3.211620e-01 5.076363e-05 3.895260e-01 5 5.707950e-01 1.625302e-04 3.952524e-01 6 8.915490e-01 4.035024e-04 4.026994e-01 7 1.283270e+00 8.537131e-04 4.118720e-01 8 1.745770e+00 1.617753e-03 4.227323e-01 9 2.278840e+00 2.825521e-03 4.351946e-01 10 2.882210e+00 4.628287e-03 4.491279e-01 11 3.555600e+00 7.186869e-03 4.643396e-01 12 4.298690e+00 1.065064e-02 4.805440e-01 13 5.111130e+00 1.512952e-02 4.973439e-01 14 5.992520e+00 2.066528e-02 5.142330e-01 15 6.942460e+00 2.721100e-02 5.306314e-01 16 7.960480e+00 3.462617e-02 5.459532e-01 17 9.046110e+00 4.269030e-02 5.596784e-01 18 1.019880e+01 5.113145e-02 5.714121e-01 19 1.141810e+01 5.966314e-02 5.809317e-01 20 1.270330e+01 6.801995e-02 5.882032e-01 21 1.405380e+01 7.598309e-02 5.933646e-01 22 1.546910e+01 8.339456e-02 5.966922e-01 23 1.694840e+01 9.015845e-02 5.985476e-01 24 1.849100e+01 9.623253e-02 5.993206e-01 25 2.009620e+01 1.016161e-01 5.993893e-01 26 2.176320e+01 1.063366e-01 5.990914e-01 27 2.349130e+01 1.104356e-01 5.987025e-01 28 2.527960e+01 1.139583e-01 5.984279e-01 29 2.712720e+01 1.169474e-01 5.983982e-01 30 2.903330e+01 1.194410e-01 5.986674e-01 31 3.099700e+01 1.214792e-01 5.992566e-01 32 3.301730e+01 1.231042e-01 6.001946e-01 33 3.509330e+01 1.243643e-01 6.015099e-01 34 3.722400e+01 1.253031e-01 6.032191e-01 35 3.940840e+01 1.259562e-01 6.053241e-01 36 4.164540e+01 1.263484e-01 6.078094e-01 37 4.393400e+01 1.264959e-01 6.106411e-01 38 4.627300e+01 1.264071e-01 6.137549e-01 39 4.866150e+01 1.260761e-01 6.170229e-01 40 5.109810e+01 1.254845e-01 6.202630e-01 41 5.358190e+01 1.246132e-01 6.233002e-01 42 5.611150e+01 1.234556e-01 6.260065e-01 43 5.868580e+01 1.220144e-01 6.283310e-01 44 6.130360e+01 1.202930e-01 6.302902e-01 45 6.396350e+01 1.182895e-01 6.319005e-01 46 6.666450e+01 1.160070e-01 6.331401e-01 47 6.940510e+01 1.134548e-01 6.339633e-01 48 7.218400e+01 1.106444e-01 6.343076e-01 49 7.500000e+01 1.075823e-01 6.341046e-01 50 7.785170e+01 1.042805e-01 6.333145e-01 51 8.073770e+01 1.007561e-01 6.319014e-01 52 8.365670e+01 9.702899e-02 6.297912e-01 53 8.660730e+01 9.311401e-02 6.269388e-01 54 8.958800e+01 8.902534e-02 6.233733e-01 55 9.259750e+01 8.477957e-02 6.191139e-01 56 9.563430e+01 8.040149e-02 6.141214e-01 57 9.869700e+01 7.592427e-02 6.083401e-01 58 1.017840e+02 7.138098e-02 6.017038e-01 59 1.048940e+02 6.680069e-02 5.941209e-01 60 1.080260e+02 6.221196e-02 5.854917e-01 61 1.111770e+02 5.764484e-02 5.757058e-01 62 1.143470e+02 5.313533e-02 5.646326e-01 63 1.175340e+02 4.872890e-02 5.521331e-01 64 1.207360e+02 4.448104e-02 5.381520e-01 65 1.239530e+02 4.045452e-02 5.228284e-01 66 1.271810e+02 3.671265e-02 5.064995e-01 67 1.304210e+02 3.331139e-02 4.896161e-01 68 1.336700e+02 3.029574e-02 4.727026e-01 69 1.369270e+02 2.770297e-02 4.563671e-01 70 1.401900e+02 2.556542e-02 4.413473e-01 71 1.434570e+02 2.391192e-02 4.285259e-01 72 1.467280e+02 2.276747e-02 4.188480e-01 73 1.500000e+02 2.215060e-02 4.131213e-01 j y+ - -/(v_rms*t_rms) (vt)_rms S(vt) F(vt) 1 1.000000e-40 6.727864e-34 3.596742e-03 1.866790e-31 1.000000e-40 1.000000e-40 2 3.569590e-02 3.798535e-10 2.810376e-01 1.872584e-09 -1.111972e+01 1.088163e+02 3 1.427670e-01 2.418584e-08 2.839214e-01 1.178290e-07 -1.105883e+01 1.061639e+02 4 3.211620e-01 2.730288e-07 2.886307e-01 1.304893e-06 -1.095781e+01 1.018084e+02 5 5.707950e-01 1.513683e-06 2.950234e-01 7.050829e-06 -1.081656e+01 9.585246e+01 6 8.915490e-01 5.669125e-06 3.029096e-01 2.559599e-05 -1.063669e+01 8.848999e+01 7 1.283270e+00 1.652734e-05 3.120810e-01 7.201721e-05 -1.042466e+01 8.003818e+01 8 1.745770e+00 4.044658e-05 3.223229e-01 1.695789e-04 -1.019025e+01 7.097366e+01 9 2.278840e+00 8.692666e-05 3.334381e-01 3.500667e-04 -9.942098e+00 6.192599e+01 10 2.882210e+00 1.689498e-04 3.452671e-01 6.532071e-04 -9.681826e+00 5.353038e+01 11 3.555600e+00 3.030650e-04 3.577044e-01 1.125545e-03 -9.399563e+00 4.620377e+01 12 4.298690e+00 5.092631e-04 3.706986e-01 1.819088e-03 -9.078064e+00 4.005462e+01 13 5.111130e+00 8.107192e-04 3.842391e-01 2.789710e-03 -8.704575e+00 3.497992e+01 14 5.992520e+00 1.233451e-03 3.983330e-01 4.095054e-03 -8.279913e+00 3.079852e+01 15 6.942460e+00 1.805843e-03 4.129764e-01 5.791614e-03 -7.817150e+00 2.734336e+01 16 7.960480e+00 2.557900e-03 4.281354e-01 7.930809e-03 -7.334268e+00 2.448108e+01 17 9.046110e+00 3.520115e-03 4.437341e-01 1.055441e-02 -6.848190e+00 2.208597e+01 18 1.019880e+01 4.721766e-03 4.596527e-01 1.369041e-02 -6.372429e+00 2.003365e+01 19 1.141810e+01 6.188771e-03 4.757347e-01 1.734969e-02 -5.917235e+00 1.821714e+01 20 1.270330e+01 7.941258e-03 4.917979e-01 2.152474e-02 -5.490227e+00 1.657711e+01 21 1.405380e+01 9.991103e-03 5.076497e-01 2.618994e-02 -5.096544e+00 1.509399e+01 22 1.546910e+01 1.234010e-02 5.231041e-01 3.130331e-02 -4.738956e+00 1.377189e+01 23 1.694840e+01 1.497866e-02 5.379959e-01 3.680995e-02 -4.418321e+00 1.262511e+01 24 1.849100e+01 1.788581e-02 5.521877e-01 4.264589e-02 -4.134058e+00 1.165698e+01 25 2.009620e+01 2.102986e-02 5.655691e-01 4.874178e-02 -3.884541e+00 1.085537e+01 26 2.176320e+01 2.437029e-02 5.780535e-01 5.502620e-02 -3.667475e+00 1.019235e+01 27 2.349130e+01 2.785970e-02 5.895798e-01 6.142781e-02 -3.480195e+00 9.633999e+00 28 2.527960e+01 3.144597e-02 6.001182e-01 6.787569e-02 -3.319964e+00 9.159514e+00 29 2.712720e+01 3.507447e-02 6.096683e-01 7.430001e-02 -3.184205e+00 8.764772e+00 30 2.903330e+01 3.869011e-02 6.182566e-01 8.063317e-02 -3.070573e+00 8.450919e+00 31 3.099700e+01 4.223878e-02 6.259211e-01 8.681144e-02 -2.976959e+00 8.220031e+00 32 3.301730e+01 4.566939e-02 6.327154e-01 9.277492e-02 -2.901463e+00 8.069324e+00 33 3.509330e+01 4.893494e-02 6.387054e-01 9.846661e-02 -2.842340e+00 7.987556e+00 34 3.722400e+01 5.199388e-02 6.439557e-01 1.038331e-01 -2.797948e+00 7.964603e+00 35 3.940840e+01 5.481134e-02 6.485176e-01 1.088274e-01 -2.766686e+00 7.997244e+00 36 4.164540e+01 5.735920e-02 6.524327e-01 1.134103e-01 -2.746958e+00 8.080847e+00 37 4.393400e+01 5.961608e-02 6.557439e-01 1.175501e-01 -2.737276e+00 8.207286e+00 38 4.627300e+01 6.156681e-02 6.584989e-01 1.212226e-01 -2.736333e+00 8.371643e+00 39 4.866150e+01 6.320176e-02 6.607381e-01 1.244134e-01 -2.743066e+00 8.569464e+00 40 5.109810e+01 6.451630e-02 6.624844e-01 1.271143e-01 -2.756613e+00 8.790404e+00 41 5.358190e+01 6.551024e-02 6.637404e-01 1.293217e-01 -2.776207e+00 9.026890e+00 42 5.611150e+01 6.618678e-02 6.645011e-01 1.310385e-01 -2.801136e+00 9.279752e+00 43 5.868580e+01 6.655246e-02 6.647646e-01 1.322696e-01 -2.830770e+00 9.550404e+00 44 6.130360e+01 6.661670e-02 6.645468e-01 1.330183e-01 -2.864574e+00 9.838257e+00 45 6.396350e+01 6.639073e-02 6.638914e-01 1.332878e-01 -2.902187e+00 1.014573e+01 46 6.666450e+01 6.588731e-02 6.628590e-01 1.330839e-01 -2.943368e+00 1.047366e+01 47 6.940510e+01 6.512139e-02 6.614942e-01 1.324181e-01 -2.987870e+00 1.082112e+01 48 7.218400e+01 6.411005e-02 6.598145e-01 1.313066e-01 -3.035416e+00 1.118486e+01 49 7.500000e+01 6.287174e-02 6.578157e-01 1.297716e-01 -3.085622e+00 1.155396e+01 50 7.785170e+01 6.142559e-02 6.554634e-01 1.278358e-01 -3.138113e+00 1.192200e+01 51 8.073770e+01 5.978993e-02 6.526922e-01 1.255258e-01 -3.192610e+00 1.229725e+01 52 8.365670e+01 5.798139e-02 6.494234e-01 1.228689e-01 -3.248867e+00 1.269751e+01 53 8.660730e+01 5.601467e-02 6.455738e-01 1.198928e-01 -3.306796e+00 1.313238e+01 54 8.958800e+01 5.390364e-02 6.410374e-01 1.166225e-01 -3.366555e+00 1.359444e+01 55 9.259750e+01 5.166206e-02 6.356594e-01 1.130865e-01 -3.428589e+00 1.407300e+01 56 9.563430e+01 4.930439e-02 6.292421e-01 1.093138e-01 -3.493461e+00 1.456676e+01 57 9.869700e+01 4.684515e-02 6.215566e-01 1.053401e-01 -3.561362e+00 1.507419e+01 58 1.017840e+02 4.429830e-02 6.123479e-01 1.012034e-01 -3.631888e+00 1.559523e+01 59 1.048940e+02 4.167693e-02 6.013467e-01 9.693909e-02 -3.704090e+00 1.615746e+01 60 1.080260e+02 3.899221e-02 5.882653e-01 9.258116e-02 -3.776511e+00 1.675961e+01 61 1.111770e+02 3.625351e-02 5.727861e-01 8.815672e-02 -3.847391e+00 1.734628e+01 62 1.143470e+02 3.346845e-02 5.545385e-01 8.368776e-02 -3.914913e+00 1.789264e+01 63 1.175340e+02 3.064283e-02 5.330677e-01 7.920038e-02 -3.976541e+00 1.838060e+01 64 1.207360e+02 2.778228e-02 5.078074e-01 7.473380e-02 -4.027293e+00 1.874675e+01 65 1.239530e+02 2.489238e-02 4.780919e-01 7.034291e-02 -4.057683e+00 1.892110e+01 66 1.271810e+02 2.197856e-02 4.432113e-01 6.609411e-02 -4.051694e+00 1.884552e+01 67 1.304210e+02 1.904538e-02 4.024912e-01 6.206170e-02 -3.985084e+00 1.847794e+01 68 1.336700e+02 1.609593e-02 3.553842e-01 5.832800e-02 -3.823838e+00 1.787058e+01 69 1.369270e+02 1.313212e-02 3.015825e-01 5.498617e-02 -3.524140e+00 1.713629e+01 70 1.401900e+02 1.015554e-02 2.411413e-01 5.214105e-02 -3.038230e+00 1.639240e+01 71 1.434570e+02 7.167751e-03 1.746294e-01 4.990349e-02 -2.330410e+00 1.570779e+01 72 1.467280e+02 4.170580e-03 1.032237e-01 4.837578e-02 -1.402889e+00 1.514273e+01 73 1.500000e+02 1.165829e-03 2.867938e-02 4.763414e-02 -3.169505e-01 1.480948e+01 j y+ nu_t alfa_t Pr_t 1 1.000000e-40 0.158445E-31 0.268235E-31 6.253822e-01 2 3.569590e-02 0.320087E-07 0.151492E-07 2.112696e+00 3 1.427670e-01 0.206194E-05 0.964642E-06 2.137322e+00 4 3.211620e-01 0.237368E-04 0.108895E-04 2.179594e+00 5 5.707950e-01 0.135250E-03 0.603739E-04 2.240010e+00 6 8.915490e-01 0.524335E-03 0.226145E-03 2.318397e+00 7 1.283270e+00 0.159133E-02 0.659411E-03 2.413124e+00 8 1.745770e+00 0.406821E-02 0.161427E-02 2.520075e+00 9 2.278840e+00 0.913949E-02 0.347118E-02 2.632982e+00 10 2.882210e+00 0.185269E-01 0.675163E-02 2.744206e+00 11 3.555600e+00 0.345003E-01 0.121242E-01 2.845876e+00 12 4.298690e+00 0.598070E-01 0.204033E-01 2.931694e+00 13 5.111130e+00 0.975538E-01 0.325437E-01 2.998206e+00 14 5.992520e+00 0.151097E+00 0.496363E-01 3.044764e+00 15 6.942460e+00 0.223978E+00 0.728992E-01 3.073169e+00 16 7.960480e+00 0.319892E+00 0.103657E+00 3.086783e+00 17 9.046110e+00 0.442670E+00 0.143316E+00 3.089446e+00 18 1.019880e+01 0.596225E+00 0.193308E+00 3.084937e+00 19 1.141810e+01 0.784473E+00 0.255010E+00 3.076732e+00 20 1.270330e+01 0.101123E+01 0.329672E+00 3.067756e+00 21 1.405380e+01 0.128013E+01 0.418310E+00 3.060481e+00 22 1.546910e+01 0.159452E+01 0.521616E+00 3.056978e+00 23 1.694840e+01 0.195732E+01 0.639910E+00 3.058684e+00 24 1.849100e+01 0.237081E+01 0.773107E+00 3.066390e+00 25 2.009620e+01 0.283629E+01 0.920693E+00 3.080264e+00 26 2.176320e+01 0.335386E+01 0.108179E+01 3.099838e+00 27 2.349130e+01 0.392208E+01 0.125519E+01 3.124142e+00 28 2.527960e+01 0.453735E+01 0.143939E+01 3.151636e+00 29 2.712720e+01 0.519375E+01 0.163269E+01 3.180377e+00 30 2.903330e+01 0.588322E+01 0.183324E+01 3.208419e+00 31 3.099700e+01 0.659461E+01 0.203902E+01 3.233439e+00 32 3.301730e+01 0.731410E+01 0.224803E+01 3.252925e+00 33 3.509330e+01 0.802861E+01 0.245825E+01 3.265556e+00 34 3.722400e+01 0.872678E+01 0.266772E+01 3.271074e+00 35 3.940840e+01 0.939565E+01 0.287465E+01 3.268562e+00 36 4.164540e+01 0.100213E+02 0.307746E+01 3.256805e+00 37 4.393400e+01 0.105952E+02 0.327468E+01 3.236291e+00 38 4.627300e+01 0.111171E+02 0.346512E+01 3.209419e+00 39 4.866150e+01 0.115897E+02 0.364779E+01 3.178606e+00 40 5.109810e+01 0.120149E+02 0.382179E+01 3.145405e+00 41 5.358190e+01 0.123978E+02 0.398652E+01 3.111744e+00 42 5.611150e+01 0.127458E+02 0.414147E+01 3.079531e+00 43 5.868580e+01 0.130554E+02 0.428626E+01 3.047799e+00 44 6.130360e+01 0.133115E+02 0.442070E+01 3.012981e+00 45 6.396350e+01 0.135047E+02 0.454474E+01 2.973125e+00 46 6.666450e+01 0.136387E+02 0.465832E+01 2.929288e+00 47 6.940510e+01 0.137221E+02 0.476165E+01 2.883167e+00 48 7.218400e+01 0.137627E+02 0.485511E+01 2.835946e+00 49 7.500000e+01 0.137675E+02 0.493918E+01 2.788473e+00 50 7.785170e+01 0.137422E+02 0.501453E+01 2.741311e+00 51 8.073770e+01 0.136924E+02 0.508188E+01 2.694965e+00 52 8.365670e+01 0.136212E+02 0.514174E+01 2.649624e+00 53 8.660730e+01 0.135278E+02 0.519464E+01 2.604655e+00 54 8.958800e+01 0.134110E+02 0.524106E+01 2.559388e+00 55 9.259750e+01 0.132754E+02 0.528143E+01 2.514277e+00 56 9.563430e+01 0.131295E+02 0.531646E+01 2.470442e+00 57 9.869700e+01 0.129767E+02 0.534703E+01 2.428060e+00 58 1.017840e+02 0.128116E+02 0.537398E+01 2.385796e+00 59 1.048940e+02 0.126260E+02 0.539835E+01 2.341594e+00 60 1.080260e+02 0.124139E+02 0.542121E+01 2.293724e+00 61 1.111770e+02 0.121758E+02 0.544342E+01 2.241809e+00 62 1.143470e+02 0.119259E+02 0.546601E+01 2.188075e+00 63 1.175340e+02 0.116909E+02 0.549008E+01 2.137037e+00 64 1.207360e+02 0.114942E+02 0.551678E+01 2.092440e+00 65 1.239530e+02 0.113469E+02 0.554815E+01 2.055360e+00 66 1.271810e+02 0.112496E+02 0.558735E+01 2.024669e+00 67 1.304210e+02 0.111922E+02 0.563878E+01 1.997086e+00 68 1.336700e+02 0.111619E+02 0.571030E+01 1.967910e+00 69 1.369270e+02 0.111594E+02 0.581694E+01 1.932871e+00 70 1.401900e+02 0.112033E+02 0.599244E+01 1.885232e+00 71 1.434570e+02 0.113247E+02 0.633894E+01 1.802362e+00 72 1.467280e+02 0.115439E+02 0.736185E+01 1.576168e+00 73 1.500000e+02 0.294857E+02 -0.341731E+01 -9.168572e-01 4.2 Budgets of temperature variance, its dissipation rates and turbulent heat fluxes 4.2.1 Budget for temperature variance t+**2/2 j y+ Prod. Diss. Turb.Diff. Mole.Diff. 1 1.000000e-40 5.160782e-34 -4.919443e-04 1.451219e-13 4.919425e-04 2 3.569590e-02 2.803990e-10 -4.919463e-04 2.625707e-12 4.919463e-04 3 1.427670e-01 4.963401e-09 -4.919819e-04 1.697961e-10 4.919790e-04 4 3.211620e-01 2.910391e-08 -4.921148e-04 1.877687e-09 4.920834e-04 5 5.707950e-01 1.092155e-07 -4.924475e-04 1.012098e-08 4.923234e-04 6 8.915490e-01 3.190403e-07 -4.931209e-04 3.655931e-08 4.927667e-04 7 1.283270e+00 7.885664e-07 -4.942815e-04 1.020077e-07 4.933948e-04 8 1.745770e+00 1.722756e-06 -4.960576e-04 2.372066e-07 4.940909e-04 9 2.278840e+00 3.415764e-06 -4.985730e-04 4.813516e-07 4.946708e-04 10 2.882210e+00 6.257091e-06 -5.019348e-04 8.789388e-07 4.947999e-04 11 3.555600e+00 1.072688e-05 -5.062167e-04 1.476395e-06 4.940003e-04 12 4.298690e+00 1.738117e-05 -5.114787e-04 2.319804e-06 4.917585e-04 13 5.111130e+00 2.683029e-05 -5.177816e-04 3.453567e-06 4.874838e-04 14 5.992520e+00 3.971219e-05 -5.251762e-04 4.917911e-06 4.805135e-04 15 6.942460e+00 5.666539e-05 -5.337176e-04 6.741926e-06 4.702577e-04 16 7.960480e+00 7.830295e-05 -5.434713e-04 8.930381e-06 4.561847e-04 17 9.046110e+00 1.051797e-04 -5.545005e-04 1.144575e-05 4.377934e-04 18 1.019880e+01 1.377546e-04 -5.668531e-04 1.418979e-05 4.147889e-04 19 1.141810e+01 1.763541e-04 -5.805704e-04 1.699178e-05 3.870895e-04 20 1.270330e+01 2.211172e-04 -5.956613e-04 1.961112e-05 3.547543e-04 21 1.405380e+01 2.719500e-04 -6.120965e-04 2.175699e-05 3.181482e-04 22 1.546910e+01 3.285029e-04 -6.298089e-04 2.312541e-05 2.779034e-04 23 1.694840e+01 3.901456e-04 -6.486837e-04 2.344455e-05 2.347531e-04 24 1.849100e+01 4.559845e-04 -6.685450e-04 2.251449e-05 1.896172e-04 25 2.009620e+01 5.249102e-04 -6.891649e-04 2.023540e-05 1.435351e-04 26 2.176320e+01 5.956396e-04 -7.102569e-04 1.661754e-05 9.743792e-05 27 2.349130e+01 6.667908e-04 -7.314716e-04 1.177141e-05 5.224155e-05 28 2.527960e+01 7.369634e-04 -7.524201e-04 5.891114e-06 8.829580e-06 29 2.712720e+01 8.047745e-04 -7.726817e-04 -7.613764e-07 -3.214890e-05 30 2.903330e+01 8.689243e-04 -7.918181e-04 -7.877891e-06 -7.015806e-05 31 3.099700e+01 9.282591e-04 -8.093963e-04 -1.513306e-05 -1.047277e-04 32 3.301730e+01 9.817776e-04 -8.250041e-04 -2.221414e-05 -1.356294e-04 33 3.509330e+01 1.028661e-03 -8.382588e-04 -2.884270e-05 -1.627352e-04 34 3.722400e+01 1.068319e-03 -8.488286e-04 -3.478802e-05 -1.859354e-04 35 3.940840e+01 1.100335e-03 -8.564419e-04 -3.987020e-05 -2.053154e-04 36 4.164540e+01 1.124508e-03 -8.608907e-04 -4.395456e-05 -2.210394e-04 37 4.393400e+01 1.140801e-03 -8.620438e-04 -4.695925e-05 -2.332240e-04 38 4.627300e+01 1.149338e-03 -8.598504e-04 -4.886885e-05 -2.420768e-04 39 4.866150e+01 1.150337e-03 -8.543348e-04 -4.971594e-05 -2.478135e-04 40 5.109810e+01 1.144151e-03 -8.455847e-04 -4.955586e-05 -2.505637e-04 41 5.358190e+01 1.131185e-03 -8.337434e-04 -4.847599e-05 -2.505310e-04 42 5.611150e+01 1.111915e-03 -8.189986e-04 -4.660053e-05 -2.479237e-04 43 5.868580e+01 1.086879e-03 -8.015689e-04 -4.406302e-05 -2.428604e-04 44 6.130360e+01 1.056632e-03 -7.816972e-04 -4.098453e-05 -2.355524e-04 45 6.396350e+01 1.021738e-03 -7.596485e-04 -3.747198e-05 -2.262425e-04 46 6.666450e+01 9.827928e-04 -7.356940e-04 -3.361879e-05 -2.150926e-04 47 6.940510e+01 9.403793e-04 -7.101053e-04 -2.948620e-05 -2.023681e-04 48 7.218400e+01 8.950798e-04 -6.831507e-04 -2.509501e-05 -1.884150e-04 49 7.500000e+01 8.474922e-04 -6.551028e-04 -2.046529e-05 -1.734776e-04 50 7.785170e+01 7.981699e-04 -6.262398e-04 -1.566126e-05 -1.577763e-04 51 8.073770e+01 7.476363e-04 -5.968420e-04 -1.079741e-05 -1.414871e-04 52 8.365670e+01 6.963857e-04 -5.671847e-04 -6.007670e-06 -1.246457e-04 53 8.660730e+01 6.448510e-04 -5.375237e-04 -1.404242e-06 -1.073174e-04 54 8.958800e+01 5.934332e-04 -5.080963e-04 2.936397e-06 -8.963571e-05 55 9.259750e+01 5.425287e-04 -4.791202e-04 6.958311e-06 -7.168145e-05 56 9.563430e+01 4.925026e-04 -4.507870e-04 1.061906e-05 -5.358205e-05 57 9.869700e+01 4.437014e-04 -4.232726e-04 1.389788e-05 -3.553244e-05 58 1.017840e+02 3.964567e-04 -3.967314e-04 1.679982e-05 -1.767833e-05 59 1.048940e+02 3.510504e-04 -3.712984e-04 1.935467e-05 -1.927196e-07 60 1.080260e+02 3.077314e-04 -3.470949e-04 2.161039e-05 1.671094e-05 61 1.111770e+02 2.667272e-04 -3.242326e-04 2.361707e-05 3.289509e-05 62 1.143470e+02 2.282263e-04 -3.028136e-04 2.540667e-05 4.824978e-05 63 1.175340e+02 1.923998e-04 -2.829369e-04 2.697759e-05 6.267083e-05 64 1.207360e+02 1.594153e-04 -2.646903e-04 2.830523e-05 7.612589e-05 65 1.239530e+02 1.294216e-04 -2.481484e-04 2.937209e-05 8.856811e-05 66 1.271810e+02 1.025545e-04 -2.333770e-04 3.018669e-05 9.988997e-05 67 1.304210e+02 7.893571e-05 -2.204322e-04 3.078190e-05 1.100105e-04 68 1.336700e+02 5.865762e-05 -2.093599e-04 3.119991e-05 1.188530e-04 69 1.369270e+02 4.179782e-05 -2.001971e-04 3.147637e-05 1.263155e-04 70 1.401900e+02 2.842548e-05 -1.929711e-04 3.163745e-05 1.323422e-04 71 1.434570e+02 1.859549e-05 -1.876984e-04 3.170740e-05 1.368832e-04 72 1.467280e+02 1.235295e-05 -1.843924e-04 3.171000e-05 1.398610e-04 73 1.500000e+02 9.732026e-06 -1.830621e-04 3.166160e-05 1.412405e-04 4.2.2 Budget for dissipation rate of temparature variance e_t j y+ M.G.Prod. Turb.Prod. Dissipation Turb.Trans. Grad.Prod. Mole.Diff. 1 1.000000e-40 1.697600e-05 -8.126367e-21 -2.880812e-04 2.088734e-12 2.696413e-22 2.286104e-04 2 3.569590e-02 1.823274e-05 2.532397e-07 -1.860525e-04 8.460100e-08 -3.182755e-11 1.744374e-04 3 1.427670e-01 2.197534e-05 9.857518e-07 -1.507613e-04 3.315764e-07 -4.115235e-11 1.147535e-04 4 3.211620e-01 2.811089e-05 2.117486e-06 -1.484486e-04 7.206020e-07 1.147106e-10 1.096523e-04 5 5.707950e-01 3.645943e-05 3.521984e-06 -1.494669e-04 1.218345e-06 -1.760637e-09 1.085530e-04 6 8.915490e-01 4.674286e-05 5.041066e-06 -1.498421e-04 1.779266e-06 -5.630056e-09 9.814379e-05 7 1.283270e+00 5.858478e-05 6.510621e-06 -1.511306e-04 2.347625e-06 -1.421671e-08 8.234823e-05 8 1.745770e+00 7.152223e-05 7.795262e-06 -1.538459e-04 2.861180e-06 -3.967739e-08 7.083223e-05 9 2.278840e+00 8.506205e-05 8.821983e-06 -1.569841e-04 3.258616e-06 -8.558691e-08 6.050351e-05 10 2.882210e+00 9.876579e-05 9.598565e-06 -1.613289e-04 3.489482e-06 -1.640527e-07 4.937661e-05 11 3.555600e+00 1.123241e-04 1.020125e-05 -1.671100e-04 3.522440e-06 -3.034678e-07 4.074180e-05 12 4.298690e+00 1.256338e-04 1.073122e-05 -1.739282e-04 3.351063e-06 -5.102148e-07 3.486304e-05 13 5.111130e+00 1.388275e-04 1.125930e-05 -1.822004e-04 2.993871e-06 -8.017886e-07 2.981863e-05 14 5.992520e+00 1.522284e-04 1.178441e-05 -1.919071e-04 2.486197e-06 -1.212144e-06 2.616926e-05 15 6.942460e+00 1.662610e-04 1.222457e-05 -2.027241e-04 1.873258e-06 -1.734481e-06 2.403508e-05 16 7.960480e+00 1.813419e-04 1.244702e-05 -2.147556e-04 1.205066e-06 -2.372699e-06 2.200649e-05 17 9.046110e+00 1.977544e-04 1.231822e-05 -2.277951e-04 5.290098e-07 -3.144447e-06 1.992459e-05 18 1.019880e+01 2.155794e-04 1.174944e-05 -2.415088e-04 -1.114679e-07 -4.012925e-06 1.808101e-05 19 1.141810e+01 2.346796e-04 1.072976e-05 -2.558199e-04 -6.761904e-07 -4.953880e-06 1.579101e-05 20 1.270330e+01 2.547095e-04 9.338331e-06 -2.704248e-04 -1.135274e-06 -5.956869e-06 1.298991e-05 21 1.405380e+01 2.751789e-04 7.730862e-06 -2.849878e-04 -1.469763e-06 -6.954878e-06 1.009132e-05 22 1.546910e+01 2.955356e-04 6.105427e-06 -2.993243e-04 -1.670177e-06 -7.901273e-06 6.816184e-06 23 1.694840e+01 3.152166e-04 4.659673e-06 -3.131012e-04 -1.740962e-06 -8.770716e-06 3.106870e-06 24 1.849100e+01 3.337028e-04 3.555343e-06 -3.260130e-04 -1.696303e-06 -9.494271e-06 -6.887484e-07 25 2.009620e+01 3.505511e-04 2.894665e-06 -3.378556e-04 -1.556184e-06 -1.003688e-05 -4.671952e-06 26 2.176320e+01 3.653788e-04 2.710432e-06 -3.483486e-04 -1.349076e-06 -1.039378e-05 -8.830664e-06 27 2.349130e+01 3.778701e-04 2.975712e-06 -3.572912e-04 -1.108521e-06 -1.053085e-05 -1.279214e-05 28 2.527960e+01 3.877885e-04 3.628836e-06 -3.645679e-04 -8.665637e-07 -1.044927e-05 -1.645779e-05 29 2.712720e+01 3.949739e-04 4.603648e-06 -3.700278e-04 -6.476673e-07 -1.017517e-05 -1.977529e-05 30 2.903330e+01 3.993582e-04 5.837324e-06 -3.736054e-04 -4.675104e-07 -9.709679e-06 -2.251852e-05 31 3.099700e+01 4.009739e-04 7.248181e-06 -3.752900e-04 -3.375059e-07 -9.079749e-06 -2.466179e-05 32 3.301730e+01 3.999038e-04 8.741701e-06 -3.750574e-04 -2.631625e-07 -8.326374e-06 -2.623063e-05 33 3.509330e+01 3.962734e-04 1.024520e-05 -3.729619e-04 -2.404977e-07 -7.468222e-06 -2.712887e-05 34 3.722400e+01 3.902506e-04 1.170861e-05 -3.690714e-04 -2.592460e-07 -6.538269e-06 -2.739510e-05 35 3.940840e+01 3.820304e-04 1.308691e-05 -3.634589e-04 -3.065502e-07 -5.572672e-06 -2.712761e-05 36 4.164540e+01 3.718400e-04 1.433122e-05 -3.562808e-04 -3.773957e-07 -4.587915e-06 -2.630463e-05 37 4.393400e+01 3.599409e-04 1.539834e-05 -3.476866e-04 -4.725123e-07 -3.605004e-06 -2.495709e-05 38 4.627300e+01 3.466031e-04 1.628031e-05 -3.378027e-04 -5.825131e-07 -2.642954e-06 -2.324159e-05 39 4.866150e+01 3.321023e-04 1.698827e-05 -3.268062e-04 -6.917645e-07 -1.709561e-06 -2.127656e-05 40 5.109810e+01 3.167026e-04 1.752001e-05 -3.148554e-04 -7.865786e-07 -8.147599e-07 -1.914045e-05 41 5.358190e+01 3.006323e-04 1.789239e-05 -3.021066e-04 -8.542855e-07 3.508292e-08 -1.694549e-05 42 5.611150e+01 2.841010e-04 1.813915e-05 -2.887479e-04 -8.885015e-07 8.385586e-07 -1.477145e-05 43 5.868580e+01 2.673094e-04 1.825951e-05 -2.749258e-04 -8.924796e-07 1.594770e-06 -1.263896e-05 44 6.130360e+01 2.504353e-04 1.824341e-05 -2.607776e-04 -8.724292e-07 2.306391e-06 -1.057854e-05 45 6.396350e+01 2.336417e-04 1.811217e-05 -2.464540e-04 -8.329463e-07 2.973588e-06 -8.646438e-06 46 6.666450e+01 2.170752e-04 1.788773e-05 -2.320633e-04 -7.777211e-07 3.596098e-06 -6.877777e-06 47 6.940510e+01 2.008485e-04 1.756649e-05 -2.177218e-04 -7.140799e-07 4.176214e-06 -5.250943e-06 48 7.218400e+01 1.850495e-04 1.713898e-05 -2.035691e-04 -6.506083e-07 4.710881e-06 -3.724292e-06 49 7.500000e+01 1.697491e-04 1.661474e-05 -1.896944e-04 -5.883196e-07 5.200646e-06 -2.274704e-06 50 7.785170e+01 1.550004e-04 1.602105e-05 -1.761746e-04 -5.218007e-07 5.651338e-06 -8.985903e-07 51 8.073770e+01 1.408520e-04 1.538649e-05 -1.630829e-04 -4.474250e-07 6.061820e-06 3.663285e-07 52 8.365670e+01 1.273615e-04 1.473434e-05 -1.504540e-04 -3.654319e-07 6.434741e-06 1.477444e-06 53 8.660730e+01 1.145742e-04 1.407630e-05 -1.383302e-04 -2.792864e-07 6.776594e-06 2.441720e-06 54 8.958800e+01 1.025196e-04 1.340809e-05 -1.267649e-04 -1.937006e-07 7.084276e-06 3.266570e-06 55 9.259750e+01 9.120989e-05 1.272861e-05 -1.157761e-04 -1.099740e-07 7.359360e-06 3.957015e-06 56 9.563430e+01 8.064472e-05 1.204891e-05 -1.053877e-04 -2.607344e-08 7.608770e-06 4.546482e-06 57 9.869700e+01 7.082085e-05 1.137485e-05 -9.562769e-05 5.982081e-08 7.830245e-06 5.033989e-06 58 1.017840e+02 6.173758e-05 1.070669e-05 -8.650351e-05 1.468742e-07 8.026782e-06 5.420794e-06 59 1.048940e+02 5.338716e-05 1.004743e-05 -7.803457e-05 2.320644e-07 8.206104e-06 5.755464e-06 60 1.080260e+02 4.575286e-05 9.395405e-06 -7.022800e-05 3.129893e-07 8.365314e-06 6.045001e-06 61 1.111770e+02 3.881202e-05 8.744639e-06 -6.306927e-05 3.878823e-07 8.506185e-06 6.296836e-06 62 1.143470e+02 3.253807e-05 8.103146e-06 -5.655141e-05 4.574400e-07 8.634779e-06 6.545139e-06 63 1.175340e+02 2.690460e-05 7.492192e-06 -5.065671e-05 5.253358e-07 8.746093e-06 6.756574e-06 64 1.207360e+02 2.188618e-05 6.926101e-06 -4.536319e-05 5.924180e-07 8.840228e-06 6.912970e-06 65 1.239530e+02 1.745718e-05 6.408135e-06 -4.066474e-05 6.569523e-07 8.922616e-06 7.053322e-06 66 1.271810e+02 1.359552e-05 5.939603e-06 -3.654549e-05 7.185242e-07 8.988963e-06 7.167837e-06 67 1.304210e+02 1.028467e-05 5.523865e-06 -3.299006e-05 7.766615e-07 9.041005e-06 7.246680e-06 68 1.336700e+02 7.509833e-06 5.166856e-06 -2.999635e-05 8.310933e-07 9.085486e-06 7.313465e-06 69 1.369270e+02 5.256421e-06 4.873498e-06 -2.755140e-05 8.820851e-07 9.118653e-06 7.352153e-06 70 1.401900e+02 3.510342e-06 4.643459e-06 -2.564511e-05 9.278349e-07 9.141961e-06 7.361074e-06 71 1.434570e+02 2.259698e-06 4.471869e-06 -2.427817e-05 9.649586e-07 9.161591e-06 7.375615e-06 72 1.467280e+02 1.496950e-06 4.353812e-06 -2.344023e-05 9.916647e-07 9.173171e-06 7.390604e-06 73 1.500000e+02 1.218322e-06 4.287896e-06 -2.312760e-05 1.006741e-06 9.177221e-06 7.401256e-06 4.2.3 Budget for j y+ Prod. Diss. T-dp/dx Turb.Diff. Mole.Diff. 1 1.000000e-40 3.379599e-31 -1.984217e-02 4.259256e-19 1.159756e-09 1.984220e-02 2 3.569590e-02 7.386089e-08 -1.991430e-02 -1.772057e-06 -2.350372e-10 1.991511e-02 3 1.427670e-01 1.237305e-06 -2.013912e-02 -7.085090e-06 2.256515e-08 2.014492e-02 4 3.211620e-01 6.736458e-06 -2.053350e-02 -1.593195e-05 2.480771e-07 2.054378e-02 5 5.707950e-01 2.340158e-05 -2.111148e-02 -2.830791e-05 1.384956e-06 2.111412e-02 6 8.915490e-01 6.379882e-05 -2.187828e-02 -4.422058e-05 5.214938e-06 2.185297e-02 7 1.283270e+00 1.491104e-04 -2.281664e-02 -6.370201e-05 1.527710e-05 2.271748e-02 8 1.745770e+00 3.121487e-04 -2.386862e-02 -8.682109e-05 3.729775e-05 2.360530e-02 9 2.278840e+00 5.991166e-04 -2.492926e-02 -1.136933e-04 7.875095e-05 2.436430e-02 10 2.882210e+00 1.067958e-03 -2.585016e-02 -1.444826e-04 1.466298e-04 2.478155e-02 11 3.555600e+00 1.781112e-03 -2.645716e-02 -1.794006e-04 2.433888e-04 2.461134e-02 12 4.298690e+00 2.792360e-03 -2.659139e-02 -2.186792e-04 3.624832e-04 2.365379e-02 13 5.111130e+00 4.130883e-03 -2.615640e-02 -2.625415e-04 4.863162e-04 2.180262e-02 14 5.992520e+00 5.787846e-03 -2.514835e-02 -3.111651e-04 5.886688e-04 1.908173e-02 15 6.942460e+00 7.711499e-03 -2.366189e-02 -3.646299e-04 6.414236e-04 1.567127e-02 16 7.960480e+00 9.813132e-03 -2.186571e-02 -4.228823e-04 6.227957e-04 1.185271e-02 17 9.046110e+00 1.198153e-02 -1.995907e-02 -4.857052e-04 5.236641e-04 7.937791e-03 18 1.019880e+01 1.410164e-02 -1.812930e-02 -5.526937e-04 3.496118e-04 4.228005e-03 19 1.141810e+01 1.607199e-02 -1.652123e-02 -6.232584e-04 1.186906e-04 9.534169e-04 20 1.270330e+01 1.781571e-02 -1.522142e-02 -6.966529e-04 -1.437138e-04 -1.755528e-03 21 1.405380e+01 1.928468e-02 -1.425951e-02 -7.720049e-04 -4.109533e-04 -3.844473e-03 22 1.546910e+01 2.045841e-02 -1.361916e-02 -8.483799e-04 -6.599419e-04 -5.331112e-03 23 1.694840e+01 2.133769e-02 -1.325294e-02 -9.248606e-04 -8.736183e-04 -6.287161e-03 24 1.849100e+01 2.193897e-02 -1.309734e-02 -1.000597e-03 -1.042012e-03 -6.800059e-03 25 2.009620e+01 2.228828e-02 -1.308592e-02 -1.074874e-03 -1.161563e-03 -6.965151e-03 26 2.176320e+01 2.241634e-02 -1.315673e-02 -1.147174e-03 -1.233045e-03 -6.878356e-03 27 2.349130e+01 2.235541e-02 -1.325734e-02 -1.217143e-03 -1.260330e-03 -6.619013e-03 28 2.527960e+01 2.213721e-02 -1.334833e-02 -1.284575e-03 -1.250002e-03 -6.250680e-03 29 2.712720e+01 2.179112e-02 -1.340299e-02 -1.349331e-03 -1.210394e-03 -5.823349e-03 30 2.903330e+01 2.134358e-02 -1.340683e-02 -1.411317e-03 -1.150820e-03 -5.368244e-03 31 3.099700e+01 2.081841e-02 -1.335755e-02 -1.470464e-03 -1.080098e-03 -4.901549e-03 32 3.301730e+01 2.023535e-02 -1.325797e-02 -1.526676e-03 -1.003961e-03 -4.436088e-03 33 3.509330e+01 1.961051e-02 -1.310637e-02 -1.579684e-03 -9.255476e-04 -3.986979e-03 34 3.722400e+01 1.895641e-02 -1.289821e-02 -1.629086e-03 -8.477595e-04 -3.567894e-03 35 3.940840e+01 1.828300e-02 -1.263399e-02 -1.674434e-03 -7.736197e-04 -3.186678e-03 36 4.164540e+01 1.759882e-02 -1.231923e-02 -1.715246e-03 -7.056126e-04 -2.844455e-03 37 4.393400e+01 1.690962e-02 -1.196018e-02 -1.751006e-03 -6.430666e-04 -2.540980e-03 38 4.627300e+01 1.621799e-02 -1.156052e-02 -1.781174e-03 -5.817508e-04 -2.280196e-03 39 4.866150e+01 1.552589e-02 -1.112466e-02 -1.805216e-03 -5.188655e-04 -2.063177e-03 40 5.109810e+01 1.483529e-02 -1.066297e-02 -1.822653e-03 -4.558642e-04 -1.879789e-03 41 5.358190e+01 1.414701e-02 -1.018779e-02 -1.833127e-03 -3.948374e-04 -1.717160e-03 42 5.611150e+01 1.346184e-02 -9.707837e-03 -1.836341e-03 -3.354738e-04 -1.568755e-03 43 5.868580e+01 1.278248e-02 -9.229814e-03 -1.832103e-03 -2.770296e-04 -1.430747e-03 44 6.130360e+01 1.211258e-02 -8.758314e-03 -1.820414e-03 -2.211338e-04 -1.300789e-03 45 6.396350e+01 1.145448e-02 -8.294044e-03 -1.801295e-03 -1.701473e-04 -1.178969e-03 46 6.666450e+01 1.080861e-02 -7.837191e-03 -1.774887e-03 -1.235396e-04 -1.064653e-03 47 6.940510e+01 1.017467e-02 -7.388014e-03 -1.741537e-03 -7.818028e-05 -9.600795e-04 48 7.218400e+01 9.552866e-03 -6.946773e-03 -1.701683e-03 -3.134386e-05 -8.681324e-04 49 7.500000e+01 8.943524e-03 -6.517248e-03 -1.655835e-03 1.724163e-05 -7.840925e-04 50 7.785170e+01 8.347020e-03 -6.103614e-03 -1.604578e-03 6.614163e-05 -7.027574e-04 51 8.073770e+01 7.763947e-03 -5.706622e-03 -1.548345e-03 1.149852e-04 -6.237125e-04 52 8.365670e+01 7.195039e-03 -5.325627e-03 -1.487602e-03 1.638525e-04 -5.470427e-04 53 8.660730e+01 6.641359e-03 -4.960486e-03 -1.422779e-03 2.117141e-04 -4.727804e-04 54 8.958800e+01 6.103853e-03 -4.612430e-03 -1.354182e-03 2.573771e-04 -3.992652e-04 55 9.259750e+01 5.582917e-03 -4.282695e-03 -1.282425e-03 3.004530e-04 -3.236311e-04 56 9.563430e+01 5.078980e-03 -3.970856e-03 -1.208310e-03 3.410730e-04 -2.463928e-04 57 9.869700e+01 4.593195e-03 -3.676769e-03 -1.132570e-03 3.795147e-04 -1.688684e-04 58 1.017840e+02 4.127306e-03 -3.401967e-03 -1.055979e-03 4.151246e-04 -8.944594e-05 59 1.048940e+02 3.683058e-03 -3.147236e-03 -9.793375e-04 4.466259e-04 -7.491285e-06 60 1.080260e+02 3.261744e-03 -2.911963e-03 -9.033119e-04 4.740976e-04 7.537364e-05 61 1.111770e+02 2.864102e-03 -2.695596e-03 -8.286001e-04 4.986528e-04 1.580269e-04 62 1.143470e+02 2.490394e-03 -2.497094e-03 -7.558434e-04 5.209874e-04 2.387858e-04 63 1.175340e+02 2.140926e-03 -2.314830e-03 -6.855598e-04 5.412858e-04 3.157640e-04 64 1.207360e+02 1.816597e-03 -2.147826e-03 -6.183984e-04 5.597978e-04 3.879007e-04 65 1.239530e+02 1.518954e-03 -1.996151e-03 -5.551758e-04 5.766731e-04 4.541411e-04 66 1.271810e+02 1.249925e-03 -1.861045e-03 -4.967321e-04 5.919877e-04 5.144243e-04 67 1.304210e+02 1.011586e-03 -1.744305e-03 -4.439047e-04 6.055464e-04 5.699574e-04 68 1.336700e+02 8.057146e-04 -1.646720e-03 -3.974279e-04 6.165305e-04 6.211712e-04 69 1.369270e+02 6.335177e-04 -1.567694e-03 -3.578874e-04 6.242705e-04 6.675269e-04 70 1.401900e+02 4.958342e-04 -1.505732e-03 -3.258439e-04 6.288208e-04 7.075014e-04 71 1.434570e+02 3.934164e-04 -1.459533e-03 -3.018147e-04 6.303511e-04 7.390647e-04 72 1.467280e+02 3.269291e-04 -1.429025e-03 -2.861936e-04 6.293389e-04 7.612117e-04 73 1.500000e+02 2.968876e-04 -1.414974e-03 -2.792551e-04 6.266117e-04 7.737752e-04 4.2.4 Budget for j y+ Prod. Diss. t-dp/dy Turb.Diff. Mole.Diff. 1 1.000000e-40 -7.402619e-34 4.263978e-19 6.187833e-04 -1.235701e-10 -4.994259e-10 2 3.569590e-02 -1.706248e-11 2.561628e-05 6.182374e-04 6.080088e-11 -2.621006e-05 3 1.427670e-01 -1.636927e-09 1.017036e-04 6.166320e-04 -3.296471e-10 -1.040422e-04 4 3.211620e-01 -2.817748e-08 2.258719e-04 6.143677e-04 -6.266411e-09 -2.309744e-04 5 5.707950e-01 -2.244711e-07 3.938440e-04 6.121859e-04 -5.660489e-08 -4.024109e-04 6 8.915490e-01 -1.129511e-06 5.992867e-04 6.107221e-04 -2.919281e-07 -6.112524e-04 7 1.283270e+00 -4.169876e-06 8.339953e-04 6.106440e-04 -1.054594e-06 -8.475787e-04 8 1.745770e+00 -1.229971e-05 1.088622e-03 6.126317e-04 -2.951419e-06 -1.098744e-03 9 2.278840e+00 -3.058525e-05 1.354034e-03 6.170173e-04 -6.819173e-06 -1.350309e-03 10 2.882210e+00 -6.648469e-05 1.623048e-03 6.239839e-04 -1.357755e-05 -1.587463e-03 11 3.555600e+00 -1.296346e-04 1.891882e-03 6.336427e-04 -2.405821e-05 -1.796751e-03 12 4.298690e+00 -2.311303e-04 2.161008e-03 6.457788e-04 -3.890758e-05 -1.967804e-03 13 5.111130e+00 -3.824717e-04 2.434971e-03 6.600829e-04 -5.860424e-05 -2.094041e-03 14 5.992520e+00 -5.944077e-04 2.721090e-03 6.762190e-04 -8.348995e-05 -2.172141e-03 15 6.942460e+00 -8.759521e-04 3.027614e-03 6.936109e-04 -1.136493e-04 -2.201534e-03 16 7.960480e+00 -1.233697e-03 3.361802e-03 7.117218e-04 -1.485328e-04 -2.183229e-03 17 9.046110e+00 -1.671294e-03 3.728328e-03 7.301926e-04 -1.864449e-04 -2.118265e-03 18 1.019880e+01 -2.189076e-03 4.128291e-03 7.487109e-04 -2.241339e-04 -2.008107e-03 19 1.141810e+01 -2.783867e-03 4.559194e-03 7.672757e-04 -2.567822e-04 -1.854869e-03 20 1.270330e+01 -3.448682e-03 5.015333e-03 7.861852e-04 -2.784951e-04 -1.661049e-03 21 1.405380e+01 -4.172754e-03 5.488786e-03 8.057548e-04 -2.832526e-04 -1.431339e-03 22 1.546910e+01 -4.941925e-03 5.970648e-03 8.263540e-04 -2.661233e-04 -1.173093e-03 23 1.694840e+01 -5.739106e-03 6.451885e-03 8.482479e-04 -2.243259e-04 -8.951202e-04 24 1.849100e+01 -6.545351e-03 6.923936e-03 8.713855e-04 -1.577499e-04 -6.082798e-04 25 2.009620e+01 -7.341405e-03 7.378942e-03 8.955112e-04 -6.898651e-05 -3.242313e-04 26 2.176320e+01 -8.108777e-03 7.809576e-03 9.201343e-04 3.728241e-05 -5.252433e-05 27 2.349130e+01 -8.830921e-03 8.208834e-03 9.445489e-04 1.555923e-04 1.991301e-04 28 2.527960e+01 -9.493867e-03 8.570280e-03 9.680164e-04 2.804823e-04 4.249775e-04 29 2.712720e+01 -1.008597e-02 8.888363e-03 9.897306e-04 4.062251e-04 6.222188e-04 30 2.903330e+01 -1.059822e-02 9.158908e-03 1.008836e-03 5.266820e-04 7.887165e-04 31 3.099700e+01 -1.102450e-02 9.379188e-03 1.024433e-03 6.356467e-04 9.229725e-04 32 3.301730e+01 -1.136105e-02 9.547540e-03 1.035485e-03 7.279521e-04 1.026010e-03 33 3.509330e+01 -1.160631e-02 9.663344e-03 1.041113e-03 8.003551e-04 1.098852e-03 34 3.722400e+01 -1.176143e-02 9.726951e-03 1.040695e-03 8.510486e-04 1.143027e-03 35 3.940840e+01 -1.183010e-02 9.739415e-03 1.033650e-03 8.791431e-04 1.162870e-03 36 4.164540e+01 -1.181807e-02 9.702583e-03 1.019655e-03 8.846981e-04 1.162798e-03 37 4.393400e+01 -1.173230e-02 9.619348e-03 9.986849e-04 8.690468e-04 1.146423e-03 38 4.627300e+01 -1.158005e-02 9.493717e-03 9.708800e-04 8.352172e-04 1.117313e-03 39 4.866150e+01 -1.136902e-02 9.330226e-03 9.368541e-04 7.871527e-04 1.077750e-03 40 5.109810e+01 -1.110749e-02 9.133165e-03 8.973788e-04 7.278837e-04 1.030131e-03 41 5.358190e+01 -1.080389e-02 8.906492e-03 8.530626e-04 6.598928e-04 9.779237e-04 42 5.611150e+01 -1.046596e-02 8.654145e-03 8.047499e-04 5.862001e-04 9.235690e-04 43 5.868580e+01 -1.010102e-02 8.379883e-03 7.532000e-04 5.092350e-04 8.687146e-04 44 6.130360e+01 -9.714733e-03 8.087287e-03 6.989543e-04 4.303673e-04 8.147251e-04 45 6.396350e+01 -9.311195e-03 7.780120e-03 6.427995e-04 3.515144e-04 7.607722e-04 46 6.666450e+01 -8.893688e-03 7.462129e-03 5.853908e-04 2.760173e-04 7.050360e-04 47 6.940510e+01 -8.465402e-03 7.136484e-03 5.271079e-04 2.063250e-04 6.474888e-04 48 7.218400e+01 -8.029950e-03 6.805634e-03 4.684988e-04 1.418812e-04 5.893546e-04 49 7.500000e+01 -7.591239e-03 6.471438e-03 4.101380e-04 8.071440e-05 5.322138e-04 50 7.785170e+01 -7.152997e-03 6.135292e-03 3.526196e-04 2.180258e-05 4.781484e-04 51 8.073770e+01 -6.718757e-03 5.798803e-03 2.966436e-04 -3.424719e-05 4.284772e-04 52 8.365670e+01 -6.291375e-03 5.464127e-03 2.427235e-04 -8.591289e-05 3.828014e-04 53 8.660730e+01 -5.872559e-03 5.133476e-03 1.912589e-04 -1.322772e-04 3.400311e-04 54 8.958800e+01 -5.463712e-03 4.808510e-03 1.427104e-04 -1.735572e-04 2.993976e-04 55 9.259750e+01 -5.066551e-03 4.490238e-03 9.752082e-05 -2.096060e-04 2.608941e-04 56 9.563430e+01 -4.682670e-03 4.179262e-03 5.613103e-05 -2.391276e-04 2.253849e-04 57 9.869700e+01 -4.313349e-03 3.876096e-03 1.889468e-05 -2.607719e-04 1.937679e-04 58 1.017840e+02 -3.959446e-03 3.581313e-03 -1.409281e-05 -2.742939e-04 1.662228e-04 59 1.048940e+02 -3.620943e-03 3.295434e-03 -4.289263e-05 -2.805108e-04 1.425989e-04 60 1.080260e+02 -3.297177e-03 3.018650e-03 -6.752424e-05 -2.813415e-04 1.224825e-04 61 1.111770e+02 -2.987143e-03 2.750739e-03 -8.800131e-05 -2.796688e-04 1.051306e-04 62 1.143470e+02 -2.689521e-03 2.491401e-03 -1.042991e-04 -2.771791e-04 8.965504e-05 63 1.175340e+02 -2.403142e-03 2.240377e-03 -1.162565e-04 -2.726253e-04 7.501481e-05 64 1.207360e+02 -2.127390e-03 1.997138e-03 -1.238085e-04 -2.631636e-04 6.075391e-05 65 1.239530e+02 -1.861874e-03 1.760841e-03 -1.270352e-04 -2.471880e-04 4.765270e-05 66 1.271810e+02 -1.606198e-03 1.530504e-03 -1.259534e-04 -2.253711e-04 3.677420e-05 67 1.304210e+02 -1.359728e-03 1.305282e-03 -1.207353e-04 -1.993421e-04 2.846513e-05 68 1.336700e+02 -1.121332e-03 1.084630e-03 -1.117511e-04 -1.705256e-04 2.240293e-05 69 1.369270e+02 -8.896544e-04 8.680486e-04 -9.935618e-05 -1.396446e-04 1.792645e-05 70 1.401900e+02 -6.634037e-04 6.548077e-04 -8.410792e-05 -1.070365e-04 1.447717e-05 71 1.434570e+02 -4.411954e-04 4.440693e-04 -6.673643e-05 -7.358020e-05 1.188024e-05 72 1.467280e+02 -2.216038e-04 2.350179e-04 -4.788629e-05 -4.061470e-05 9.893582e-06 73 1.500000e+02 -3.300938e-06 2.688737e-05 -2.826915e-05 -9.066428e-06 7.975626e-06 4.2.5 Budget for j y+ t-dp/dy p.Diff. p-dt/dy 1 0.100000E-39 0.330000E-08 -0.618780E-03 0.618783E-03 2 0.356959E-01 0.582400E-06 -0.617655E-03 0.618237E-03 3 0.142767E+00 0.239330E-05 -0.614239E-03 0.616632E-03 4 0.321162E+00 0.518630E-05 -0.609181E-03 0.614368E-03 5 0.570795E+00 0.886530E-05 -0.603321E-03 0.612186E-03 6 0.891549E+00 0.135804E-04 -0.597142E-03 0.610722E-03 7 0.128327E+01 0.189084E-04 -0.591736E-03 0.610644E-03 8 0.174577E+01 0.252914E-04 -0.587340E-03 0.612632E-03 9 0.227884E+01 0.336370E-04 -0.583380E-03 0.617017E-03 10 0.288221E+01 0.439164E-04 -0.580068E-03 0.623984E-03 11 0.355560E+01 0.573163E-04 -0.576326E-03 0.633643E-03 12 0.429869E+01 0.752471E-04 -0.570532E-03 0.645779E-03 13 0.511113E+01 0.974844E-04 -0.562599E-03 0.660083E-03 14 0.599252E+01 0.125208E-03 -0.551011E-03 0.676219E-03 15 0.694246E+01 0.159449E-03 -0.534162E-03 0.693611E-03 16 0.796048E+01 0.198565E-03 -0.513157E-03 0.711722E-03 17 0.904611E+01 0.241928E-03 -0.488265E-03 0.730193E-03 18 0.101988E+02 0.287849E-03 -0.460862E-03 0.748711E-03 19 0.114181E+02 0.331139E-03 -0.436137E-03 0.767276E-03 20 0.127033E+02 0.368360E-03 -0.417825E-03 0.786185E-03 21 0.140538E+02 0.396196E-03 -0.409559E-03 0.805755E-03 22 0.154691E+02 0.409573E-03 -0.416781E-03 0.826354E-03 23 0.169484E+02 0.407824E-03 -0.440424E-03 0.848248E-03 24 0.184910E+02 0.392106E-03 -0.479279E-03 0.871385E-03 25 0.200962E+02 0.362676E-03 -0.532836E-03 0.895511E-03 26 0.217632E+02 0.324144E-03 -0.595990E-03 0.920134E-03 27 0.234913E+02 0.280843E-03 -0.663706E-03 0.944549E-03 28 0.252796E+02 0.233830E-03 -0.734187E-03 0.968016E-03 29 0.271272E+02 0.187340E-03 -0.802391E-03 0.989731E-03 30 0.290333E+02 0.145364E-03 -0.863472E-03 0.100884E-02 31 0.309970E+02 0.109651E-03 -0.914781E-03 0.102443E-02 32 0.330173E+02 0.844358E-04 -0.951049E-03 0.103549E-02 33 0.350933E+02 0.712961E-04 -0.969817E-03 0.104111E-02 34 0.372240E+02 0.689920E-04 -0.971703E-03 0.104069E-02 35 0.394084E+02 0.790106E-04 -0.954639E-03 0.103365E-02 36 0.416454E+02 0.100453E-03 -0.919202E-03 0.101965E-02 37 0.439340E+02 0.130634E-03 -0.868051E-03 0.998685E-03 38 0.462730E+02 0.168549E-03 -0.802331E-03 0.970880E-03 39 0.486615E+02 0.210195E-03 -0.726659E-03 0.936854E-03 40 0.510981E+02 0.252973E-03 -0.644406E-03 0.897379E-03 41 0.535819E+02 0.297514E-03 -0.555548E-03 0.853063E-03 42 0.561115E+02 0.340979E-03 -0.463771E-03 0.804750E-03 43 0.586858E+02 0.382247E-03 -0.370953E-03 0.753200E-03 44 0.613036E+02 0.422712E-03 -0.276243E-03 0.698954E-03 45 0.639635E+02 0.459711E-03 -0.183088E-03 0.642799E-03 46 0.666645E+02 0.491435E-03 -0.939555E-04 0.585391E-03 47 0.694051E+02 0.517110E-03 -0.999832E-05 0.527108E-03 48 0.721840E+02 0.535047E-03 0.665483E-04 0.468499E-03 49 0.750000E+02 0.548425E-03 0.138287E-03 0.410138E-03 50 0.778517E+02 0.559753E-03 0.207134E-03 0.352620E-03 51 0.807377E+02 0.566956E-03 0.270312E-03 0.296644E-03 52 0.836567E+02 0.570661E-03 0.327938E-03 0.242724E-03 53 0.866073E+02 0.571467E-03 0.380208E-03 0.191259E-03 54 0.895880E+02 0.568239E-03 0.425529E-03 0.142710E-03 55 0.925975E+02 0.562642E-03 0.465121E-03 0.975208E-04 56 0.956343E+02 0.554050E-03 0.497919E-03 0.561310E-04 57 0.986970E+02 0.539501E-03 0.520606E-03 0.188947E-04 58 0.101784E+03 0.519970E-03 0.534063E-03 -0.140928E-04 59 0.104894E+03 0.496198E-03 0.539091E-03 -0.428926E-04 60 0.108026E+03 0.468340E-03 0.535865E-03 -0.675242E-04 61 0.111177E+03 0.440379E-03 0.528381E-03 -0.880013E-04 62 0.114347E+03 0.413951E-03 0.518250E-03 -0.104299E-03 63 0.117534E+03 0.386661E-03 0.502918E-03 -0.116257E-03 64 0.120736E+03 0.357388E-03 0.481197E-03 -0.123808E-03 65 0.123953E+03 0.323983E-03 0.451019E-03 -0.127035E-03 66 0.127181E+03 0.285257E-03 0.411211E-03 -0.125953E-03 67 0.130421E+03 0.244566E-03 0.365301E-03 -0.120735E-03 68 0.133670E+03 0.202499E-03 0.314250E-03 -0.111751E-03 69 0.136927E+03 0.158111E-03 0.257467E-03 -0.993562E-04 70 0.140190E+03 0.114061E-03 0.198169E-03 -0.841079E-04 71 0.143457E+03 0.699394E-04 0.136676E-03 -0.667364E-04 72 0.146728E+03 0.251488E-04 0.730351E-04 -0.478863E-04 73 0.150000E+03 -0.166337E-04 0.116355E-04 -0.282692E-04 4.3 One-dimensional Energy Spectra at several points 4.3.1 Streamwise Power Spectra at y+ = 5.1 k_x*delta E(t+*t+) 1.000000e-40 5.231144e-05 4.000000e-01 7.545756e-05 8.000000e-01 4.479035e-05 1.200000e+00 3.557006e-05 1.600000e+00 2.617916e-05 2.000000e+00 1.965738e-05 2.400000e+00 1.450691e-05 2.800000e+00 1.213405e-05 3.200000e+00 8.370239e-06 3.600000e+00 6.737132e-06 4.000000e+00 5.356031e-06 4.400000e+00 4.155220e-06 4.800000e+00 3.262390e-06 5.200000e+00 2.745670e-06 5.600000e+00 2.061908e-06 6.000000e+00 1.594591e-06 6.400000e+00 1.320835e-06 6.800000e+00 1.073578e-06 7.200000e+00 8.935594e-07 7.600000e+00 7.095329e-07 8.000000e+00 5.611466e-07 8.400000e+00 4.690595e-07 8.800000e+00 3.880764e-07 9.200000e+00 3.138732e-07 9.600000e+00 2.601246e-07 1.000000e+01 2.141537e-07 1.040000e+01 1.766757e-07 1.080000e+01 1.462233e-07 1.120000e+01 1.217019e-07 1.160000e+01 1.032396e-07 1.200000e+01 8.507759e-08 1.240000e+01 7.066631e-08 1.280000e+01 5.944854e-08 1.320000e+01 4.929211e-08 1.360000e+01 4.166571e-08 1.400000e+01 3.563727e-08 1.440000e+01 2.996773e-08 1.480000e+01 2.511190e-08 1.520000e+01 2.139876e-08 1.560000e+01 1.868838e-08 1.600000e+01 1.612751e-08 1.640000e+01 1.357919e-08 1.680000e+01 1.162615e-08 1.720000e+01 9.869667e-09 1.760000e+01 8.666667e-09 1.800000e+01 7.621518e-09 1.840000e+01 6.575466e-09 1.880000e+01 5.643978e-09 1.920000e+01 5.031765e-09 1.960000e+01 4.369253e-09 2.000000e+01 3.795489e-09 2.040000e+01 3.342774e-09 2.080000e+01 2.957191e-09 2.120000e+01 2.572401e-09 2.160000e+01 2.238327e-09 2.200000e+01 1.988578e-09 2.240000e+01 1.747224e-09 2.280000e+01 1.558287e-09 2.320000e+01 1.344895e-09 2.360000e+01 1.185806e-09 2.400000e+01 1.040310e-09 2.440000e+01 9.146398e-10 2.480000e+01 8.143532e-10 2.520000e+01 7.406579e-10 at y+ = 12.7 k_x*delta E(t+*t+) 1.000000e-40 3.070419e-04 4.000000e-01 4.467952e-04 8.000000e-01 2.689824e-04 1.200000e+00 2.160657e-04 1.600000e+00 1.592056e-04 2.000000e+00 1.198406e-04 2.400000e+00 8.882199e-05 2.800000e+00 7.427939e-05 3.200000e+00 5.115931e-05 3.600000e+00 4.126199e-05 4.000000e+00 3.270228e-05 4.400000e+00 2.543032e-05 4.800000e+00 1.996145e-05 5.200000e+00 1.684246e-05 5.600000e+00 1.263366e-05 6.000000e+00 9.763821e-06 6.400000e+00 8.100171e-06 6.800000e+00 6.615968e-06 7.200000e+00 5.494977e-06 7.600000e+00 4.372206e-06 8.000000e+00 3.474525e-06 8.400000e+00 2.903363e-06 8.800000e+00 2.411710e-06 9.200000e+00 1.957616e-06 9.600000e+00 1.626376e-06 1.000000e+01 1.343047e-06 1.040000e+01 1.112130e-06 1.080000e+01 9.232870e-07 1.120000e+01 7.667679e-07 1.160000e+01 6.578392e-07 1.200000e+01 5.419310e-07 1.240000e+01 4.525519e-07 1.280000e+01 3.823069e-07 1.320000e+01 3.184695e-07 1.360000e+01 2.704841e-07 1.400000e+01 2.331030e-07 1.440000e+01 1.967848e-07 1.480000e+01 1.658629e-07 1.520000e+01 1.427299e-07 1.560000e+01 1.250615e-07 1.600000e+01 1.090163e-07 1.640000e+01 9.252791e-08 1.680000e+01 7.934561e-08 1.720000e+01 6.788386e-08 1.760000e+01 6.005531e-08 1.800000e+01 5.294708e-08 1.840000e+01 4.573196e-08 1.880000e+01 3.960840e-08 1.920000e+01 3.562001e-08 1.960000e+01 3.131969e-08 2.000000e+01 2.724184e-08 2.040000e+01 2.424937e-08 2.080000e+01 2.157044e-08 2.120000e+01 1.891546e-08 2.160000e+01 1.663439e-08 2.200000e+01 1.497613e-08 2.240000e+01 1.331334e-08 2.280000e+01 1.195841e-08 2.320000e+01 1.039365e-08 2.360000e+01 9.255454e-09 2.400000e+01 8.284110e-09 2.440000e+01 7.283613e-09 2.480000e+01 6.557075e-09 2.520000e+01 6.073491e-09 at y+ = 75.1 k_x*delta E(t+*t+) 1.000000e-40 1.899382e-03 4.000000e-01 2.904118e-03 8.000000e-01 2.022589e-03 1.200000e+00 2.158318e-03 1.600000e+00 1.575969e-03 2.000000e+00 1.174644e-03 2.400000e+00 8.680699e-04 2.800000e+00 7.553874e-04 3.200000e+00 4.901724e-04 3.600000e+00 3.972515e-04 4.000000e+00 3.119387e-04 4.400000e+00 2.446244e-04 4.800000e+00 1.892504e-04 5.200000e+00 1.674476e-04 5.600000e+00 1.269299e-04 6.000000e+00 9.559064e-05 6.400000e+00 7.501898e-05 6.800000e+00 5.622223e-05 7.200000e+00 4.599340e-05 7.600000e+00 3.469387e-05 8.000000e+00 2.769871e-05 8.400000e+00 2.175837e-05 8.800000e+00 1.908037e-05 9.200000e+00 1.518621e-05 9.600000e+00 1.229814e-05 1.000000e+01 9.848258e-06 1.040000e+01 7.859992e-06 1.080000e+01 6.190609e-06 1.120000e+01 5.329851e-06 1.160000e+01 4.223018e-06 1.200000e+01 3.606484e-06 1.240000e+01 3.012690e-06 1.280000e+01 2.413898e-06 1.320000e+01 2.054430e-06 1.360000e+01 1.696567e-06 1.400000e+01 1.453244e-06 1.440000e+01 1.267703e-06 1.480000e+01 1.002311e-06 1.520000e+01 8.470634e-07 1.560000e+01 7.437343e-07 1.600000e+01 6.426694e-07 1.640000e+01 5.526494e-07 1.680000e+01 4.715407e-07 1.720000e+01 4.005034e-07 1.760000e+01 3.490480e-07 1.800000e+01 3.077695e-07 1.840000e+01 2.717970e-07 1.880000e+01 2.351710e-07 1.920000e+01 2.071284e-07 1.960000e+01 1.897832e-07 2.000000e+01 1.634708e-07 2.040000e+01 1.442628e-07 2.080000e+01 1.293011e-07 2.120000e+01 1.125893e-07 2.160000e+01 1.046056e-07 2.200000e+01 8.979478e-08 2.240000e+01 8.345906e-08 2.280000e+01 7.537133e-08 2.320000e+01 6.856228e-08 2.360000e+01 6.076029e-08 2.400000e+01 5.547346e-08 2.440000e+01 5.105929e-08 2.480000e+01 4.579686e-08 2.520000e+01 4.251172e-08 at y+ = 150 k_x*delta E(t+*t+) 1.000000e-40 7.666155e-04 4.000000e-01 8.876934e-04 8.000000e-01 7.083542e-04 1.200000e+00 6.168478e-04 1.600000e+00 4.038297e-04 2.000000e+00 2.887900e-04 2.400000e+00 1.800919e-04 2.800000e+00 1.277416e-04 3.200000e+00 8.899459e-05 3.600000e+00 5.932070e-05 4.000000e+00 4.370271e-05 4.400000e+00 3.134184e-05 4.800000e+00 2.148545e-05 5.200000e+00 1.626816e-05 5.600000e+00 1.231696e-05 6.000000e+00 1.000499e-05 6.400000e+00 7.283345e-06 6.800000e+00 4.911415e-06 7.200000e+00 3.789844e-06 7.600000e+00 2.865024e-06 8.000000e+00 2.374748e-06 8.400000e+00 1.705778e-06 8.800000e+00 1.317760e-06 9.200000e+00 1.101261e-06 9.600000e+00 8.551335e-07 1.000000e+01 6.181186e-07 1.040000e+01 4.811337e-07 1.080000e+01 3.902871e-07 1.120000e+01 3.044243e-07 1.160000e+01 2.429255e-07 1.200000e+01 1.891671e-07 1.240000e+01 1.613450e-07 1.280000e+01 1.227683e-07 1.320000e+01 1.029242e-07 1.360000e+01 8.401330e-08 1.400000e+01 6.737802e-08 1.440000e+01 5.375928e-08 1.480000e+01 4.301314e-08 1.520000e+01 3.732994e-08 1.560000e+01 3.059288e-08 1.600000e+01 2.515403e-08 1.640000e+01 2.199717e-08 1.680000e+01 1.785073e-08 1.720000e+01 1.495399e-08 1.760000e+01 1.264131e-08 1.800000e+01 1.030272e-08 1.840000e+01 8.971738e-09 1.880000e+01 7.827668e-09 1.920000e+01 6.781010e-09 1.960000e+01 5.677749e-09 2.000000e+01 4.789769e-09 2.040000e+01 4.182174e-09 2.080000e+01 3.669321e-09 2.120000e+01 3.270600e-09 2.160000e+01 2.769256e-09 2.200000e+01 2.518812e-09 2.240000e+01 2.164429e-09 2.280000e+01 1.941392e-09 2.320000e+01 1.559436e-09 2.360000e+01 1.410070e-09 2.400000e+01 1.182927e-09 2.440000e+01 9.731889e-10 2.480000e+01 8.440546e-10 2.520000e+01 7.024574e-10 4.3.2 Spanwise power spectra at y+ = 5.1 k_z*delta E(t+*t+) 1.000000e-40 1.200737e-05 1.000000e+00 3.493129e-05 2.000000e+00 4.224453e-05 3.000000e+00 4.834155e-05 4.000000e+00 3.681815e-05 5.000000e+00 2.947635e-05 6.000000e+00 3.194585e-05 7.000000e+00 2.473084e-05 8.000000e+00 1.696954e-05 9.000000e+00 1.199676e-05 1.000000e+01 8.494935e-06 1.100000e+01 6.656525e-06 1.200000e+01 4.691295e-06 1.300000e+01 3.437529e-06 1.400000e+01 2.410579e-06 1.500000e+01 1.818640e-06 1.600000e+01 1.310494e-06 1.700000e+01 9.611480e-07 1.800000e+01 6.946823e-07 1.900000e+01 5.427729e-07 2.000000e+01 3.910024e-07 2.100000e+01 2.992402e-07 2.200000e+01 2.247934e-07 2.300000e+01 1.728752e-07 2.400000e+01 1.353101e-07 2.500000e+01 1.075170e-07 2.600000e+01 7.912332e-08 2.700000e+01 6.280615e-08 2.800000e+01 5.038595e-08 2.900000e+01 3.852091e-08 3.000000e+01 3.016427e-08 3.100000e+01 2.439602e-08 3.200000e+01 1.910369e-08 3.300000e+01 1.506941e-08 3.400000e+01 1.197037e-08 3.500000e+01 9.776878e-09 3.600000e+01 7.796206e-09 3.700000e+01 6.351518e-09 3.800000e+01 5.174522e-09 3.900000e+01 4.063893e-09 4.000000e+01 3.261652e-09 4.100000e+01 2.691667e-09 4.200000e+01 2.189851e-09 4.300000e+01 1.787706e-09 4.400000e+01 1.450367e-09 4.500000e+01 1.173130e-09 4.600000e+01 9.820131e-10 4.700000e+01 8.030094e-10 4.800000e+01 6.637045e-10 4.900000e+01 5.493862e-10 5.000000e+01 4.506468e-10 5.100000e+01 3.819545e-10 5.200000e+01 3.213271e-10 5.300000e+01 2.683648e-10 5.400000e+01 2.294586e-10 5.500000e+01 1.939064e-10 5.600000e+01 1.655516e-10 5.700000e+01 1.435809e-10 5.800000e+01 1.220617e-10 5.900000e+01 1.002367e-10 6.000000e+01 8.393164e-11 6.100000e+01 6.912031e-11 6.200000e+01 5.522295e-11 6.300000e+01 4.611209e-11 at y+ = 12.7 k_z*delta E(t+*t+) 1.000000e-40 7.317949e-05 1.000000e+00 2.118638e-04 2.000000e+00 2.558959e-04 3.000000e+00 2.931689e-04 4.000000e+00 2.223364e-04 5.000000e+00 1.783136e-04 6.000000e+00 1.912310e-04 7.000000e+00 1.486571e-04 8.000000e+00 1.012604e-04 9.000000e+00 7.108074e-05 1.000000e+01 5.014879e-05 1.100000e+01 3.885626e-05 1.200000e+01 2.731642e-05 1.300000e+01 2.001863e-05 1.400000e+01 1.376151e-05 1.500000e+01 1.038812e-05 1.600000e+01 7.369220e-06 1.700000e+01 5.375159e-06 1.800000e+01 3.884206e-06 1.900000e+01 2.978486e-06 2.000000e+01 2.132816e-06 2.100000e+01 1.617279e-06 2.200000e+01 1.207928e-06 2.300000e+01 9.309859e-07 2.400000e+01 7.099450e-07 2.500000e+01 5.634611e-07 2.600000e+01 4.070998e-07 2.700000e+01 3.221724e-07 2.800000e+01 2.577443e-07 2.900000e+01 1.974756e-07 3.000000e+01 1.516836e-07 3.100000e+01 1.230559e-07 3.200000e+01 9.605889e-08 3.300000e+01 7.546793e-08 3.400000e+01 5.961382e-08 3.500000e+01 4.814906e-08 3.600000e+01 3.902448e-08 3.700000e+01 3.121782e-08 3.800000e+01 2.510525e-08 3.900000e+01 2.009318e-08 4.000000e+01 1.595856e-08 4.100000e+01 1.310929e-08 4.200000e+01 1.068293e-08 4.300000e+01 8.744799e-09 4.400000e+01 7.056211e-09 4.500000e+01 5.769724e-09 4.600000e+01 4.820526e-09 4.700000e+01 3.942402e-09 4.800000e+01 3.285684e-09 4.900000e+01 2.745190e-09 5.000000e+01 2.313761e-09 5.100000e+01 1.929220e-09 5.200000e+01 1.672644e-09 5.300000e+01 1.410620e-09 5.400000e+01 1.200135e-09 5.500000e+01 1.068864e-09 5.600000e+01 9.285698e-10 5.700000e+01 8.271486e-10 5.800000e+01 7.292910e-10 5.900000e+01 6.242028e-10 6.000000e+01 5.401795e-10 6.100000e+01 4.592202e-10 6.200000e+01 3.786504e-10 6.300000e+01 3.275844e-10 at y+ = 75.1 k_z*delta E(t+*t+) 1.000000e-40 1.245618e-03 1.000000e+00 3.164888e-03 2.000000e+00 3.393333e-03 3.000000e+00 3.237828e-03 4.000000e+00 1.760414e-03 5.000000e+00 1.117748e-03 6.000000e+00 7.756499e-04 7.000000e+00 4.712839e-04 8.000000e+00 2.490025e-04 9.000000e+00 1.367662e-04 1.000000e+01 7.462255e-05 1.100000e+01 4.654236e-05 1.200000e+01 2.705342e-05 1.300000e+01 1.616474e-05 1.400000e+01 1.006885e-05 1.500000e+01 6.363073e-06 1.600000e+01 4.162241e-06 1.700000e+01 2.720371e-06 1.800000e+01 1.756745e-06 1.900000e+01 1.180806e-06 2.000000e+01 8.278230e-07 2.100000e+01 5.774385e-07 2.200000e+01 3.980351e-07 2.300000e+01 2.869227e-07 2.400000e+01 2.067016e-07 2.500000e+01 1.487014e-07 2.600000e+01 1.105942e-07 2.700000e+01 8.208624e-08 2.800000e+01 5.929221e-08 2.900000e+01 4.450751e-08 3.000000e+01 3.386504e-08 3.100000e+01 2.594224e-08 3.200000e+01 1.981430e-08 3.300000e+01 1.492824e-08 3.400000e+01 1.167574e-08 3.500000e+01 9.162186e-09 3.600000e+01 7.019869e-09 3.700000e+01 5.519422e-09 3.800000e+01 4.330170e-09 3.900000e+01 3.413101e-09 4.000000e+01 2.731161e-09 4.100000e+01 2.151433e-09 4.200000e+01 1.715727e-09 4.300000e+01 1.402599e-09 4.400000e+01 1.115675e-09 4.500000e+01 8.996664e-10 4.600000e+01 7.301179e-10 4.700000e+01 5.908059e-10 4.800000e+01 4.870679e-10 4.900000e+01 3.968016e-10 5.000000e+01 3.265422e-10 5.100000e+01 2.665675e-10 5.200000e+01 2.246548e-10 5.300000e+01 1.898837e-10 5.400000e+01 1.607100e-10 5.500000e+01 1.381708e-10 5.600000e+01 1.222671e-10 5.700000e+01 1.078871e-10 5.800000e+01 9.729539e-11 5.900000e+01 8.750440e-11 6.000000e+01 8.133254e-11 6.100000e+01 7.533769e-11 6.200000e+01 6.997621e-11 6.300000e+01 6.321862e-11 at y+ = 150 k_z*delta E(t+*t+) 1.000000e-40 5.622019e-04 1.000000e+00 1.491458e-03 2.000000e+00 1.225981e-03 3.000000e+00 6.140324e-04 4.000000e+00 2.363413e-04 5.000000e+00 9.191995e-05 6.000000e+00 3.909959e-05 7.000000e+00 1.728893e-05 8.000000e+00 7.434422e-06 9.000000e+00 3.408182e-06 1.000000e+01 1.612684e-06 1.100000e+01 8.465980e-07 1.200000e+01 4.594377e-07 1.300000e+01 2.456066e-07 1.400000e+01 1.446761e-07 1.500000e+01 7.976064e-08 1.600000e+01 5.081720e-08 1.700000e+01 3.109356e-08 1.800000e+01 2.019399e-08 1.900000e+01 1.288696e-08 2.000000e+01 8.275329e-09 2.100000e+01 5.630926e-09 2.200000e+01 3.802370e-09 2.300000e+01 2.647609e-09 2.400000e+01 1.769905e-09 2.500000e+01 1.241664e-09 2.600000e+01 8.803439e-10 2.700000e+01 6.228660e-10 2.800000e+01 4.495246e-10 2.900000e+01 3.271437e-10 3.000000e+01 2.364202e-10 3.100000e+01 1.733867e-10 3.200000e+01 1.299840e-10 3.300000e+01 9.604542e-11 3.400000e+01 7.167751e-11 3.500000e+01 5.356354e-11 3.600000e+01 4.044569e-11 3.700000e+01 3.025222e-11 3.800000e+01 2.319672e-11 3.900000e+01 1.751549e-11 4.000000e+01 1.333718e-11 4.100000e+01 1.040354e-11 4.200000e+01 8.056959e-12 4.300000e+01 6.227274e-12 4.400000e+01 4.893543e-12 4.500000e+01 3.862718e-12 4.600000e+01 3.019702e-12 4.700000e+01 2.420972e-12 4.800000e+01 1.913124e-12 4.900000e+01 1.530058e-12 5.000000e+01 1.219341e-12 5.100000e+01 1.001045e-12 5.200000e+01 8.216883e-13 5.300000e+01 6.780533e-13 5.400000e+01 5.681930e-13 5.500000e+01 4.829893e-13 5.600000e+01 4.148032e-13 5.700000e+01 3.596562e-13 5.800000e+01 3.201660e-13 5.900000e+01 2.872818e-13 6.000000e+01 2.500746e-13 6.100000e+01 2.155576e-13 6.200000e+01 1.811782e-13 6.300000e+01 1.532569e-13 4.4 Two-point Correlations at several points 4.4.1 Streamwise Separations at y+=5.1 x/delta R(tt) (separation) 1.000000e-40 1.000000e+00 1.227180e-01 9.652962e-01 2.454370e-01 8.797783e-01 3.681550e-01 7.754509e-01 4.908740e-01 6.733423e-01 6.135920e-01 5.825211e-01 7.363110e-01 5.050594e-01 8.590290e-01 4.402568e-01 9.817480e-01 3.864071e-01 1.104470e+00 3.416854e-01 1.227180e+00 3.043871e-01 1.349900e+00 2.731240e-01 1.472620e+00 2.467468e-01 1.595340e+00 2.243500e-01 1.718060e+00 2.052142e-01 1.840780e+00 1.888522e-01 1.963500e+00 1.748669e-01 2.086210e+00 1.629058e-01 2.208930e+00 1.525952e-01 2.331650e+00 1.435658e-01 2.454370e+00 1.354198e-01 2.577090e+00 1.278328e-01 2.699810e+00 1.205804e-01 2.822520e+00 1.136413e-01 2.945240e+00 1.071748e-01 3.067960e+00 1.014037e-01 3.190680e+00 9.639071e-02 3.313400e+00 9.206169e-02 3.436120e+00 8.822209e-02 3.558840e+00 8.465109e-02 3.681550e+00 8.119120e-02 3.804270e+00 7.787378e-02 3.926990e+00 7.480667e-02 4.049710e+00 7.209886e-02 4.172430e+00 6.974138e-02 4.295150e+00 6.758497e-02 4.417860e+00 6.536551e-02 4.540580e+00 6.285546e-02 4.663300e+00 5.990231e-02 4.786020e+00 5.645590e-02 4.908740e+00 5.250282e-02 5.031460e+00 4.815169e-02 5.154180e+00 4.362566e-02 5.276890e+00 3.923783e-02 5.399610e+00 3.528641e-02 5.522330e+00 3.200721e-02 5.645050e+00 2.945781e-02 5.767770e+00 2.754159e-02 5.890490e+00 2.602669e-02 6.013200e+00 2.470030e-02 6.135920e+00 2.342953e-02 6.258640e+00 2.218306e-02 6.381360e+00 2.092135e-02 6.504080e+00 1.960095e-02 6.626800e+00 1.814423e-02 6.749520e+00 1.648234e-02 6.872230e+00 1.453572e-02 6.994950e+00 1.227976e-02 7.117670e+00 9.745166e-03 7.240390e+00 7.063808e-03 7.363110e+00 4.428181e-03 7.485830e+00 2.078198e-03 7.608540e+00 2.183546e-04 7.731260e+00 -9.668379e-04 7.853980e+00 -1.376569e-03 at y+=12.7 x/delta R(tt) (separation) 1.000000e-40 1.000000e+00 1.227180e-01 9.643996e-01 2.454370e-01 8.771834e-01 3.681550e-01 7.712244e-01 4.908740e-01 6.676920e-01 6.135920e-01 5.756937e-01 7.363110e-01 4.972995e-01 8.590290e-01 4.318118e-01 9.817480e-01 3.775106e-01 1.104470e+00 3.325558e-01 1.227180e+00 2.951915e-01 1.349900e+00 2.639903e-01 1.472620e+00 2.377708e-01 1.595340e+00 2.156071e-01 1.718060e+00 1.967576e-01 1.840780e+00 1.807268e-01 1.963500e+00 1.670961e-01 2.086210e+00 1.554988e-01 2.208930e+00 1.455505e-01 2.331650e+00 1.368736e-01 2.454370e+00 1.290577e-01 2.577090e+00 1.217694e-01 2.699810e+00 1.147790e-01 2.822520e+00 1.080761e-01 2.945240e+00 1.018345e-01 3.067960e+00 9.629914e-02 3.190680e+00 9.153495e-02 3.313400e+00 8.747179e-02 3.436120e+00 8.391087e-02 3.558840e+00 8.062194e-02 3.681550e+00 7.742797e-02 3.804270e+00 7.436019e-02 3.926990e+00 7.152985e-02 4.049710e+00 6.905939e-02 4.172430e+00 6.694864e-02 4.295150e+00 6.504952e-02 4.417860e+00 6.308801e-02 4.540580e+00 6.082933e-02 4.663300e+00 5.810035e-02 4.786020e+00 5.483939e-02 4.908740e+00 5.102383e-02 5.031460e+00 4.677414e-02 5.154180e+00 4.233031e-02 5.276890e+00 3.801877e-02 5.399610e+00 3.412613e-02 5.522330e+00 3.088202e-02 5.645050e+00 2.834507e-02 5.767770e+00 2.643216e-02 5.890490e+00 2.491154e-02 6.013200e+00 2.358085e-02 6.135920e+00 2.231367e-02 6.258640e+00 2.108700e-02 6.381360e+00 1.985269e-02 6.504080e+00 1.856130e-02 6.626800e+00 1.712834e-02 6.749520e+00 1.549191e-02 6.872230e+00 1.357009e-02 6.994950e+00 1.132989e-02 7.117670e+00 8.781778e-03 7.240390e+00 6.058061e-03 7.363110e+00 3.360459e-03 7.485830e+00 9.434462e-04 7.608540e+00 -9.826681e-04 7.731260e+00 -2.217690e-03 7.853980e+00 -2.648006e-03 at y+=75.0 x/delta R(tt) (separation) 1.000000e-40 1.000000e+00 1.227180e-01 9.605222e-01 2.454370e-01 8.609498e-01 3.681550e-01 7.358470e-01 4.908740e-01 6.113011e-01 6.135920e-01 5.006457e-01 7.363110e-01 4.079180e-01 8.590290e-01 3.324049e-01 9.817480e-01 2.713894e-01 1.104470e+00 2.218489e-01 1.227180e+00 1.811813e-01 1.349900e+00 1.476197e-01 1.472620e+00 1.202064e-01 1.595340e+00 9.857529e-02 1.718060e+00 8.237554e-02 1.840780e+00 7.091430e-02 1.963500e+00 6.304170e-02 2.086210e+00 5.753052e-02 2.208930e+00 5.339635e-02 2.331650e+00 5.007386e-02 2.454370e+00 4.728944e-02 2.577090e+00 4.493533e-02 2.699810e+00 4.296508e-02 2.822520e+00 4.152480e-02 2.945240e+00 4.086940e-02 3.067960e+00 4.116117e-02 3.190680e+00 4.228586e-02 3.313400e+00 4.399539e-02 3.436120e+00 4.597636e-02 3.558840e+00 4.799680e-02 3.681550e+00 5.001007e-02 3.804270e+00 5.217801e-02 3.926990e+00 5.460825e-02 4.049710e+00 5.726918e-02 4.172430e+00 5.993406e-02 4.295150e+00 6.226656e-02 4.417860e+00 6.385806e-02 4.540580e+00 6.437538e-02 4.663300e+00 6.360192e-02 4.786020e+00 6.146077e-02 4.908740e+00 5.797987e-02 5.031460e+00 5.340154e-02 5.154180e+00 4.814899e-02 5.276890e+00 4.278525e-02 5.399610e+00 3.784128e-02 5.522330e+00 3.365456e-02 5.645050e+00 3.023732e-02 5.767770e+00 2.745160e-02 5.890490e+00 2.512698e-02 6.013200e+00 2.310918e-02 6.135920e+00 2.116073e-02 6.258640e+00 1.910605e-02 6.381360e+00 1.690323e-02 6.504080e+00 1.459294e-02 6.626800e+00 1.213135e-02 6.749520e+00 9.389468e-03 6.872230e+00 6.166929e-03 6.994950e+00 2.309897e-03 7.117670e+00 -2.248551e-03 7.240390e+00 -7.313366e-03 7.363110e+00 -1.244638e-02 7.485830e+00 -1.703491e-02 7.608540e+00 -2.055423e-02 7.731260e+00 -2.269936e-02 7.853980e+00 -2.341384e-02 at y+=150 x/delta R(tt) (separation) 1.000000e-40 1.000000e+00 1.227180e-01 9.790303e-01 2.454370e-01 9.220543e-01 3.681550e-01 8.420481e-01 4.908740e-01 7.517494e-01 6.135920e-01 6.603783e-01 7.363110e-01 5.734674e-01 8.590290e-01 4.938704e-01 9.817480e-01 4.227615e-01 1.104470e+00 3.603680e-01 1.227180e+00 3.063974e-01 1.349900e+00 2.603105e-01 1.472620e+00 2.214575e-01 1.595340e+00 1.891451e-01 1.718060e+00 1.626305e-01 1.840780e+00 1.410983e-01 1.963500e+00 1.236914e-01 2.086210e+00 1.096330e-01 2.208930e+00 9.832741e-02 2.331650e+00 8.938320e-02 2.454370e+00 8.255124e-02 2.577090e+00 7.762874e-02 2.699810e+00 7.436509e-02 2.822520e+00 7.243940e-02 2.945240e+00 7.149027e-02 3.067960e+00 7.116778e-02 3.190680e+00 7.118652e-02 3.313400e+00 7.138936e-02 3.436120e+00 7.176776e-02 3.558840e+00 7.241707e-02 3.681550e+00 7.340724e-02 3.804270e+00 7.468642e-02 3.926990e+00 7.606673e-02 4.049710e+00 7.731223e-02 4.172430e+00 7.825836e-02 4.295150e+00 7.887505e-02 4.417860e+00 7.922357e-02 4.540580e+00 7.937682e-02 4.663300e+00 7.938606e-02 4.786020e+00 7.930629e-02 4.908740e+00 7.920299e-02 5.031460e+00 7.913113e-02 5.154180e+00 7.911096e-02 5.276890e+00 7.912660e-02 5.399610e+00 7.913634e-02 5.522330e+00 7.909474e-02 5.645050e+00 7.895186e-02 5.767770e+00 7.863325e-02 5.890490e+00 7.802221e-02 6.013200e+00 7.697742e-02 6.135920e+00 7.538004e-02 6.258640e+00 7.320331e-02 6.381360e+00 7.053596e-02 6.504080e+00 6.753968e-02 6.626800e+00 6.438796e-02 6.749520e+00 6.122972e-02 6.872230e+00 5.815796e-02 6.994950e+00 5.520891e-02 7.117670e+00 5.240408e-02 7.240390e+00 4.980449e-02 7.363110e+00 4.751793e-02 7.485830e+00 4.565729e-02 7.608540e+00 4.429624e-02 7.731260e+00 4.347019e-02 7.853980e+00 4.319293e-02 4.4.2 Spanwise Separations at y+=5.1 z/delta R(tt) (separation) 1.000000e-40 1.000000e+00 4.908740e-02 9.557034e-01 9.817480e-02 8.368279e-01 1.472620e-01 6.750300e-01 1.963500e-01 5.022006e-01 2.454370e-01 3.412767e-01 2.945240e-01 2.049679e-01 3.436120e-01 9.789594e-02 3.926990e-01 1.937617e-02 4.417860e-01 -3.415192e-02 4.908740e-01 -6.738799e-02 5.399610e-01 -8.507231e-02 5.890490e-01 -9.145596e-02 6.381360e-01 -9.014088e-02 6.872230e-01 -8.411091e-02 7.363110e-01 -7.577684e-02 7.853980e-01 -6.702624e-02 8.344860e-01 -5.926559e-02 8.835730e-01 -5.346609e-02 9.326600e-01 -5.019269e-02 9.817480e-01 -4.963561e-02 1.030840e+00 -5.162638e-02 1.079920e+00 -5.565554e-02 1.129010e+00 -6.093367e-02 1.178100e+00 -6.652303e-02 1.227180e+00 -7.147176e-02 1.276270e+00 -7.491425e-02 1.325360e+00 -7.614713e-02 1.374450e+00 -7.469889e-02 1.423530e+00 -7.038788e-02 1.472620e+00 -6.337880e-02 1.521710e+00 -5.417315e-02 1.570800e+00 -4.349917e-02 1.619880e+00 -3.214005e-02 1.668970e+00 -2.080089e-02 1.718060e+00 -1.005475e-02 1.767150e+00 -3.546235e-04 1.816230e+00 7.959026e-03 1.865320e+00 1.465927e-02 1.914410e+00 1.960774e-02 1.963500e+00 2.270077e-02 2.012580e+00 2.387379e-02 2.061670e+00 2.317109e-02 2.110760e+00 2.079174e-02 2.159840e+00 1.703763e-02 2.208930e+00 1.222836e-02 2.258020e+00 6.663312e-03 2.307110e+00 6.529571e-04 2.356190e+00 -5.440197e-03 2.405280e+00 -1.120247e-02 2.454370e+00 -1.623611e-02 2.503460e+00 -2.022656e-02 2.552540e+00 -2.297854e-02 2.601630e+00 -2.442982e-02 2.650720e+00 -2.465732e-02 2.699810e+00 -2.385759e-02 2.748890e+00 -2.231453e-02 2.797980e+00 -2.036165e-02 2.847070e+00 -1.835333e-02 2.896160e+00 -1.661904e-02 2.945240e+00 -1.539931e-02 2.994330e+00 -1.477452e-02 3.043420e+00 -1.463571e-02 3.092510e+00 -1.473009e-02 3.141590e+00 -1.479842e-02 at y+=12.7 z/delta R(tt) (separation) 1.000000e-40 1.000000e+00 4.908740e-02 9.568386e-01 9.817480e-02 8.404459e-01 1.472620e-01 6.808326e-01 1.963500e-01 5.090162e-01 2.454370e-01 3.479376e-01 2.945240e-01 2.107007e-01 3.436120e-01 1.023433e-01 3.926990e-01 2.249152e-02 4.417860e-01 -3.222053e-02 4.908740e-01 -6.639933e-02 5.399610e-01 -8.477357e-02 5.890490e-01 -9.163219e-02 6.381360e-01 -9.062422e-02 6.872230e-01 -8.476889e-02 7.363110e-01 -7.650732e-02 7.853980e-01 -6.776303e-02 8.344860e-01 -5.998234e-02 8.835730e-01 -5.416799e-02 9.326600e-01 -5.089913e-02 9.817480e-01 -5.036539e-02 1.030840e+00 -5.239207e-02 1.079920e+00 -5.646251e-02 1.129010e+00 -6.177215e-02 1.178100e+00 -6.735341e-02 1.227180e+00 -7.222152e-02 1.276270e+00 -7.550245e-02 1.325360e+00 -7.651859e-02 1.374450e+00 -7.484690e-02 1.423530e+00 -7.035124e-02 1.472620e+00 -6.321691e-02 1.521710e+00 -5.393896e-02 1.570800e+00 -4.322770e-02 1.619880e+00 -3.184914e-02 1.668970e+00 -2.049878e-02 1.718060e+00 -9.750674e-03 1.767150e+00 -6.293235e-05 1.816230e+00 8.224699e-03 1.865320e+00 1.488766e-02 1.914410e+00 1.978041e-02 1.963500e+00 2.279088e-02 2.012580e+00 2.386157e-02 2.061670e+00 2.305493e-02 2.110760e+00 2.059047e-02 2.159840e+00 1.679504e-02 2.208930e+00 1.201771e-02 2.258020e+00 6.584506e-03 2.307110e+00 8.156282e-04 2.356190e+00 -4.952500e-03 2.405280e+00 -1.037737e-02 2.454370e+00 -1.515087e-02 2.503460e+00 -1.902032e-02 2.552540e+00 -2.180323e-02 2.601630e+00 -2.340594e-02 2.650720e+00 -2.385303e-02 2.699810e+00 -2.329475e-02 2.748890e+00 -2.199591e-02 2.797980e+00 -2.029489e-02 2.847070e+00 -1.855016e-02 2.896160e+00 -1.708149e-02 2.945240e+00 -1.611340e-02 2.994330e+00 -1.571166e-02 3.043420e+00 -1.575398e-02 3.092510e+00 -1.596976e-02 3.141590e+00 -1.608143e-02 at y+=75.0 z/delta R(tt) (separation) 1.000000e-40 1.000000e+00 4.908740e-02 9.842680e-01 9.817480e-02 9.388884e-01 1.472620e-01 8.687409e-01 1.963500e-01 7.804984e-01 2.454370e-01 6.813253e-01 2.945240e-01 5.779001e-01 3.436120e-01 4.758249e-01 3.926990e-01 3.793619e-01 4.417860e-01 2.914126e-01 4.908740e-01 2.136423e-01 5.399610e-01 1.466906e-01 5.890490e-01 9.040324e-02 6.381360e-01 4.406847e-02 6.872230e-01 6.622628e-03 7.363110e-01 -2.317159e-02 7.853980e-01 -4.658305e-02 8.344860e-01 -6.480555e-02 8.835730e-01 -7.888648e-02 9.326600e-01 -8.968653e-02 9.817480e-01 -9.786635e-02 1.030840e+00 -1.038927e-01 1.079920e+00 -1.080621e-01 1.129010e+00 -1.105307e-01 1.178100e+00 -1.113573e-01 1.227180e+00 -1.105387e-01 1.276270e+00 -1.080549e-01 1.325360e+00 -1.039068e-01 1.374450e+00 -9.814761e-02 1.423530e+00 -9.090219e-02 1.472620e+00 -8.237157e-02 1.521710e+00 -7.282322e-02 1.570800e+00 -6.257182e-02 1.619880e+00 -5.195582e-02 1.668970e+00 -4.131384e-02 1.718060e+00 -3.096539e-02 1.767150e+00 -2.119671e-02 1.816230e+00 -1.225113e-02 1.865320e+00 -4.323410e-03 1.914410e+00 2.443713e-03 1.963500e+00 7.957729e-03 2.012580e+00 1.217219e-02 2.061670e+00 1.508079e-02 2.110760e+00 1.671325e-02 2.159840e+00 1.713378e-02 2.208930e+00 1.643984e-02 2.258020e+00 1.475989e-02 2.307110e+00 1.224712e-02 2.356190e+00 9.070347e-03 2.405280e+00 5.402457e-03 2.454370e+00 1.409088e-03 2.503460e+00 -2.762350e-03 2.552540e+00 -6.990185e-03 2.601630e+00 -1.118158e-02 2.650720e+00 -1.526987e-02 2.699810e+00 -1.920780e-02 2.748890e+00 -2.295819e-02 2.797980e+00 -2.648378e-02 2.847070e+00 -2.974020e-02 2.896160e+00 -3.267179e-02 2.945240e+00 -3.521262e-02 2.994330e+00 -3.729093e-02 3.043420e+00 -3.883667e-02 3.092510e+00 -3.979075e-02 3.141590e+00 -4.011348e-02 at y+=150.0 z/delta R(tt) (separation) 1.000000e-40 1.000000e+00 4.908740e-02 9.939842e-01 9.817480e-02 9.762060e-01 1.472620e-01 9.474328e-01 1.963500e-01 9.088377e-01 2.454370e-01 8.618728e-01 2.945240e-01 8.081498e-01 3.436120e-01 7.493266e-01 3.926990e-01 6.870223e-01 4.417860e-01 6.227487e-01 4.908740e-01 5.578673e-01 5.399610e-01 4.935611e-01 5.890490e-01 4.308277e-01 6.381360e-01 3.704750e-01 6.872230e-01 3.131358e-01 7.363110e-01 2.592788e-01 7.853980e-01 2.092292e-01 8.344860e-01 1.631878e-01 8.835730e-01 1.212496e-01 9.326600e-01 8.342437e-02 9.817480e-01 4.965156e-02 1.030840e+00 1.981691e-02 1.079920e+00 -6.236218e-03 1.129010e+00 -2.869570e-02 1.178100e+00 -4.777305e-02 1.227180e+00 -6.369670e-02 1.276270e+00 -7.670722e-02 1.325360e+00 -8.705274e-02 1.374450e+00 -9.498574e-02 1.423530e+00 -1.007591e-01 1.472620e+00 -1.046219e-01 1.521710e+00 -1.068179e-01 1.570800e+00 -1.075797e-01 1.619880e+00 -1.071294e-01 1.668970e+00 -1.056743e-01 1.718060e+00 -1.034059e-01 1.767150e+00 -1.004978e-01 1.816230e+00 -9.710599e-02 1.865320e+00 -9.336795e-02 1.914410e+00 -8.940363e-02 1.963500e+00 -8.531503e-02 2.012580e+00 -8.118784e-02 2.061670e+00 -7.709340e-02 2.110760e+00 -7.308802e-02 2.159840e+00 -6.921620e-02 2.208930e+00 -6.551100e-02 2.258020e+00 -6.199654e-02 2.307110e+00 -5.868789e-02 2.356190e+00 -5.559412e-02 2.405280e+00 -5.271909e-02 2.454370e+00 -5.006392e-02 2.503460e+00 -4.762670e-02 2.552540e+00 -4.540496e-02 2.601630e+00 -4.339543e-02 2.650720e+00 -4.159443e-02 2.699810e+00 -3.999749e-02 2.748890e+00 -3.859908e-02 2.797980e+00 -3.739225e-02 2.847070e+00 -3.636909e-02 2.896160e+00 -3.552094e-02 2.945240e+00 -3.483957e-02 2.994330e+00 -3.431750e-02 3.043420e+00 -3.394876e-02 3.092510e+00 -3.372925e-02 3.141590e+00 -3.365634e-02 5. References 5.1 Ohtsubo, Y., Kasagi, N., and Tomita, Y., "Direct Numerical Simulation of Turbulent Heat Transfer of a Very Low Prandtl Number Fluid in a Two-Dimensional Channel," Proc. of 4th Computational Fluid Dynamics Symposium, Tokyo, 1990, pp. 363-366. 5.2 Ohtsubo, Y., Kasagi, N., and Tomita, Y., "Direct Numerical Simulation of Turbulent Heat Transfer of a Low Prandtl Number Fluid," Proc. of 28th National Heat Transfer Symposium of Japan, Fukuoka, 1991, pp. 16-18. 5.3 Kasagi, N., Ohtsubo, Y., and Tomita, Y., "Direct Numerical Simulation of the Low Prandtl Scalar Number Field in a Two-Dimensional Turblent Channel Flow," Proc. of 8th Symposium on Turbulent Shear Flows, Munich, 1991, Vol. 2, pp. II.11.1-II.11.2. 5.4 Kasagi, N., and Ohtsubo, Y., "Direct Numerical Simulation of Low Prandtl Number Thermal Field in a Turblent Channel Flow," in Turbulent Shear Flows VIII, F. Durst et al., eds., Springer-Verlag, Berlin, 1993, pp. 97-117. (EOF)