******************************************************************************* ******************************************************************************* ********** *********** ********** "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: Homogeneous Isotropic Flow with a Mean Temperature Gradient Code Number: IS__2_UT.HM1 Date of Release: March 1, 1992 Computors: O. Iida and N. Kasagi Department of Mechanical Engineering The University of Tokyo Bunkyo-ku, Tokyo 113 Nomenclature D = dissipation for K D_ij = (i,j) component of dissipation tensor D_tt = dissipation of tt D_vt = dissipation of vt E(k) = 3 dimensional spectral distribution of turbulent kinetic energy E_tt(k) = 3 dimensional spectral distribution of tt E_ii(k_1) = 1 dimensional spectral distribution of (i,i) component of Reynolds stress tensor E_tt(k_1) = 1 dimensional spectral distribution of tt K = turbulent kinetic energy (1/2(u**2+v**2+w**2)) k = 3 dimensional wave number ((k_1**2+k_2**2+k_3**2)**1/2) k_i = wave number in the i_th direction Lamda_ii(x1)= integral scale of u_i component (2*pi*E_ii(k_1 = 0)/(u_i**2)) Lamda_tt(x1)= integral scale of t (2*pi*E_tt(k_1 = 0)/(u_i**2)) OMG_ij = (i,j) component of vorticity tensor P_tt = production of tt P_vt = production of vt phi_vt = pressure temperature gradient correlation of vt Pr= Prandtl number PS_ij = (i,j) component of pressure strain tensor R_ii(x1) = two point correlation coefficient of u_i R_tt(x1) = two point correlation coefficient of t Re_t= turbulent Reynolds number (K**2/D/Ve) RS_ij = (i,j) component of Reynolds stress tensor St = mean temperature gradient in the y direction t = temperature fluctuation tt = temperature fluctuation covariance (t**2) tau= non-dimensional time u_i = i-th component of velocity fluctuation u, v, w = velocity fluctuations in the x-, y- and z-directions vt = turbulent heat flux in the y direction Ve = Nondimensional kinematic viscosity x, y, z = x_1, x_2 and x_3 directions 1. Description of Flow Field The flow field simulated is homogeneus isotropic turbulence with scalar transport. A linear mean temperature gradient is imposed in the x_2 (y) direction. Four simulations have been carried out at the Prandtl numbers of 0.20, 0.71 and 1.5 without initial temperature fluctuations and at the Prandtl number of 0.71 with initial temperature fluctuations. 2. Numerical Method Governing equations: three-dimensional Navier-Stokes equations (rotational form) and the energy conservation equation. Discretization method: spectral method = 96 x 96 x 96 Fourier series. Aliasing treatment: nonlinear terms computed with collocation grids 1.5 times finer in each direction. Time integration: second order Adams-Bashforth for the nonlinear terms and Crank-Nicolson for the diffusion terms. Size of computational box: 2*pai x 2*pi x 2*pi. Initial spectral distribution: E(k) = (0.49/5.0**2) * k * exp(-k/5.0) with Et(k) = (0.49/5.0**2) * k * exp(-k/5.0) or Et(k) = 0. Error in continuity equation: not applicable. Computer: HITAC-S820/80 at the Computer Center of the University of Tokyo. Computation time: 2.5 sec CPU time per one time step. 3. Flow Conditions Ve = 1/300 Pr = 0.2, 0.71, 1.5 St = -1.0 4. Numerical Data 4.1 Velocity Field 4.1.1 Reynolds Strss Tensor tau RS_11 RS_22 RS_33 0.200000D+00 0.261687D+00 0.263467D+00 0.276813D+00 0.400000D+00 0.219159D+00 0.217766D+00 0.225315D+00 0.600000D+00 0.185595D+00 0.182805D+00 0.186819D+00 0.800000D+00 0.159147D+00 0.156073D+00 0.158170D+00 0.100000D+01 0.138021D+00 0.135236D+00 0.136513D+00 0.120000D+01 0.121267D+00 0.118613D+00 0.119440D+00 0.140000D+01 0.107901D+00 0.105073D+00 0.105534D+00 0.160000D+01 0.970981D-01 0.938294D-01 0.940699D-01 0.180000D+01 0.881949D-01 0.843484D-01 0.846045D-01 0.200000D+01 0.806688D-01 0.763056D-01 0.767590D-01 0.220000D+01 0.741865D-01 0.694457D-01 0.701972D-01 0.240000D+01 0.685298D-01 0.635411D-01 0.646676D-01 0.260000D+01 0.635417D-01 0.584201D-01 0.599720D-01 0.280000D+01 0.591052D-01 0.539546D-01 0.559545D-01 0.300000D+01 0.551463D-01 0.500393D-01 0.524798D-01 0.320000D+01 0.516197D-01 0.465907D-01 0.494244D-01 0.340000D+01 0.484823D-01 0.435484D-01 0.466884D-01 0.360000D+01 0.456883D-01 0.408608D-01 0.442030D-01 0.380000D+01 0.431952D-01 0.384766D-01 0.419255D-01 0.400000D+01 0.409631D-01 0.363499D-01 0.398291D-01 0.420000D+01 0.389530D-01 0.344453D-01 0.378952D-01 0.440000D+01 0.371296D-01 0.327350D-01 0.361091D-01 0.460000D+01 0.354639D-01 0.311934D-01 0.344590D-01 0.480000D+01 0.339335D-01 0.297961D-01 0.329355D-01 0.500000D+01 0.325201D-01 0.285212D-01 0.315315D-01 0.520000D+01 0.312086D-01 0.273497D-01 0.302407D-01 0.540000D+01 0.299870D-01 0.262663D-01 0.290564D-01 tau RS_12 RS_13 RS_23 0.200000D+00 0.199526D-02 -0.422021D-02 -0.524566D-02 0.400000D+00 0.122202D-02 -0.392306D-02 -0.522052D-02 0.600000D+00 0.122219D-02 -0.416557D-02 -0.524015D-02 0.800000D+00 0.156897D-02 -0.439465D-02 -0.518171D-02 0.100000D+01 0.165979D-02 -0.443364D-02 -0.492557D-02 0.120000D+01 0.143764D-02 -0.402277D-02 -0.446787D-02 0.140000D+01 0.119364D-02 -0.329882D-02 -0.400776D-02 0.160000D+01 0.111608D-02 -0.257034D-02 -0.361250D-02 0.180000D+01 0.118338D-02 -0.199530D-02 -0.329726D-02 0.200000D+01 0.124852D-02 -0.159871D-02 -0.303494D-02 0.220000D+01 0.122711D-02 -0.135944D-02 -0.277689D-02 0.240000D+01 0.113994D-02 -0.124581D-02 -0.251295D-02 0.260000D+01 0.104770D-02 -0.122017D-02 -0.224665D-02 0.280000D+01 0.992352D-03 -0.124166D-02 -0.197799D-02 0.300000D+01 0.983273D-03 -0.126821D-02 -0.170324D-02 0.320000D+01 0.101256D-02 -0.126865D-02 -0.142523D-02 0.340000D+01 0.106638D-02 -0.123053D-02 -0.115684D-02 0.360000D+01 0.113061D-02 -0.115762D-02 -0.913231D-03 0.380000D+01 0.119521D-02 -0.106231D-02 -0.704009D-03 0.400000D+01 0.125563D-02 -0.957265D-03 -0.530874D-03 0.420000D+01 0.130942D-02 -0.849450D-03 -0.389799D-03 0.440000D+01 0.135372D-02 -0.739082D-03 -0.274872D-03 0.460000D+01 0.138724D-02 -0.623606D-03 -0.180939D-03 0.480000D+01 0.141150D-02 -0.502815D-03 -0.104463D-03 0.500000D+01 0.142946D-02 -0.380662D-03 -0.430576D-04 0.520000D+01 0.144354D-02 -0.263459D-03 0.529697D-05 0.540000D+01 0.145503D-02 -0.157147D-03 0.425650D-04 4.1.2 Dissipation Tensor tau D_11 D_22 D_33 0.200000D+00 0.249996D+00 0.261060D+00 0.271686D+00 0.400000D+00 0.199072D+00 0.203043D+00 0.209879D+00 0.600000D+00 0.152792D+00 0.153978D+00 0.158452D+00 0.800000D+00 0.118936D+00 0.118414D+00 0.121379D+00 0.100000D+01 0.935653D-01 0.931292D-01 0.948741D-01 0.120000D+01 0.747176D-01 0.750269D-01 0.760343D-01 0.140000D+01 0.606897D-01 0.614208D-01 0.620867D-01 0.160000D+01 0.500138D-01 0.508780D-01 0.513293D-01 0.180000D+01 0.418309D-01 0.426116D-01 0.428258D-01 0.200000D+01 0.354537D-01 0.360915D-01 0.360803D-01 0.220000D+01 0.303529D-01 0.308893D-01 0.307377D-01 0.240000D+01 0.262101D-01 0.266659D-01 0.264801D-01 0.260000D+01 0.228044D-01 0.231816D-01 0.230290D-01 0.280000D+01 0.199709D-01 0.202748D-01 0.201890D-01 0.300000D+01 0.175848D-01 0.178334D-01 0.178413D-01 0.320000D+01 0.155573D-01 0.157695D-01 0.158851D-01 0.340000D+01 0.138279D-01 0.140197D-01 0.142325D-01 0.360000D+01 0.123473D-01 0.125350D-01 0.128185D-01 0.380000D+01 0.110753D-01 0.112684D-01 0.115958D-01 0.400000D+01 0.998415D-02 0.101747D-01 0.105291D-01 0.420000D+01 0.904989D-02 0.921986D-02 0.959111D-02 0.440000D+01 0.824805D-02 0.838375D-02 0.876014D-02 0.460000D+01 0.755521D-02 0.765262D-02 0.801994D-02 0.480000D+01 0.695037D-02 0.701408D-02 0.735751D-02 0.500000D+01 0.641652D-02 0.645511D-02 0.676254D-02 0.520000D+01 0.594084D-02 0.596250D-02 0.622778D-02 0.540000D+01 0.551337D-02 0.552427D-02 0.574843D-02 tau D_12 D_13 D_23 0.200000D+00 0.367780D-04 -0.672225D-03 -0.438978D-03 0.400000D+00 -0.121439D-02 -0.241433D-04 0.685364D-04 0.600000D+00 -0.148445D-02 -0.338171D-03 0.984568D-04 0.800000D+00 -0.103619D-02 -0.532345D-03 -0.291972D-03 0.100000D+01 -0.366484D-03 -0.865936D-03 -0.621889D-03 0.120000D+01 -0.106644D-03 -0.980936D-03 -0.548031D-03 0.140000D+01 0.331775D-05 -0.774036D-03 -0.374044D-03 0.160000D+01 -0.415909D-05 -0.462679D-03 -0.219518D-03 0.180000D+01 -0.112094D-05 -0.237239D-03 -0.798893D-04 0.200000D+01 0.538337D-04 -0.910946D-04 -0.352153D-04 0.220000D+01 0.759313D-04 0.227766D-04 -0.549091D-04 0.240000D+01 0.496573D-04 0.939006D-04 -0.100141D-03 0.260000D+01 -0.743018D-05 0.123483D-03 -0.142218D-03 0.280000D+01 -0.722579D-04 0.112130D-03 -0.180166D-03 0.300000D+01 -0.119060D-03 0.673641D-04 -0.204702D-03 0.320000D+01 -0.132175D-03 0.122238D-04 -0.201597D-03 0.340000D+01 -0.118602D-03 -0.325093D-04 -0.171177D-03 0.360000D+01 -0.952656D-04 -0.593819D-04 -0.125641D-03 0.380000D+01 -0.730218D-04 -0.696739D-04 -0.770806D-04 0.400000D+01 -0.521350D-04 -0.708958D-04 -0.336750D-04 0.420000D+01 -0.302417D-04 -0.719132D-04 0.774076D-06 0.440000D+01 -0.911680D-05 -0.761141D-04 0.262669D-04 0.460000D+01 0.725113D-05 -0.808438D-04 0.442540D-04 0.480000D+01 0.168501D-04 -0.820292D-04 0.555130D-04 0.500000D+01 0.204528D-04 -0.776301D-04 0.602605D-04 0.520000D+01 0.201625D-04 -0.683582D-04 0.596721D-04 0.540000D+01 0.177324D-04 -0.565762D-04 0.561696D-04 4.1.3 Pressure Strain Correlation tau PS_11 PS_22 PS_33 0.200000D+00 0.172558D-01 0.302844D-02 -0.202843D-01 0.400000D+00 0.939482D-02 0.351463D-02 -0.129095D-01 0.600000D+00 0.519819D-02 0.184303D-02 -0.704121D-02 0.800000D+00 0.804931D-03 0.128977D-02 -0.209470D-02 0.100000D+01 -0.252345D-03 0.633174D-03 -0.380829D-03 0.120000D+01 0.184956D-03 0.424385D-03 -0.609341D-03 0.140000D+01 0.842281D-03 0.449244D-04 -0.887205D-03 0.160000D+01 0.123894D-02 -0.564298D-03 -0.674640D-03 0.180000D+01 0.109583D-02 -0.960953D-03 -0.134875D-03 0.200000D+01 0.642973D-03 -0.947676D-03 0.304703D-03 0.220000D+01 0.157351D-03 -0.846833D-03 0.689482D-03 0.240000D+01 -0.286335D-03 -0.771004D-03 0.105734D-02 0.260000D+01 -0.673728D-03 -0.683199D-03 0.135693D-02 0.280000D+01 -0.970638D-03 -0.591345D-03 0.156198D-02 0.300000D+01 -0.109332D-02 -0.514000D-03 0.160732D-02 0.320000D+01 -0.106304D-02 -0.411275D-03 0.147431D-02 0.340000D+01 -0.962391D-03 -0.261180D-03 0.122357D-02 0.360000D+01 -0.836704D-03 -0.101976D-03 0.938680D-03 0.380000D+01 -0.704832D-03 0.256347D-04 0.679198D-03 0.400000D+01 -0.589292D-03 0.121727D-03 0.467565D-03 0.420000D+01 -0.506526D-03 0.204103D-03 0.302423D-03 0.440000D+01 -0.452804D-03 0.274372D-03 0.178432D-03 0.460000D+01 -0.417362D-03 0.324779D-03 0.925837D-04 0.480000D+01 -0.394632D-03 0.350944D-03 0.436880D-04 0.500000D+01 -0.383758D-03 0.353632D-03 0.301257D-04 0.520000D+01 -0.382784D-03 0.337037D-03 0.457472D-04 0.540000D+01 -0.386045D-03 0.307145D-03 0.788998D-04 tau PS_12 PS_13 PS_23 0.200000D+00 -0.541541D-02 0.376175D-02 0.975906D-03 0.400000D+00 -0.297312D-02 -0.282849D-03 -0.330867D-03 0.600000D+00 0.883313D-04 -0.176782D-02 0.222412D-03 0.800000D+00 0.420558D-03 -0.143165D-02 0.362753D-03 0.100000D+01 -0.856349D-03 -0.618079D-04 0.132623D-02 0.120000D+01 -0.151601D-02 0.210528D-02 0.189695D-02 0.140000D+01 -0.890589D-03 0.306470D-02 0.176473D-02 0.160000D+01 0.544672D-04 0.286898D-02 0.157483D-02 0.180000D+01 0.448807D-03 0.218653D-02 0.130169D-02 0.200000D+01 0.184012D-03 0.148301D-02 0.123551D-02 0.220000D+01 -0.238029D-03 0.878528D-03 0.124482D-02 0.240000D+01 -0.449015D-03 0.414352D-03 0.122572D-02 0.260000D+01 -0.398998D-03 0.995214D-04 0.119136D-02 0.280000D+01 -0.236126D-03 -0.408321D-04 0.117651D-02 0.300000D+01 -0.634778D-04 -0.208950D-04 0.118495D-02 0.320000D+01 0.828245D-04 0.100723D-03 0.117882D-02 0.340000D+01 0.182669D-03 0.249929D-03 0.112146D-02 0.360000D+01 0.228514D-03 0.370416D-03 0.101276D-02 0.380000D+01 0.237746D-03 0.438646D-03 0.878795D-03 0.400000D+01 0.231918D-03 0.463500D-03 0.748567D-03 0.420000D+01 0.213846D-03 0.471788D-03 0.637244D-03 0.440000D+01 0.182388D-03 0.487228D-03 0.546157D-03 0.460000D+01 0.147008D-03 0.512419D-03 0.469397D-03 0.480000D+01 0.117841D-03 0.531575D-03 0.400000D-03 0.500000D+01 0.972940D-04 0.528313D-03 0.334519D-03 0.520000D+01 0.820858D-04 0.497179D-03 0.273541D-03 0.540000D+01 0.688256D-04 0.442944D-03 0.219202D-03 4.1.4 Vorticity Tensor tau OMG_11 OMG_22 OMG_33 0.200000D+00 0.402989D+02 0.393717D+02 0.377406D+02 0.400000D+00 0.308416D+02 0.309436D+02 0.300139D+02 0.600000D+00 0.232461D+02 0.234997D+02 0.230375D+02 0.800000D+00 0.178469D+02 0.181294D+02 0.178330D+02 0.100000D+01 0.140232D+02 0.142202D+02 0.139919D+02 0.120000D+01 0.112708D+02 0.113823D+02 0.112137D+02 0.140000D+01 0.920671D+01 0.926589D+01 0.915697D+01 0.160000D+01 0.762876D+01 0.763296D+01 0.757145D+01 0.180000D+01 0.639209D+01 0.635509D+01 0.634307D+01 0.200000D+01 0.540834D+01 0.535054D+01 0.538494D+01 0.220000D+01 0.462329D+01 0.455887D+01 0.461482D+01 0.240000D+01 0.399073D+01 0.392706D+01 0.398562D+01 0.260000D+01 0.347279D+01 0.341209D+01 0.346736D+01 0.280000D+01 0.304205D+01 0.298652D+01 0.303663D+01 0.300000D+01 0.268114D+01 0.263195D+01 0.267583D+01 0.320000D+01 0.237835D+01 0.233225D+01 0.237118D+01 0.340000D+01 0.212370D+01 0.207562D+01 0.211271D+01 0.360000D+01 0.190772D+01 0.185503D+01 0.189238D+01 0.380000D+01 0.172203D+01 0.166562D+01 0.170328D+01 0.400000D+01 0.156012D+01 0.150305D+01 0.154002D+01 0.420000D+01 0.141768D+01 0.136292D+01 0.139852D+01 0.440000D+01 0.129185D+01 0.124135D+01 0.127559D+01 0.460000D+01 0.118037D+01 0.113530D+01 0.116850D+01 0.480000D+01 0.108128D+01 0.104224D+01 0.107477D+01 0.500000D+01 0.992939D+00 0.960075D+00 0.992113D+00 0.520000D+01 0.914106D+00 0.887046D+00 0.918517D+00 tau OMG_12 OMG_13 OMG_23 0.200000D+00 0.121262D+00 0.718921D-01 0.961702D-01 0.400000D+00 0.119772D+00 -0.134112D+00 -0.528899D-01 0.600000D+00 0.887430D-01 -0.101413D+00 -0.652585D-01 0.800000D+00 0.121369D+00 -0.733911D-01 -0.308450D-01 0.100000D+01 0.813011D-01 -0.420279D-01 0.218231D-01 0.120000D+01 0.348209D-01 -0.419913D-01 0.479465D-01 0.140000D+01 -0.736839D-02 -0.640368D-01 0.771447D-01 0.160000D+01 -0.276412D-01 -0.770727D-01 0.881196D-01 0.180000D+01 -0.338122D-01 -0.730408D-01 0.767024D-01 0.200000D+01 -0.348214D-01 -0.640502D-01 0.563890D-01 0.220000D+01 -0.373411D-01 -0.563587D-01 0.389518D-01 0.240000D+01 -0.423883D-01 -0.506911D-01 0.297666D-01 0.260000D+01 -0.469016D-01 -0.443681D-01 0.263887D-01 0.280000D+01 -0.482908D-01 -0.349419D-01 0.268828D-01 0.300000D+01 -0.483670D-01 -0.236175D-01 0.283968D-01 0.320000D+01 -0.495733D-01 -0.135285D-01 0.290012D-01 0.340000D+01 -0.515501D-01 -0.659464D-02 0.283705D-01 0.360000D+01 -0.529951D-01 -0.308477D-02 0.268470D-01 0.380000D+01 -0.531841D-01 -0.236282D-02 0.247527D-01 0.400000D+01 -0.520572D-01 -0.330874D-02 0.223187D-01 0.420000D+01 -0.498973D-01 -0.454234D-02 0.196558D-01 0.440000D+01 -0.470376D-01 -0.516008D-02 0.168670D-01 0.460000D+01 -0.437402D-01 -0.504913D-02 0.141684D-01 0.480000D+01 -0.402674D-01 -0.441651D-02 0.118918D-01 0.500000D+01 -0.368841D-01 -0.347075D-02 0.103038D-01 0.520000D+01 -0.338119D-01 -0.241455D-02 0.937357D-02 0.540000D+01 -0.311846D-01 -0.141373D-02 0.881425D-02 4.1.5 Skewness Factor of du/dx tau SF du/dx 0.200000D+00 -0.465077D+00 0.400000D+00 -0.464715D+00 0.600000D+00 -0.469586D+00 0.800000D+00 -0.495606D+00 0.100000D+01 -0.502174D+00 0.120000D+01 -0.501206D+00 0.140000D+01 -0.507355D+00 0.160000D+01 -0.504072D+00 0.180000D+01 -0.501976D+00 0.200000D+01 -0.498927D+00 0.220000D+01 -0.490696D+00 0.240000D+01 -0.487916D+00 0.260000D+01 -0.489835D+00 0.280000D+01 -0.496655D+00 0.300000D+01 -0.510955D+00 0.320000D+01 -0.529905D+00 0.340000D+01 -0.547139D+00 0.360000D+01 -0.559776D+00 0.380000D+01 -0.567015D+00 0.400000D+01 -0.569112D+00 0.420000D+01 -0.568033D+00 0.440000D+01 -0.563190D+00 0.460000D+01 -0.552583D+00 0.480000D+01 -0.536680D+00 0.500000D+01 -0.519280D+00 0.520000D+01 -0.505168D+00 0.540000D+01 -0.496848D+00 4.1.6 Budget of Turbulent Kinetic Energy tau K D 0.200000D+00 0.400983D+00 0.391371D+00 0.400000D+00 0.331120D+00 0.305997D+00 0.600000D+00 0.277609D+00 0.232611D+00 0.800000D+00 0.236695D+00 0.179364D+00 0.100000D+01 0.204885D+00 0.140784D+00 0.120000D+01 0.179660D+00 0.112889D+00 0.140000D+01 0.159254D+00 0.920986D-01 0.160000D+01 0.142499D+00 0.761106D-01 0.180000D+01 0.128574D+00 0.636341D-01 0.200000D+01 0.116867D+00 0.538127D-01 0.220000D+01 0.106915D+00 0.459899D-01 0.240000D+01 0.983692D-01 0.396781D-01 0.260000D+01 0.909669D-01 0.345075D-01 0.280000D+01 0.845072D-01 0.302173D-01 0.300000D+01 0.788327D-01 0.266297D-01 0.320000D+01 0.738174D-01 0.236059D-01 0.340000D+01 0.693596D-01 0.210401D-01 0.360000D+01 0.653761D-01 0.188504D-01 0.380000D+01 0.617986D-01 0.169697D-01 0.400000D+01 0.585710D-01 0.153440D-01 0.420000D+01 0.556468D-01 0.139304D-01 0.440000D+01 0.529868D-01 0.126960D-01 0.460000D+01 0.505581D-01 0.116139D-01 0.480000D+01 0.483326D-01 0.106610D-01 0.500000D+01 0.462864D-01 0.981709D-02 0.520000D+01 0.443995D-01 0.906556D-02 0.540000D+01 0.426549D-01 0.839304D-02 4.1.7 Turbulent Reynolds Number tau RE_t 0.200000D+00 0.123250D+03 0.400000D+00 0.107492D+03 0.600000D+00 0.993937D+02 0.800000D+00 0.937053D+02 0.100000D+01 0.894512D+02 0.120000D+01 0.857768D+02 0.140000D+01 0.826129D+02 0.160000D+01 0.800383D+02 0.180000D+01 0.779357D+02 0.200000D+01 0.761409D+02 0.220000D+01 0.745647D+02 0.240000D+01 0.731627D+02 0.260000D+01 0.719407D+02 0.280000D+01 0.709009D+02 0.300000D+01 0.700111D+02 0.320000D+01 0.692496D+02 0.340000D+01 0.685940D+02 0.360000D+01 0.680202D+02 0.380000D+01 0.675155D+02 0.400000D+01 0.670733D+02 0.420000D+01 0.666863D+02 0.440000D+01 0.663424D+02 0.460000D+01 0.660276D+02 0.480000D+01 0.657361D+02 0.500000D+01 0.654705D+02 0.520000D+01 0.652354D+02 0.540000D+01 0.650338D+02 4.1.8 Integral Scales tau Lamda_11(x_1) Lamda_22(x_1) Lamda_33(x_1) 0.200000D+00 0.971830D+00 0.374309D+00 0.436610D+00 0.400000D+00 0.104462D+01 0.376248D+00 0.447933D+00 0.600000D+00 0.110455D+01 0.383055D+00 0.462805D+00 0.800000D+00 0.114875D+01 0.395825D+00 0.474236D+00 0.100000D+01 0.120277D+01 0.418623D+00 0.488510D+00 0.120000D+01 0.126359D+01 0.441037D+00 0.513223D+00 0.140000D+01 0.132414D+01 0.456280D+00 0.537969D+00 0.160000D+01 0.138766D+01 0.469972D+00 0.562685D+00 0.180000D+01 0.144681D+01 0.483264D+00 0.584122D+00 0.200000D+01 0.149788D+01 0.494791D+00 0.600198D+00 0.220000D+01 0.155166D+01 0.503020D+00 0.609099D+00 0.240000D+01 0.161278D+01 0.509484D+00 0.613137D+00 0.260000D+01 0.168161D+01 0.516688D+00 0.617895D+00 0.280000D+01 0.175315D+01 0.526139D+00 0.625912D+00 0.300000D+01 0.182124D+01 0.539745D+00 0.635675D+00 0.320000D+01 0.188425D+01 0.557808D+00 0.645488D+00 0.340000D+01 0.194101D+01 0.579242D+00 0.655256D+00 0.360000D+01 0.199135D+01 0.602589D+00 0.665195D+00 0.380000D+01 0.203758D+01 0.626638D+00 0.675342D+00 0.400000D+01 0.208078D+01 0.650592D+00 0.686038D+00 0.420000D+01 0.212117D+01 0.674025D+00 0.697661D+00 0.440000D+01 0.215984D+01 0.696968D+00 0.710362D+00 0.460000D+01 0.219684D+01 0.719403D+00 0.724276D+00 0.400000D+01 0.208078D+01 0.650592D+00 0.686038D+00 0.420000D+01 0.212117D+01 0.674025D+00 0.697661D+00 0.440000D+01 0.215984D+01 0.696968D+00 0.710362D+00 0.460000D+01 0.219684D+01 0.719403D+00 0.724276D+00 0.480000D+01 0.223177D+01 0.741170D+00 0.739439D+00 0.500000D+01 0.226523D+01 0.762231D+00 0.755758D+00 0.520000D+01 0.229882D+01 0.782585D+00 0.773165D+00 0.540000D+01 0.233379D+01 0.802071D+00 0.791748D+00 4.1.9 Two Point Correlations tau 0.200000D+01 x_1 R_11(x_1) R_22(x_1) R_33(x_1) 0.0 0.100000D+01 0.100000D+01 0.100000D+01 0.872665D-01 0.953697D+00 0.902615D+00 0.904112D+00 0.174533D+00 0.847016D+00 0.701823D+00 0.707167D+00 0.261799D+00 0.728578D+00 0.511418D+00 0.521312D+00 0.349066D+00 0.622669D+00 0.367243D+00 0.381835D+00 0.436332D+00 0.534935D+00 0.265430D+00 0.285408D+00 0.523599D+00 0.463812D+00 0.193891D+00 0.219163D+00 0.610865D+00 0.406161D+00 0.143027D+00 0.172155D+00 0.698132D+00 0.358873D+00 0.107048D+00 0.137875D+00 0.785398D+00 0.319238D+00 0.815245D-01 0.111609D+00 0.872665D+00 0.285221D+00 0.617122D-01 0.895554D-01 0.959931D+00 0.255525D+00 0.434259D-01 0.695791D-01 0.104720D+01 0.229415D+00 0.251190D-01 0.509140D-01 0.113446D+01 0.206622D+00 0.875518D-02 0.336233D-01 0.122173D+01 0.187114D+00 -0.270871D-02 0.174510D-01 0.130900D+01 0.170625D+00 -0.846019D-02 0.208187D-02 0.139626D+01 0.156399D+00 -0.109612D-01 -0.121706D-01 0.148353D+01 0.143562D+00 -0.141247D-01 -0.251041D-01 0.157080D+01 0.131618D+00 -0.195679D-01 -0.367206D-01 0.165806D+01 0.120458D+00 -0.258813D-01 -0.471083D-01 0.174533D+01 0.110078D+00 -0.315208D-01 -0.553145D-01 0.183260D+01 0.100506D+00 -0.362034D-01 -0.591049D-01 0.191986D+01 0.916996D-01 -0.401122D-01 -0.575314D-01 0.200713D+01 0.836187D-01 -0.436917D-01 -0.519172D-01 0.209440D+01 0.763007D-01 -0.482827D-01 -0.447026D-01 0.218166D+01 0.695128D-01 -0.551761D-01 -0.385057D-01 0.226893D+01 0.628899D-01 -0.631138D-01 -0.352284D-01 0.235619D+01 0.564170D-01 -0.695064D-01 -0.351791D-01 0.244346D+01 0.504592D-01 -0.730924D-01 -0.371090D-01 0.253073D+01 0.453977D-01 -0.743297D-01 -0.389744D-01 0.261799D+01 0.412453D-01 -0.739206D-01 -0.393076D-01 0.270526D+01 0.376233D-01 -0.723399D-01 -0.376697D-01 0.279253D+01 0.342166D-01 -0.703838D-01 -0.342098D-01 0.287979D+01 0.311418D-01 -0.693312D-01 -0.291994D-01 0.296706D+01 0.287668D-01 -0.695720D-01 -0.233298D-01 0.305433D+01 0.273495D-01 -0.703946D-01 -0.183614D-01 tau 0.500000D+01 x_1 R_11(x_1) R_22(x_1) R_33(x_1) 0.0 0.100000D+01 0.100000D+01 0.100000D+01 0.872665D-01 0.978349D+00 0.949856D+00 0.954178D+00 0.174533D+00 0.921626D+00 0.826776D+00 0.841352D+00 0.261799D+00 0.846694D+00 0.680946D+00 0.706453D+00 0.349066D+00 0.767868D+00 0.546717D+00 0.579553D+00 0.436332D+00 0.693385D+00 0.437210D+00 0.471965D+00 0.523599D+00 0.626654D+00 0.352407D+00 0.384489D+00 0.610865D+00 0.568293D+00 0.286859D+00 0.314050D+00 0.698132D+00 0.517634D+00 0.234460D+00 0.256888D+00 0.785398D+00 0.473601D+00 0.190557D+00 0.209520D+00 0.872665D+00 0.435194D+00 0.152356D+00 0.169139D+00 0.959931D+00 0.401673D+00 0.118529D+00 0.133836D+00 0.104720D+01 0.372511D+00 0.887857D-01 0.102464D+00 0.113446D+01 0.347250D+00 0.634139D-01 0.743790D-01 0.122173D+01 0.325379D+00 0.425895D-01 0.491982D-01 0.130900D+01 0.306317D+00 0.257008D-01 0.266006D-01 0.139626D+01 0.289511D+00 0.112332D-01 0.636077D-02 0.148353D+01 0.274499D+00 -0.237697D-02 -0.115842D-01 0.157080D+01 0.260862D+00 -0.157371D-01 -0.273319D-01 0.165806D+01 0.248197D+00 -0.284069D-01 -0.412851D-01 0.174533D+01 0.236182D+00 -0.396720D-01 -0.540498D-01 0.183260D+01 0.224644D+00 -0.494071D-01 -0.658219D-01 0.191986D+01 0.213571D+00 -0.582645D-01 -0.761477D-01 0.200713D+01 0.203048D+00 -0.670459D-01 -0.844621D-01 0.209440D+01 0.193206D+00 -0.757945D-01 -0.905950D-01 0.218166D+01 0.184199D+00 -0.833362D-01 -0.946007D-01 0.226893D+01 0.176133D+00 -0.878839D-01 -0.963891D-01 0.235619D+01 0.168976D+00 -0.883098D-01 -0.959369D-01 0.244346D+01 0.162532D+00 -0.848450D-01 -0.936484D-01 0.253073D+01 0.156545D+00 -0.788689D-01 -0.902261D-01 0.261799D+01 0.150868D+00 -0.721485D-01 -0.863825D-01 0.270526D+01 0.145548D+00 -0.659740D-01 -0.828668D-01 0.279253D+01 0.140749D+00 -0.607143D-01 -0.804476D-01 0.287979D+01 0.136664D+00 -0.561784D-01 -0.794337D-01 0.296706D+01 0.133515D+00 -0.523345D-01 -0.794115D-01 0.305433D+01 0.131527D+00 -0.495713D-01 -0.797061D-01 4.1.10 One Dimensional Energy Spectrum tau 0.200000D+01 k_1 E_11(k_1) E_22(k_1) E_33(k_1) 0.0 0.192310D-01 0.600895D-02 0.733237D-02 0.100000D+01 0.121342D-01 0.936378D-02 0.911251D-02 0.200000D+01 0.606879D-02 0.616955D-02 0.693242D-02 0.300000D+01 0.395981D-02 0.469352D-02 0.413791D-02 0.400000D+01 0.253308D-02 0.364989D-02 0.315944D-02 0.500000D+01 0.172223D-02 0.254153D-02 0.267859D-02 0.600000D+01 0.119746D-02 0.207528D-02 0.218392D-02 0.700000D+01 0.867264D-03 0.160254D-02 0.139127D-02 0.800000D+01 0.620902D-03 0.120118D-02 0.126627D-02 0.900000D+01 0.444322D-03 0.943704D-03 0.904558D-03 0.100000D+02 0.298311D-03 0.607903D-03 0.652211D-03 0.110000D+02 0.223637D-03 0.484502D-03 0.522817D-03 0.120000D+02 0.165507D-03 0.419388D-03 0.413094D-03 0.130000D+02 0.121270D-03 0.333531D-03 0.295915D-03 0.140000D+02 0.933870D-04 0.242139D-03 0.238609D-03 0.150000D+02 0.637882D-04 0.183079D-03 0.181733D-03 0.160000D+02 0.498238D-04 0.129684D-03 0.142752D-03 0.170000D+02 0.375819D-04 0.108776D-03 0.103132D-03 0.180000D+02 0.279542D-04 0.875901D-04 0.803613D-04 0.190000D+02 0.209531D-04 0.619624D-04 0.649358D-04 0.200000D+02 0.157017D-04 0.512073D-04 0.507666D-04 0.210000D+02 0.117202D-04 0.412641D-04 0.396920D-04 0.220000D+02 0.908879D-05 0.317404D-04 0.320671D-04 0.230000D+02 0.720334D-05 0.248505D-04 0.261052D-04 0.240000D+02 0.538086D-05 0.198450D-04 0.201919D-04 0.250000D+02 0.411121D-05 0.155597D-04 0.160984D-04 0.260000D+02 0.333404D-05 0.125551D-04 0.131705D-04 0.270000D+02 0.252805D-05 0.101134D-04 0.105297D-04 0.280000D+02 0.194391D-05 0.764347D-05 0.785620D-05 0.290000D+02 0.156239D-05 0.631440D-05 0.633728D-05 0.300000D+02 0.124004D-05 0.510911D-05 0.516718D-05 0.310000D+02 0.959129D-06 0.415982D-05 0.429354D-05 0.320000D+02 0.754952D-06 0.332943D-05 0.342903D-05 0.330000D+02 0.622765D-06 0.280130D-05 0.275858D-05 0.340000D+02 0.482260D-06 0.221884D-05 0.225145D-05 0.350000D+02 0.388155D-06 0.172558D-05 0.186206D-05 0.360000D+02 0.303891D-06 0.151612D-05 0.146320D-05 0.370000D+02 0.246401D-06 0.122084D-05 0.120806D-05 0.380000D+02 0.201293D-06 0.987027D-06 0.970057D-06 0.390000D+02 0.162523D-06 0.828495D-06 0.813530D-06 0.400000D+02 0.137379D-06 0.662746D-06 0.694198D-06 0.410000D+02 0.109063D-06 0.570307D-06 0.565045D-06 0.420000D+02 0.945059D-07 0.498183D-06 0.493004D-06 0.430000D+02 0.842964D-07 0.436437D-06 0.448064D-06 0.440000D+02 0.731338D-07 0.406494D-06 0.393376D-06 0.450000D+02 0.661049D-07 0.361888D-06 0.368075D-06 0.460000D+02 0.625916D-07 0.359944D-06 0.366070D-06 0.470000D+02 0.565654D-07 0.358896D-06 0.353871D-06 tau 0.500000D+01 k_1 E_11(k_1) E_22(k_1) E_33(k_1) 0.0 0.117243D-01 0.345998D-02 0.379269D-02 0.100000D+01 0.503655D-02 0.452078D-02 0.536693D-02 0.200000D+01 0.217363D-02 0.281824D-02 0.317065D-02 0.300000D+01 0.131156D-02 0.149607D-02 0.162957D-02 0.400000D+01 0.728829D-03 0.121260D-02 0.120010D-02 0.500000D+01 0.430952D-03 0.720180D-03 0.797684D-03 0.600000D+01 0.249709D-03 0.526271D-03 0.521367D-03 0.700000D+01 0.173656D-03 0.401649D-03 0.390491D-03 0.800000D+01 0.105186D-03 0.261076D-03 0.243029D-03 0.900000D+01 0.660227D-04 0.193674D-03 0.170983D-03 0.100000D+02 0.430612D-04 0.125436D-03 0.113234D-03 0.110000D+02 0.262617D-04 0.692004D-04 0.814792D-04 0.120000D+02 0.171096D-04 0.593170D-04 0.542830D-04 0.130000D+02 0.113800D-04 0.391162D-04 0.373020D-04 0.140000D+02 0.754613D-05 0.254472D-04 0.273977D-04 0.150000D+02 0.539320D-05 0.172099D-04 0.194655D-04 0.160000D+02 0.342758D-05 0.123711D-04 0.129174D-04 0.170000D+02 0.227897D-05 0.879836D-05 0.876229D-05 0.180000D+02 0.163844D-05 0.645223D-05 0.707857D-05 0.190000D+02 0.109499D-05 0.459048D-05 0.447978D-05 0.200000D+02 0.791212D-06 0.319931D-05 0.328143D-05 0.210000D+02 0.519581D-06 0.237732D-05 0.242545D-05 0.220000D+02 0.385502D-06 0.175786D-05 0.172892D-05 0.230000D+02 0.262096D-06 0.123205D-05 0.129771D-05 0.240000D+02 0.197890D-06 0.951145D-06 0.927923D-06 0.250000D+02 0.139990D-06 0.655573D-06 0.697805D-06 0.260000D+02 0.972807D-07 0.505579D-06 0.490737D-06 0.270000D+02 0.698578D-07 0.370792D-06 0.360332D-06 0.280000D+02 0.507123D-07 0.285124D-06 0.250663D-06 0.290000D+02 0.372126D-07 0.193561D-06 0.193622D-06 0.300000D+02 0.264424D-07 0.150280D-06 0.144315D-06 0.310000D+02 0.192967D-07 0.107988D-06 0.100172D-06 0.320000D+02 0.141061D-07 0.819430D-07 0.741916D-07 0.330000D+02 0.103257D-07 0.637519D-07 0.560303D-07 0.340000D+02 0.783349D-08 0.466426D-07 0.427260D-07 0.350000D+02 0.560577D-08 0.357159D-07 0.312569D-07 0.360000D+02 0.423584D-08 0.262749D-07 0.241826D-07 0.370000D+02 0.315377D-08 0.197840D-07 0.178542D-07 0.380000D+02 0.228915D-08 0.145361D-07 0.135483D-07 0.390000D+02 0.173265D-08 0.114200D-07 0.100246D-07 0.400000D+02 0.125768D-08 0.817590D-08 0.749084D-08 0.410000D+02 0.964661D-09 0.657238D-08 0.606024D-08 0.420000D+02 0.728554D-09 0.490014D-08 0.455115D-08 0.430000D+02 0.550233D-09 0.382801D-08 0.346692D-08 0.440000D+02 0.430063D-09 0.307919D-08 0.280015D-08 0.450000D+02 0.379207D-09 0.262843D-08 0.239803D-08 0.460000D+02 0.328865D-09 0.252361D-08 0.216663D-08 0.470000D+02 0.302189D-09 0.236831D-08 0.214624D-08 4.2 Thermal Field 4.2.1 Pr=0.71 Without Initial Temperature Fluctuations 4.2.1.1 Temperature Variance and Heat Flux tau tt vt 0.200000D+00 0.101079D-01 0.496246D-01 0.400000D+00 0.301417D-01 0.736427D-01 0.600000D+00 0.523198D-01 0.851810D-01 0.800000D+00 0.742285D-01 0.911545D-01 0.100000D+01 0.953365D-01 0.943699D-01 0.120000D+01 0.115505D+00 0.960929D-01 0.140000D+01 0.134752D+00 0.969552D-01 0.160000D+01 0.153189D+00 0.971480D-01 0.180000D+01 0.170875D+00 0.968320D-01 0.200000D+01 0.187801D+00 0.962241D-01 0.220000D+01 0.204029D+00 0.954937D-01 0.240000D+01 0.219694D+00 0.946840D-01 0.260000D+01 0.234892D+00 0.937942D-01 0.280000D+01 0.249656D+00 0.928567D-01 0.300000D+01 0.264015D+00 0.919192D-01 0.320000D+01 0.278025D+00 0.910155D-01 0.340000D+01 0.291769D+00 0.901631D-01 0.360000D+01 0.305332D+00 0.893664D-01 0.380000D+01 0.318759D+00 0.886197D-01 0.400000D+01 0.332046D+00 0.879144D-01 0.420000D+01 0.345169D+00 0.872474D-01 0.440000D+01 0.358104D+00 0.866221D-01 0.460000D+01 0.370853D+00 0.860436D-01 0.480000D+01 0.383446D+00 0.855147D-01 0.500000D+01 0.395940D+00 0.850328D-01 0.520000D+01 0.408393D+00 0.845888D-01 0.540000D+01 0.420844D+00 0.841685D-01 4.2.1.2 vt Budget tau P_vt fai_vt D_vt 0.200000D+00 0.263467D+00 -0.391314D-01 0.537244D-01 0.400000D+00 0.217766D+00 -0.716120D-01 0.661521D-01 0.600000D+00 0.182805D+00 -0.799650D-01 0.632050D-01 0.800000D+00 0.156073D+00 -0.773858D-01 0.576288D-01 0.100000D+01 0.135236D+00 -0.718619D-01 0.522984D-01 0.120000D+01 0.118613D+00 -0.650367D-01 0.477588D-01 0.140000D+01 0.105073D+00 -0.588669D-01 0.439921D-01 0.160000D+01 0.938294D-01 -0.539135D-01 0.406371D-01 0.180000D+01 0.843484D-01 -0.494723D-01 0.375938D-01 0.200000D+01 0.763056D-01 -0.450575D-01 0.348779D-01 0.220000D+01 0.694457D-01 -0.409293D-01 0.325363D-01 0.240000D+01 0.635411D-01 -0.374747D-01 0.304705D-01 0.260000D+01 0.584201D-01 -0.345767D-01 0.285774D-01 0.280000D+01 0.539546D-01 -0.319966D-01 0.267909D-01 0.300000D+01 0.500393D-01 -0.296673D-01 0.250917D-01 0.320000D+01 0.465907D-01 -0.275669D-01 0.235083D-01 0.340000D+01 0.435484D-01 -0.256769D-01 0.220693D-01 0.360000D+01 0.408608D-01 -0.240079D-01 0.207712D-01 0.380000D+01 0.384766D-01 -0.225621D-01 0.195979D-01 0.400000D+01 0.363499D-01 -0.212957D-01 0.185382D-01 0.420000D+01 0.344453D-01 -0.201494D-01 0.175784D-01 0.440000D+01 0.327350D-01 -0.190890D-01 0.167029D-01 0.460000D+01 0.311934D-01 -0.181006D-01 0.159015D-01 0.480000D+01 0.297961D-01 -0.171845D-01 0.151701D-01 0.500000D+01 0.285212D-01 -0.163542D-01 0.145053D-01 0.520000D+01 0.273497D-01 -0.156272D-01 0.139014D-01 0.540000D+01 0.262663D-01 -0.150123D-01 0.133511D-01 4.2.1.3 tt Budget tau P_tt D_tt 0.200000D+00 0.992492D-01 0.139296D-01 0.400000D+00 0.147285D+00 0.385136D-01 0.600000D+00 0.170362D+00 0.594082D-01 0.800000D+00 0.182309D+00 0.747256D-01 0.100000D+01 0.188740D+00 0.855654D-01 0.120000D+01 0.192186D+00 0.937888D-01 0.140000D+01 0.193910D+00 0.998410D-01 0.160000D+01 0.194296D+00 0.104019D+00 0.180000D+01 0.193664D+00 0.107161D+00 0.200000D+01 0.192448D+00 0.109687D+00 0.220000D+01 0.190987D+00 0.111380D+00 0.240000D+01 0.189368D+00 0.112273D+00 0.260000D+01 0.187588D+00 0.112709D+00 0.280000D+01 0.185713D+00 0.112948D+00 0.300000D+01 0.183838D+00 0.112984D+00 0.320000D+01 0.182031D+00 0.112727D+00 0.340000D+01 0.180326D+00 0.112124D+00 0.360000D+01 0.178733D+00 0.111280D+00 0.380000D+01 0.177239D+00 0.110441D+00 0.400000D+01 0.175829D+00 0.109784D+00 0.420000D+01 0.174495D+00 0.109340D+00 0.440000D+01 0.173244D+00 0.109048D+00 0.460000D+01 0.172087D+00 0.108774D+00 0.480000D+01 0.171029D+00 0.108366D+00 0.500000D+01 0.170066D+00 0.107744D+00 0.520000D+01 0.169178D+00 0.106940D+00 0.540000D+01 0.168337D+00 0.106058D+00 4.2.1.4 Thermal Integreal Scale tau Lamda_tt(x_1) 0.200000D+00 0.379771D+00 0.400000D+00 0.399920D+00 0.600000D+00 0.424845D+00 0.800000D+00 0.454236D+00 0.100000D+01 0.487015D+00 0.120000D+01 0.516698D+00 0.140000D+01 0.540935D+00 0.160000D+01 0.567490D+00 0.180000D+01 0.597852D+00 0.200000D+01 0.628418D+00 0.220000D+01 0.653510D+00 0.240000D+01 0.673721D+00 0.260000D+01 0.688843D+00 0.280000D+01 0.699703D+00 0.300000D+01 0.709970D+00 0.320000D+01 0.723209D+00 0.340000D+01 0.739802D+00 0.360000D+01 0.758035D+00 0.380000D+01 0.775975D+00 0.400000D+01 0.792959D+00 0.420000D+01 0.809147D+00 0.440000D+01 0.824508D+00 0.460000D+01 0.839352D+00 0.480000D+01 0.854490D+00 0.500000D+01 0.870726D+00 0.520000D+01 0.888649D+00 0.540000D+01 0.908467D+00 4.2.1.5 Thermal Two Point Correlation tau = 0.200000D+01 x_1 R_tt(x_1) 0.0 0.100000D+01 0.872665D-01 0.930882D+00 0.174533D+00 0.783930D+00 0.261799D+00 0.632776D+00 0.349066D+00 0.503228D+00 0.436332D+00 0.398893D+00 0.523599D+00 0.317131D+00 0.610865D+00 0.253498D+00 0.698132D+00 0.203400D+00 0.785398D+00 0.162670D+00 0.872665D+00 0.127735D+00 0.959931D+00 0.967278D-01 0.104720D+01 0.696860D-01 0.113446D+01 0.468592D-01 0.122173D+01 0.281884D-01 0.130900D+01 0.136378D-01 0.139626D+01 0.217270D-02 0.148353D+01 -0.821961D-02 0.157080D+01 -0.190580D-01 0.165806D+01 -0.304937D-01 0.174533D+01 -0.416665D-01 0.183260D+01 -0.516029D-01 0.191986D+01 -0.598716D-01 0.200713D+01 -0.670553D-01 0.209440D+01 -0.740290D-01 0.218166D+01 -0.808889D-01 0.226893D+01 -0.871273D-01 0.235619D+01 -0.921305D-01 0.244346D+01 -0.956028D-01 0.253073D+01 -0.979693D-01 0.261799D+01 -0.998463D-01 0.270526D+01 -0.101499D+00 0.279253D+01 -0.102818D+00 0.287979D+01 -0.103526D+00 0.296706D+01 -0.103427D+00 0.305433D+01 -0.102797D+00 tau = 0.500000D+01 x_1 R_tt(x_1) 0.0 0.100000D+01 0.872665D-01 0.966129D+00 0.174533D+00 0.881730D+00 0.261799D+00 0.777706D+00 0.349066D+00 0.674740D+00 0.436332D+00 0.581483D+00 0.523599D+00 0.499835D+00 0.610865D+00 0.428755D+00 0.698132D+00 0.366199D+00 0.785398D+00 0.310188D+00 0.872665D+00 0.259407D+00 0.959931D+00 0.213339D+00 0.104720D+01 0.172040D+00 0.113446D+01 0.135649D+00 0.122173D+01 0.103867D+00 0.130900D+01 0.757960D-01 0.139626D+01 0.502401D-01 0.148353D+01 0.262358D-01 0.157080D+01 0.332977D-02 0.165806D+01 -0.184730D-01 0.174533D+01 -0.389530D-01 0.183260D+01 -0.579590D-01 0.191986D+01 -0.754142D-01 0.200713D+01 -0.911767D-01 0.209440D+01 -0.105003D+00 0.218166D+01 -0.116598D+00 0.226893D+01 -0.125747D+00 0.235619D+01 -0.132496D+00 0.244346D+01 -0.137256D+00 0.253073D+01 -0.140782D+00 0.261799D+01 -0.143980D+00 0.270526D+01 -0.147533D+00 0.279253D+01 -0.151510D+00 0.287979D+01 -0.155379D+00 0.296706D+01 -0.158493D+00 0.305433D+01 -0.160458D+00 4.2.1.6 One Dimensinal Energy Spectrum tau 0.200000D+01 k_1 E_tt(k_1) 0.0 0.187830D-01 0.100000D+01 0.295465D-01 0.200000D+01 0.166656D-01 0.300000D+01 0.108988D-01 0.400000D+01 0.770154D-02 0.500000D+01 0.513460D-02 0.600000D+01 0.371022D-02 0.700000D+01 0.277262D-02 0.800000D+01 0.208993D-02 0.900000D+01 0.148770D-02 0.100000D+02 0.101179D-02 0.110000D+02 0.725717D-03 0.120000D+02 0.629862D-03 0.130000D+02 0.456894D-03 0.140000D+02 0.350628D-03 0.150000D+02 0.276731D-03 0.160000D+02 0.221259D-03 0.170000D+02 0.169591D-03 0.180000D+02 0.133003D-03 0.190000D+02 0.101854D-03 0.200000D+02 0.826749D-04 0.210000D+02 0.672730D-04 0.220000D+02 0.562536D-04 0.230000D+02 0.433510D-04 0.240000D+02 0.333950D-04 0.250000D+02 0.266516D-04 0.260000D+02 0.211194D-04 0.270000D+02 0.171597D-04 0.280000D+02 0.143615D-04 0.290000D+02 0.114554D-04 0.300000D+02 0.908496D-05 0.310000D+02 0.753359D-05 0.320000D+02 0.610763D-05 0.330000D+02 0.505930D-05 0.340000D+02 0.407499D-05 0.350000D+02 0.328292D-05 0.360000D+02 0.272306D-05 0.370000D+02 0.226978D-05 0.380000D+02 0.180054D-05 0.390000D+02 0.152207D-05 0.400000D+02 0.123773D-05 0.410000D+02 0.104400D-05 0.420000D+02 0.911044D-06 0.430000D+02 0.803190D-06 0.440000D+02 0.715262D-06 0.450000D+02 0.676462D-06 0.460000D+02 0.636544D-06 0.470000D+02 0.597816D-06 tau 0.500000D+01 k_1 E_tt(k_1) 0.0 0.548695D-01 0.100000D+01 0.833126D-01 0.200000D+01 0.357462D-01 0.300000D+01 0.183085D-01 0.400000D+01 0.116368D-01 0.500000D+01 0.718628D-02 0.600000D+01 0.413906D-02 0.700000D+01 0.334212D-02 0.800000D+01 0.215786D-02 0.900000D+01 0.153430D-02 0.100000D+02 0.983704D-03 0.110000D+02 0.597599D-03 0.120000D+02 0.458457D-03 0.130000D+02 0.316181D-03 0.140000D+02 0.236984D-03 0.150000D+02 0.158702D-03 0.160000D+02 0.115634D-03 0.170000D+02 0.832773D-04 0.180000D+02 0.593887D-04 0.190000D+02 0.440866D-04 0.200000D+02 0.311475D-04 0.210000D+02 0.233483D-04 0.220000D+02 0.162276D-04 0.230000D+02 0.122242D-04 0.240000D+02 0.909001D-05 0.250000D+02 0.661242D-05 0.260000D+02 0.485306D-05 0.270000D+02 0.362090D-05 0.280000D+02 0.279731D-05 0.290000D+02 0.198051D-05 0.300000D+02 0.146540D-05 0.310000D+02 0.107645D-05 0.320000D+02 0.818283D-06 0.330000D+02 0.610250D-06 0.340000D+02 0.432283D-06 0.350000D+02 0.329764D-06 0.360000D+02 0.250814D-06 0.370000D+02 0.181960D-06 0.380000D+02 0.137855D-06 0.390000D+02 0.103102D-06 0.400000D+02 0.780351D-07 0.410000D+02 0.602080D-07 0.420000D+02 0.439553D-07 0.430000D+02 0.341441D-07 0.440000D+02 0.274260D-07 0.450000D+02 0.233804D-07 0.460000D+02 0.204045D-07 0.470000D+02 0.192816D-07 4.2.2 Pr=0.71 With Initial Temperature Fluctuations 4.2.2.1 Temperature Variance and Heat Flux tau tt vt 0.200000D+00 0.731224D+00 0.384283D-01 0.400000D+00 0.541246D+00 0.636461D-01 0.600000D+00 0.422320D+00 0.747979D-01 0.800000D+00 0.350988D+00 0.809139D-01 0.100000D+01 0.308802D+00 0.851098D-01 0.120000D+01 0.285074D+00 0.882324D-01 0.140000D+01 0.273046D+00 0.904143D-01 0.160000D+01 0.268409D+00 0.915546D-01 0.180000D+01 0.268455D+00 0.918206D-01 0.200000D+01 0.271417D+00 0.915385D-01 0.220000D+01 0.276138D+00 0.909991D-01 0.240000D+01 0.282002D+00 0.903136D-01 0.260000D+01 0.288738D+00 0.895058D-01 0.280000D+01 0.296177D+00 0.886205D-01 0.300000D+01 0.304163D+00 0.877195D-01 0.320000D+01 0.312571D+00 0.868513D-01 0.340000D+01 0.321331D+00 0.860438D-01 0.360000D+01 0.330419D+00 0.853070D-01 0.380000D+01 0.339799D+00 0.846360D-01 0.400000D+01 0.349408D+00 0.840200D-01 0.420000D+01 0.359181D+00 0.834539D-01 0.440000D+01 0.369067D+00 0.829392D-01 0.460000D+01 0.379041D+00 0.824791D-01 0.480000D+01 0.389109D+00 0.820742D-01 0.500000D+01 0.399303D+00 0.817192D-01 0.520000D+01 0.409654D+00 0.814029D-01 0.540000D+01 0.420182D+00 0.811099D-01 4.2.2.2 vt Budget tau P_vt phi_vt D_vt 0.200000D+00 0.263467D+00 -0.312295D-01 0.471879D-01 0.400000D+00 0.217766D+00 -0.733931D-01 0.643566D-01 0.600000D+00 0.182805D+00 -0.834750D-01 0.615161D-01 0.800000D+00 0.156073D+00 -0.766748D-01 0.551707D-01 0.100000D+01 0.135236D+00 -0.680948D-01 0.497780D-01 0.120000D+01 0.118613D+00 -0.596998D-01 0.458812D-01 0.140000D+01 0.105073D+00 -0.541694D-01 0.429288D-01 0.160000D+01 0.938294D-01 -0.507443D-01 0.400360D-01 0.180000D+01 0.843484D-01 -0.477584D-01 0.371434D-01 0.200000D+01 0.763056D-01 -0.443261D-01 0.343960D-01 0.220000D+01 0.694457D-01 -0.406570D-01 0.320504D-01 0.240000D+01 0.635411D-01 -0.373607D-01 0.300799D-01 0.260000D+01 0.584201D-01 -0.345366D-01 0.282930D-01 0.280000D+01 0.539546D-01 -0.320053D-01 0.265744D-01 0.300000D+01 0.500393D-01 -0.296820D-01 0.249089D-01 0.320000D+01 0.465907D-01 -0.275321D-01 0.233491D-01 0.340000D+01 0.435484D-01 -0.255537D-01 0.219331D-01 0.360000D+01 0.408608D-01 -0.237879D-01 0.206511D-01 0.380000D+01 0.384766D-01 -0.222581D-01 0.194868D-01 0.400000D+01 0.363499D-01 -0.209231D-01 0.184339D-01 0.420000D+01 0.344453D-01 -0.197170D-01 0.174813D-01 0.440000D+01 0.327350D-01 -0.186033D-01 0.166145D-01 0.460000D+01 0.311934D-01 -0.175707D-01 0.158237D-01 0.480000D+01 0.297961D-01 -0.166214D-01 0.151047D-01 0.500000D+01 0.285212D-01 -0.157694D-01 0.144527D-01 0.520000D+01 0.273497D-01 -0.150305D-01 0.138600D-01 0.540000D+01 0.262663D-01 -0.144110D-01 0.133179D-01 4.2.2.3 tt Budget tau P_tt D_tt 0.200000D+00 0.768565D-01 0.121471D+01 0.400000D+00 0.127292D+00 0.886982D+00 0.600000D+00 0.149596D+00 0.606753D+00 0.800000D+00 0.161828D+00 0.434663D+00 0.100000D+01 0.170220D+00 0.328356D+00 0.120000D+01 0.176465D+00 0.261483D+00 0.140000D+01 0.180829D+00 0.219761D+00 0.160000D+01 0.183109D+00 0.192841D+00 0.180000D+01 0.183641D+00 0.174957D+00 0.200000D+01 0.183077D+00 0.163160D+00 0.220000D+01 0.181998D+00 0.155237D+00 0.240000D+01 0.180627D+00 0.148989D+00 0.260000D+01 0.179012D+00 0.143447D+00 0.280000D+01 0.177241D+00 0.138568D+00 0.300000D+01 0.175439D+00 0.134374D+00 0.320000D+01 0.173703D+00 0.130759D+00 0.340000D+01 0.172088D+00 0.127458D+00 0.360000D+01 0.170614D+00 0.124405D+00 0.380000D+01 0.169272D+00 0.121744D+00 0.400000D+01 0.168040D+00 0.119537D+00 0.420000D+01 0.166908D+00 0.117732D+00 0.440000D+01 0.165878D+00 0.116224D+00 0.460000D+01 0.164958D+00 0.114872D+00 0.480000D+01 0.164148D+00 0.113526D+00 0.500000D+01 0.163438D+00 0.112103D+00 0.520000D+01 0.162806D+00 0.110614D+00 0.540000D+01 0.162220D+00 0.109140D+00 4.2.2.4 Thermal Integral scale tau Lamda_tt(x_1) 0.200000D+00 0.602171D+00 0.400000D+00 0.626168D+00 0.600000D+00 0.628967D+00 0.800000D+00 0.624814D+00 0.100000D+01 0.618943D+00 0.120000D+01 0.613361D+00 0.140000D+01 0.602031D+00 0.160000D+01 0.596568D+00 0.180000D+01 0.599008D+00 0.200000D+01 0.599850D+00 0.220000D+01 0.598473D+00 0.240000D+01 0.598778D+00 0.260000D+01 0.600890D+00 0.280000D+01 0.602770D+00 0.300000D+01 0.605653D+00 0.320000D+01 0.613520D+00 0.340000D+01 0.626698D+00 0.360000D+01 0.643041D+00 0.380000D+01 0.660317D+00 0.400000D+01 0.677341D+00 0.420000D+01 0.694102D+00 0.440000D+01 0.710443D+00 0.460000D+01 0.726176D+00 0.480000D+01 0.741692D+00 0.500000D+01 0.757787D+00 0.520000D+01 0.775254D+00 0.540000D+01 0.794563D+00 4.2.2.5 Thermal Two Point Correlation tau 0.200000D+01 x_1 R_tt(x_1) 0.0 0.100000D+01 0.872665D-01 0.928873D+00 0.174533D+00 0.781891D+00 0.261799D+00 0.636672D+00 0.349066D+00 0.516339D+00 0.436332D+00 0.420702D+00 0.523599D+00 0.344625D+00 0.610865D+00 0.283237D+00 0.698132D+00 0.232844D+00 0.785398D+00 0.190654D+00 0.872665D+00 0.154916D+00 0.959931D+00 0.124768D+00 0.104720D+01 0.995990D-01 0.113446D+01 0.788366D-01 0.122173D+01 0.621403D-01 0.130900D+01 0.488866D-01 0.139626D+01 0.371674D-01 0.148353D+01 0.245555D-01 0.157080D+01 0.971955D-02 0.165806D+01 -0.728442D-02 0.174533D+01 -0.254472D-01 0.183260D+01 -0.438874D-01 0.191986D+01 -0.621206D-01 0.200713D+01 -0.799623D-01 0.209440D+01 -0.974267D-01 0.218166D+01 -0.114060D+00 0.226893D+01 -0.129093D+00 0.235619D+01 -0.141331D+00 0.244346D+01 -0.149967D+00 0.253073D+01 -0.155564D+00 0.261799D+01 -0.158929D+00 0.270526D+01 -0.160676D+00 0.279253D+01 -0.161074D+00 0.287979D+01 -0.159980D+00 0.296706D+01 -0.158059D+00 0.305433D+01 -0.156605D+00 tau 0.500000D+01 x_1 R_tt(x_1) 0.0 0.100000D+01 0.872665D-01 0.964568D+00 0.174533D+00 0.876557D+00 0.261799D+00 0.768662D+00 0.349066D+00 0.662641D+00 0.436332D+00 0.567555D+00 0.523599D+00 0.485315D+00 0.610865D+00 0.414616D+00 0.698132D+00 0.353045D+00 0.785398D+00 0.298323D+00 0.872665D+00 0.248970D+00 0.959931D+00 0.204383D+00 0.104720D+01 0.164500D+00 0.113446D+01 0.129212D+00 0.122173D+01 0.979254D-01 0.130900D+01 0.695749D-01 0.139626D+01 0.430314D-01 0.148353D+01 0.175869D-01 0.157080D+01 -0.691911D-02 0.165806D+01 -0.303215D-01 0.174533D+01 -0.524221D-01 0.183260D+01 -0.731860D-01 0.191986D+01 -0.926438D-01 0.200713D+01 -0.110708D+00 0.209440D+01 -0.127107D+00 0.218166D+01 -0.141403D+00 0.226893D+01 -0.153128D+00 0.235619D+01 -0.162077D+00 0.244346D+01 -0.168555D+00 0.253073D+01 -0.173387D+00 0.261799D+01 -0.177641D+00 0.270526D+01 -0.182159D+00 0.279253D+01 -0.187099D+00 0.287979D+01 -0.191918D+00 0.296706D+01 -0.195877D+00 0.305433D+01 -0.198447D+00 4.2.2.6 One Dimensional Energy Spectrum tau 0.200000D+01 k_1 E_tt(k_1) 0.0 0.259119D-01 0.100000D+01 0.483040D-01 0.200000D+01 0.205154D-01 0.300000D+01 0.144268D-01 0.400000D+01 0.118112D-01 0.500000D+01 0.662795D-02 0.600000D+01 0.493813D-02 0.700000D+01 0.375731D-02 0.800000D+01 0.295188D-02 0.900000D+01 0.221785D-02 0.100000D+02 0.158506D-02 0.110000D+02 0.116071D-02 0.120000D+02 0.996293D-03 0.130000D+02 0.738994D-03 0.140000D+02 0.564465D-03 0.150000D+02 0.441908D-03 0.160000D+02 0.342325D-03 0.170000D+02 0.286640D-03 0.180000D+02 0.217702D-03 0.190000D+02 0.172474D-03 0.200000D+02 0.133132D-03 0.210000D+02 0.109809D-03 0.220000D+02 0.860563D-04 0.230000D+02 0.731100D-04 0.240000D+02 0.550220D-04 0.250000D+02 0.457322D-04 0.260000D+02 0.357890D-04 0.270000D+02 0.286487D-04 0.280000D+02 0.247834D-04 0.290000D+02 0.186121D-04 0.300000D+02 0.150689D-04 0.310000D+02 0.128510D-04 0.320000D+02 0.102757D-04 0.330000D+02 0.842030D-05 0.340000D+02 0.692500D-05 0.350000D+02 0.556426D-05 0.360000D+02 0.460075D-05 0.370000D+02 0.383740D-05 0.380000D+02 0.300425D-05 0.390000D+02 0.246474D-05 0.400000D+02 0.212074D-05 0.410000D+02 0.178200D-05 0.420000D+02 0.155031D-05 0.430000D+02 0.135239D-05 0.440000D+02 0.118945D-05 0.450000D+02 0.108799D-05 0.460000D+02 0.108556D-05 0.470000D+02 0.101796D-05 tau 0.500000D+01 k_1 E_tt(k_1) 0.0 0.481581D-01 0.100000D+01 0.868262D-01 0.200000D+01 0.347494D-01 0.300000D+01 0.186310D-01 0.400000D+01 0.123150D-01 0.500000D+01 0.767986D-02 0.600000D+01 0.449166D-02 0.700000D+01 0.358179D-02 0.800000D+01 0.222344D-02 0.900000D+01 0.166808D-02 0.100000D+02 0.107216D-02 0.110000D+02 0.641879D-03 0.120000D+02 0.483879D-03 0.130000D+02 0.331148D-03 0.140000D+02 0.251225D-03 0.150000D+02 0.172167D-03 0.160000D+02 0.123492D-03 0.170000D+02 0.896850D-04 0.180000D+02 0.644156D-04 0.190000D+02 0.476097D-04 0.200000D+02 0.337002D-04 0.210000D+02 0.255443D-04 0.220000D+02 0.177693D-04 0.230000D+02 0.134772D-04 0.240000D+02 0.986120D-05 0.250000D+02 0.721562D-05 0.260000D+02 0.528065D-05 0.270000D+02 0.394960D-05 0.280000D+02 0.305277D-05 0.290000D+02 0.215292D-05 0.300000D+02 0.158838D-05 0.310000D+02 0.116034D-05 0.320000D+02 0.878117D-06 0.330000D+02 0.661067D-06 0.340000D+02 0.470818D-06 0.350000D+02 0.361340D-06 0.360000D+02 0.269783D-06 0.370000D+02 0.198215D-06 0.380000D+02 0.149421D-06 0.390000D+02 0.111082D-06 0.400000D+02 0.844339D-07 0.410000D+02 0.658548D-07 0.420000D+02 0.473380D-07 0.430000D+02 0.371096D-07 0.440000D+02 0.294538D-07 0.450000D+02 0.248473D-07 0.460000D+02 0.217755D-07 0.470000D+02 0.204970D-07 4.2.3 Pr=1.5 Without Initial Temperature Fluctuations 4.2.3.1 Temperature Variance and Turbulent Heat Flux tau tt vt 0.200000D+00 0.107663D-01 0.509837D-01 0.400000D+00 0.332896D-01 0.762770D-01 0.600000D+00 0.588770D-01 0.883410D-01 0.800000D+00 0.844239D-01 0.945521D-01 0.100000D+01 0.109154D+00 0.979260D-01 0.120000D+01 0.132934D+00 0.997914D-01 0.140000D+01 0.155756D+00 0.100789D+00 0.160000D+01 0.177680D+00 0.101080D+00 0.180000D+01 0.198778D+00 0.100825D+00 0.200000D+01 0.219066D+00 0.100261D+00 0.220000D+01 0.238572D+00 0.995767D-01 0.240000D+01 0.257403D+00 0.988072D-01 0.260000D+01 0.275673D+00 0.979436D-01 0.280000D+01 0.293443D+00 0.970179D-01 0.300000D+01 0.310732D+00 0.960780D-01 0.320000D+01 0.327569D+00 0.951598D-01 0.340000D+01 0.344022D+00 0.942877D-01 0.360000D+01 0.360188D+00 0.934711D-01 0.380000D+01 0.376157D+00 0.927046D-01 0.400000D+01 0.391968D+00 0.919781D-01 0.420000D+01 0.407611D+00 0.912890D-01 0.440000D+01 0.423054D+00 0.906420D-01 0.460000D+01 0.438272D+00 0.900436D-01 0.480000D+01 0.453271D+00 0.894991D-01 0.500000D+01 0.468091D+00 0.890082D-01 0.520000D+01 0.482793D+00 0.885630D-01 0.540000D+01 0.497440D+00 0.881486D-01 4.2.3.2 vt Budget tau P_vt phi_vt D_vt 0.200000D+00 0.263467D+00 -0.429015D-01 0.413248D-01 0.400000D+00 0.217766D+00 -0.806377D-01 0.531500D-01 0.600000D+00 0.182805D+00 -0.904315D-01 0.511806D-01 0.800000D+00 0.156073D+00 -0.874612D-01 0.467105D-01 0.100000D+01 0.135236D+00 -0.810882D-01 0.424188D-01 0.120000D+01 0.118613D+00 -0.733946D-01 0.387284D-01 0.140000D+01 0.105073D+00 -0.665976D-01 0.357055D-01 0.160000D+01 0.938294D-01 -0.611759D-01 0.330245D-01 0.180000D+01 0.843484D-01 -0.562611D-01 0.305976D-01 0.200000D+01 0.763056D-01 -0.513318D-01 0.284109D-01 0.220000D+01 0.694457D-01 -0.467182D-01 0.265474D-01 0.240000D+01 0.635411D-01 -0.428734D-01 0.249256D-01 0.260000D+01 0.584201D-01 -0.396336D-01 0.234457D-01 0.280000D+01 0.539546D-01 -0.367315D-01 0.220499D-01 0.300000D+01 0.500393D-01 -0.341193D-01 0.207020D-01 0.320000D+01 0.465907D-01 -0.317680D-01 0.194137D-01 0.340000D+01 0.435484D-01 -0.296363D-01 0.182247D-01 0.360000D+01 0.408608D-01 -0.277351D-01 0.171544D-01 0.380000D+01 0.384766D-01 -0.260812D-01 0.161920D-01 0.400000D+01 0.363499D-01 -0.246304D-01 0.153230D-01 0.420000D+01 0.344453D-01 -0.233131D-01 0.145346D-01 0.440000D+01 0.327350D-01 -0.220920D-01 0.138130D-01 0.460000D+01 0.311934D-01 -0.209503D-01 0.131494D-01 0.480000D+01 0.297961D-01 -0.198831D-01 0.125411D-01 0.500000D+01 0.285212D-01 -0.189035D-01 0.119872D-01 0.520000D+01 0.273497D-01 -0.180356D-01 0.114850D-01 0.540000D+01 0.262663D-01 -0.172961D-01 0.110283D-01 4.2.3.3 tt Budget tau P_tt D_tt 0.200000D+00 0.101967D+00 0.856482D-02 0.400000D+00 0.152554D+00 0.284289D-01 0.600000D+00 0.176682D+00 0.479993D-01 0.800000D+00 0.189104D+00 0.635614D-01 0.100000D+01 0.195852D+00 0.747932D-01 0.120000D+01 0.199583D+00 0.833260D-01 0.140000D+01 0.201579D+00 0.899413D-01 0.160000D+01 0.202161D+00 0.947594D-01 0.180000D+01 0.201650D+00 0.982826D-01 0.200000D+01 0.200523D+00 0.101164D+00 0.220000D+01 0.199153D+00 0.103486D+00 0.240000D+01 0.197614D+00 0.104991D+00 0.260000D+01 0.195887D+00 0.105853D+00 0.280000D+01 0.194036D+00 0.106423D+00 0.300000D+01 0.192156D+00 0.106901D+00 0.320000D+01 0.190320D+00 0.107184D+00 0.340000D+01 0.188575D+00 0.107129D+00 0.360000D+01 0.186942D+00 0.106673D+00 0.380000D+01 0.185409D+00 0.105975D+00 0.400000D+01 0.183956D+00 0.105308D+00 0.420000D+01 0.182578D+00 0.104843D+00 0.440000D+01 0.181284D+00 0.104625D+00 0.460000D+01 0.180087D+00 0.104570D+00 0.480000D+01 0.178998D+00 0.104504D+00 0.500000D+01 0.178016D+00 0.104269D+00 0.520000D+01 0.177126D+00 0.103802D+00 0.540000D+01 0.176297D+00 0.103122D+00 4.2.3.4 Thermal Integral Scale tau lamda_tt(x_1) 0.200000D+00 0.367289D+00 0.400000D+00 0.380026D+00 0.600000D+00 0.400071D+00 0.800000D+00 0.424670D+00 0.100000D+01 0.453621D+00 0.120000D+01 0.480407D+00 0.140000D+01 0.501075D+00 0.160000D+01 0.524682D+00 0.180000D+01 0.552549D+00 0.200000D+01 0.581221D+00 0.220000D+01 0.604067D+00 0.240000D+01 0.622591D+00 0.260000D+01 0.636540D+00 0.280000D+01 0.646282D+00 0.300000D+01 0.655493D+00 0.320000D+01 0.668023D+00 0.340000D+01 0.683932D+00 0.360000D+01 0.701689D+00 0.380000D+01 0.718966D+00 0.400000D+01 0.734635D+00 0.420000D+01 0.749068D+00 0.440000D+01 0.762323D+00 0.460000D+01 0.774637D+00 0.480000D+01 0.786756D+00 0.500000D+01 0.799629D+00 0.520000D+01 0.814290D+00 0.540000D+01 0.831515D+00 4.2.3.5 Thermal Two Point Correlation tau 0.200000D+01 x_1 R_tt(x_1) 0.0 0.100000D+01 0.872665D-01 0.896683D+00 0.174533D+00 0.719412D+00 0.261799D+00 0.562900D+00 0.349066D+00 0.438517D+00 0.436332D+00 0.342982D+00 0.523599D+00 0.270108D+00 0.610865D+00 0.214643D+00 0.698132D+00 0.172070D+00 0.785398D+00 0.137916D+00 0.872665D+00 0.108620D+00 0.959931D+00 0.823022D-01 0.104720D+01 0.589786D-01 0.113446D+01 0.394765D-01 0.122173D+01 0.236047D-01 0.130900D+01 0.114861D-01 0.139626D+01 0.241992D-02 0.148353D+01 -0.586759D-02 0.157080D+01 -0.152804D-01 0.165806D+01 -0.258128D-01 0.174533D+01 -0.362066D-01 0.183260D+01 -0.453140D-01 0.191986D+01 -0.523032D-01 0.200713D+01 -0.580421D-01 0.209440D+01 -0.640471D-01 0.218166D+01 -0.700376D-01 0.226893D+01 -0.752428D-01 0.235619D+01 -0.792520D-01 0.244346D+01 -0.816238D-01 0.253073D+01 -0.830519D-01 0.261799D+01 -0.843884D-01 0.270526D+01 -0.857990D-01 0.279253D+01 -0.871585D-01 0.287979D+01 -0.878505D-01 0.296706D+01 -0.871235D-01 0.305433D+01 -0.853502D-01 tau 0.500000D+01 x_1 R_tt(x_1) 0.0 0.100000D+01 0.872665D-01 0.945636D+00 0.174533D+00 0.828478D+00 0.261799D+00 0.705523D+00 0.349066D+00 0.597027D+00 0.436332D+00 0.505900D+00 0.523599D+00 0.430078D+00 0.610865D+00 0.366407D+00 0.698132D+00 0.311616D+00 0.785398D+00 0.262972D+00 0.872665D+00 0.218905D+00 0.959931D+00 0.178948D+00 0.104720D+01 0.143434D+00 0.113446D+01 0.112725D+00 0.122173D+01 0.865209D-01 0.130900D+01 0.637497D-01 0.139626D+01 0.429177D-01 0.148353D+01 0.228893D-01 0.157080D+01 0.324218D-02 0.165806D+01 -0.158000D-01 0.174533D+01 -0.336460D-01 0.183260D+01 -0.500877D-01 0.191986D+01 -0.652779D-01 0.200713D+01 -0.791772D-01 0.209440D+01 -0.914874D-01 0.218166D+01 -0.101801D+00 0.226893D+01 -0.109802D+00 0.235619D+01 -0.115380D+00 0.244346D+01 -0.118738D+00 0.253073D+01 -0.120621D+00 0.261799D+01 -0.122161D+00 0.270526D+01 -0.124427D+00 0.279253D+01 -0.127700D+00 0.287979D+01 -0.131248D+00 0.296706D+01 -0.134105D+00 0.305433D+01 -0.135803D+00 4.2.3.6 One Dimensional Energy Spectrum tau 0.200000D+01 k_1 E_tt(k_1) 0.0 0.202646D-01 0.100000D+01 0.309256D-01 0.200000D+01 0.181605D-01 0.300000D+01 0.122421D-01 0.400000D+01 0.908686D-02 0.500000D+01 0.636377D-02 0.600000D+01 0.477491D-02 0.700000D+01 0.371068D-02 0.800000D+01 0.294411D-02 0.900000D+01 0.218182D-02 0.100000D+02 0.160501D-02 0.110000D+02 0.120305D-02 0.120000D+02 0.110654D-02 0.130000D+02 0.838069D-03 0.140000D+02 0.688058D-03 0.150000D+02 0.564610D-03 0.160000D+02 0.483744D-03 0.170000D+02 0.383961D-03 0.180000D+02 0.324506D-03 0.190000D+02 0.264914D-03 0.200000D+02 0.227550D-03 0.210000D+02 0.194266D-03 0.220000D+02 0.171000D-03 0.230000D+02 0.139735D-03 0.240000D+02 0.114480D-03 0.250000D+02 0.980748D-04 0.260000D+02 0.822598D-04 0.270000D+02 0.709935D-04 0.280000D+02 0.624475D-04 0.290000D+02 0.519394D-04 0.300000D+02 0.441589D-04 0.310000D+02 0.391257D-04 0.320000D+02 0.337320D-04 0.330000D+02 0.296027D-04 0.340000D+02 0.250216D-04 0.350000D+02 0.214701D-04 0.360000D+02 0.186472D-04 0.370000D+02 0.165627D-04 0.380000D+02 0.142210D-04 0.390000D+02 0.127560D-04 0.400000D+02 0.112173D-04 0.410000D+02 0.101363D-04 0.420000D+02 0.954757D-05 0.430000D+02 0.919757D-05 0.440000D+02 0.878265D-05 0.450000D+02 0.885338D-05 0.460000D+02 0.900808D-05 0.470000D+02 0.923350D-05 tau 0.500000D+01 k_1 E_tt(k_1) 0.0 0.595715D-01 0.100000D+01 0.883825D-01 0.200000D+01 0.405097D-01 0.300000D+01 0.223438D-01 0.400000D+01 0.154751D-01 0.500000D+01 0.101680D-01 0.600000D+01 0.646326D-02 0.700000D+01 0.544795D-02 0.800000D+01 0.381207D-02 0.900000D+01 0.296839D-02 0.100000D+02 0.205813D-02 0.110000D+02 0.140854D-02 0.120000D+02 0.115393D-02 0.130000D+02 0.868870D-03 0.140000D+02 0.703866D-03 0.150000D+02 0.515136D-03 0.160000D+02 0.417573D-03 0.170000D+02 0.324842D-03 0.180000D+02 0.251912D-03 0.190000D+02 0.200374D-03 0.200000D+02 0.158905D-03 0.210000D+02 0.126224D-03 0.220000D+02 0.981803D-04 0.230000D+02 0.798829D-04 0.240000D+02 0.636397D-04 0.250000D+02 0.500337D-04 0.260000D+02 0.398976D-04 0.270000D+02 0.326159D-04 0.280000D+02 0.270976D-04 0.290000D+02 0.210450D-04 0.300000D+02 0.168165D-04 0.310000D+02 0.135259D-04 0.320000D+02 0.108938D-04 0.330000D+02 0.886327D-05 0.340000D+02 0.716395D-05 0.350000D+02 0.571027D-05 0.360000D+02 0.471429D-05 0.370000D+02 0.378901D-05 0.380000D+02 0.300767D-05 0.390000D+02 0.245170D-05 0.400000D+02 0.204660D-05 0.410000D+02 0.171362D-05 0.420000D+02 0.137769D-05 0.430000D+02 0.118496D-05 0.440000D+02 0.107482D-05 0.450000D+02 0.104025D-05 0.460000D+02 0.108237D-05 0.470000D+02 0.118914D-05 4.2.4 Pr=0.2 Without Initial Temperature Fluctuations 4.2.4.1 Temperature Variance and Turbulent Het Flux tau tt vt 0.200000D+00 0.785341D-02 0.437130D-01 0.400000D+00 0.222800D-01 0.638576D-01 0.600000D+00 0.377608D-01 0.736300D-01 0.800000D+00 0.529142D-01 0.787363D-01 0.100000D+01 0.673675D-01 0.814083D-01 0.120000D+01 0.810157D-01 0.826975D-01 0.140000D+01 0.939448D-01 0.831653D-01 0.160000D+01 0.106251D+00 0.830702D-01 0.180000D+01 0.117969D+00 0.825886D-01 0.200000D+01 0.129157D+00 0.818869D-01 0.220000D+01 0.139910D+00 0.810871D-01 0.240000D+01 0.150305D+00 0.802336D-01 0.260000D+01 0.160392D+00 0.793417D-01 0.280000D+01 0.170209D+00 0.784450D-01 0.300000D+01 0.179804D+00 0.775790D-01 0.320000D+01 0.189223D+00 0.767612D-01 0.340000D+01 0.198504D+00 0.759969D-01 0.360000D+01 0.207666D+00 0.752854D-01 0.380000D+01 0.216716D+00 0.746204D-01 0.400000D+01 0.225648D+00 0.739943D-01 0.420000D+01 0.234464D+00 0.734039D-01 0.440000D+01 0.243171D+00 0.728503D-01 0.460000D+01 0.251789D+00 0.723346D-01 0.480000D+01 0.260334D+00 0.718545D-01 0.500000D+01 0.268810D+00 0.714038D-01 0.520000D+01 0.277204D+00 0.709730D-01 0.540000D+01 0.285488D+00 0.705519D-01 4.2.4.2 vt Budget tau P_vt phi_vt D_tt 0.200000D+00 0.263467D+00 -0.265364D-01 0.925704D-01 0.400000D+00 0.217766D+00 -0.456064D-01 0.104804D+00 0.600000D+00 0.182805D+00 -0.501243D-01 0.986554D-01 0.800000D+00 0.156073D+00 -0.483749D-01 0.897076D-01 0.100000D+01 0.135236D+00 -0.449048D-01 0.813655D-01 0.120000D+01 0.118613D+00 -0.405132D-01 0.742267D-01 0.140000D+01 0.105073D+00 -0.364722D-01 0.680098D-01 0.160000D+01 0.938294D-01 -0.331545D-01 0.623994D-01 0.180000D+01 0.843484D-01 -0.301813D-01 0.573834D-01 0.200000D+01 0.763056D-01 -0.272868D-01 0.529514D-01 0.220000D+01 0.694457D-01 -0.246249D-01 0.490622D-01 0.240000D+01 0.635411D-01 -0.223946D-01 0.456095D-01 0.260000D+01 0.584201D-01 -0.205381D-01 0.424563D-01 0.280000D+01 0.539546D-01 -0.189019D-01 0.395412D-01 0.300000D+01 0.500393D-01 -0.174202D-01 0.368880D-01 0.320000D+01 0.465907D-01 -0.160821D-01 0.345107D-01 0.340000D+01 0.435484D-01 -0.148943D-01 0.323800D-01 0.360000D+01 0.408608D-01 -0.138698D-01 0.304593D-01 0.380000D+01 0.384766D-01 -0.130032D-01 0.287254D-01 0.400000D+01 0.363499D-01 -0.122607D-01 0.271561D-01 0.420000D+01 0.344453D-01 -0.116027D-01 0.257280D-01 0.440000D+01 0.327350D-01 -0.110039D-01 0.244261D-01 0.460000D+01 0.311934D-01 -0.104554D-01 0.232438D-01 0.480000D+01 0.297961D-01 -0.995874D-02 0.221759D-01 0.500000D+01 0.285212D-01 -0.952031D-02 0.212132D-01 0.520000D+01 0.273497D-01 -0.914420D-02 0.203429D-01 0.540000D+01 0.262663D-01 -0.882800D-02 0.195500D-01 4.2.4.3 tt Budget tau P_tt D_tt 0.200000D+00 0.874259D-01 0.237290D-01 0.400000D+00 0.127715D+00 0.509638D-01 0.600000D+00 0.147260D+00 0.702144D-01 0.800000D+00 0.157473D+00 0.832927D-01 0.100000D+01 0.162817D+00 0.925873D-01 0.120000D+01 0.165395D+00 0.990722D-01 0.140000D+01 0.166331D+00 0.103296D+00 0.160000D+01 0.166140D+00 0.106111D+00 0.180000D+01 0.165177D+00 0.107987D+00 0.200000D+01 0.163774D+00 0.109007D+00 0.220000D+01 0.162174D+00 0.109359D+00 0.240000D+01 0.160467D+00 0.109296D+00 0.260000D+01 0.158683D+00 0.108961D+00 0.280000D+01 0.156890D+00 0.108404D+00 0.300000D+01 0.155158D+00 0.107664D+00 0.320000D+01 0.153522D+00 0.106799D+00 0.340000D+01 0.151994D+00 0.105896D+00 0.360000D+01 0.150571D+00 0.105041D+00 0.380000D+01 0.149241D+00 0.104284D+00 0.400000D+01 0.147989D+00 0.103622D+00 0.420000D+01 0.146808D+00 0.103014D+00 0.440000D+01 0.145701D+00 0.102405D+00 0.460000D+01 0.144669D+00 0.101773D+00 0.480000D+01 0.143709D+00 0.101153D+00 0.500000D+01 0.142808D+00 0.100616D+00 0.520000D+01 0.141946D+00 0.100225D+00 0.540000D+01 0.141104D+00 0.100005D+00 4.2.4.4 Thermal Integral Scale tau Lamda_tt(x_1) 0.200000D+00 0.414261D+00 0.400000D+00 0.447871D+00 0.600000D+00 0.481770D+00 0.800000D+00 0.518679D+00 0.100000D+01 0.557321D+00 0.120000D+01 0.592218D+00 0.140000D+01 0.623438D+00 0.160000D+01 0.655217D+00 0.180000D+01 0.688910D+00 0.200000D+01 0.721037D+00 0.220000D+01 0.748031D+00 0.240000D+01 0.769571D+00 0.260000D+01 0.786418D+00 0.280000D+01 0.800389D+00 0.300000D+01 0.814328D+00 0.320000D+01 0.830186D+00 0.340000D+01 0.848240D+00 0.360000D+01 0.867798D+00 0.380000D+01 0.888200D+00 0.400000D+01 0.909209D+00 0.420000D+01 0.930735D+00 0.440000D+01 0.952703D+00 0.460000D+01 0.975264D+00 0.480000D+01 0.998744D+00 0.500000D+01 0.102337D+01 0.520000D+01 0.104917D+01 0.540000D+01 0.107598D+01 4.2.4.5 Thermal Two Point Correlation tau 0.200000D+01 x_1 R_tt(x_1) 0.0 0.100000D+01 0.872665D-01 0.967729D+00 0.174533D+00 0.883171D+00 0.261799D+00 0.771780D+00 0.349066D+00 0.655384D+00 0.436332D+00 0.546561D+00 0.523599D+00 0.450512D+00 0.610865D+00 0.368126D+00 0.698132D+00 0.298157D+00 0.785398D+00 0.238521D+00 0.872665D+00 0.187145D+00 0.959931D+00 0.142541D+00 0.104720D+01 0.103960D+00 0.113446D+01 0.711057D-01 0.122173D+01 0.437251D-01 0.130900D+01 0.212350D-01 0.139626D+01 0.251888D-02 0.148353D+01 -0.138270D-01 0.157080D+01 -0.289335D-01 0.165806D+01 -0.433006D-01 0.174533D+01 -0.569052D-01 0.183260D+01 -0.695846D-01 0.191986D+01 -0.813445D-01 0.200713D+01 -0.923876D-01 0.209440D+01 -0.102905D+00 0.218166D+01 -0.112889D+00 0.226893D+01 -0.122100D+00 0.235619D+01 -0.130190D+00 0.244346D+01 -0.136919D+00 0.253073D+01 -0.142258D+00 0.261799D+01 -0.146327D+00 0.270526D+01 -0.149325D+00 0.279253D+01 -0.151502D+00 0.287979D+01 -0.153109D+00 0.296706D+01 -0.154312D+00 0.305433D+01 -0.155113D+00 tau 0.500000D+01 x_1 R_tt(x_1) 0.0 0.100000D+01 0.872665D-01 0.985245D+00 0.174533D+00 0.943755D+00 0.261799D+00 0.882421D+00 0.349066D+00 0.809278D+00 0.436332D+00 0.731161D+00 0.523599D+00 0.652792D+00 0.610865D+00 0.576897D+00 0.698132D+00 0.504777D+00 0.785398D+00 0.436908D+00 0.872665D+00 0.373408D+00 0.959931D+00 0.314310D+00 0.104720D+01 0.259647D+00 0.113446D+01 0.209406D+00 0.122173D+01 0.163435D+00 0.130900D+01 0.121404D+00 0.139626D+01 0.828558D-01 0.148353D+01 0.473337D-01 0.157080D+01 0.144742D-01 0.165806D+01 -0.159574D-01 0.174533D+01 -0.440855D-01 0.183260D+01 -0.699574D-01 0.191986D+01 -0.935647D-01 0.200713D+01 -0.114853D+00 0.209440D+01 -0.133748D+00 0.218166D+01 -0.150208D+00 0.226893D+01 -0.164294D+00 0.235619D+01 -0.176212D+00 0.244346D+01 -0.186290D+00 0.253073D+01 -0.194899D+00 0.261799D+01 -0.202347D+00 0.270526D+01 -0.208802D+00 0.279253D+01 -0.214269D+00 0.287979D+01 -0.218655D+00 0.296706D+01 -0.221851D+00 0.305433D+01 -0.223789D+00 4.2.4.6 One Dimensional Energy Spectrum tau 0.200000D+01 k_1 E_tt(k_1) 0.0 0.148217D-01 0.100000D+01 0.255668D-01 0.200000D+01 0.127028D-01 0.300000D+01 0.752974D-02 0.400000D+01 0.448997D-02 0.500000D+01 0.247621D-02 0.600000D+01 0.158477D-02 0.700000D+01 0.103918D-02 0.800000D+01 0.667534D-03 0.900000D+01 0.419074D-03 0.100000D+02 0.226494D-03 0.110000D+02 0.147267D-03 0.120000D+02 0.107367D-03 0.130000D+02 0.723995D-04 0.140000D+02 0.440679D-04 0.150000D+02 0.305265D-04 0.160000D+02 0.203331D-04 0.170000D+02 0.141233D-04 0.180000D+02 0.915366D-05 0.190000D+02 0.604476D-05 0.200000D+02 0.420984D-05 0.210000D+02 0.297675D-05 0.220000D+02 0.211253D-05 0.230000D+02 0.148773D-05 0.240000D+02 0.956846D-06 0.250000D+02 0.657413D-06 0.260000D+02 0.476691D-06 0.270000D+02 0.318267D-06 0.280000D+02 0.241645D-06 0.290000D+02 0.170251D-06 0.300000D+02 0.116765D-06 0.310000D+02 0.839634D-07 0.320000D+02 0.617651D-07 0.330000D+02 0.439151D-07 0.340000D+02 0.322826D-07 0.350000D+02 0.230711D-07 0.360000D+02 0.177231D-07 0.370000D+02 0.127243D-07 0.380000D+02 0.900476D-08 0.390000D+02 0.684902D-08 0.400000D+02 0.501632D-08 0.410000D+02 0.381887D-08 0.420000D+02 0.293870D-08 0.430000D+02 0.252375D-08 0.440000D+02 0.191465D-08 0.450000D+02 0.163666D-08 0.460000D+02 0.143691D-08 0.470000D+02 0.118657D-08 tau 0.500000D+01 k_1 E_tt(k_1) 0.0 0.437825D-01 0.100000D+01 0.693554D-01 0.200000D+01 0.238761D-01 0.300000D+01 0.959958D-02 0.400000D+01 0.472608D-02 0.500000D+01 0.234293D-02 0.600000D+01 0.109127D-02 0.700000D+01 0.716470D-03 0.800000D+01 0.381653D-03 0.900000D+01 0.198381D-03 0.100000D+02 0.108568D-03 0.110000D+02 0.466190D-04 0.120000D+02 0.301633D-04 0.130000D+02 0.174563D-04 0.140000D+02 0.100611D-04 0.150000D+02 0.544464D-05 0.160000D+02 0.303150D-05 0.170000D+02 0.182689D-05 0.180000D+02 0.103611D-05 0.190000D+02 0.703357D-06 0.200000D+02 0.365584D-06 0.210000D+02 0.232450D-06 0.220000D+02 0.129763D-06 0.230000D+02 0.824247D-07 0.240000D+02 0.549608D-07 0.250000D+02 0.322825D-07 0.260000D+02 0.196745D-07 0.270000D+02 0.121291D-07 0.280000D+02 0.785428D-08 0.290000D+02 0.478346D-08 0.300000D+02 0.307275D-08 0.310000D+02 0.188117D-08 0.320000D+02 0.126240D-08 0.330000D+02 0.790091D-09 0.340000D+02 0.492545D-09 0.350000D+02 0.331678D-09 0.360000D+02 0.219689D-09 0.370000D+02 0.135258D-09 0.380000D+02 0.921948D-10 0.390000D+02 0.616987D-10 0.400000D+02 0.399294D-10 0.410000D+02 0.278110D-10 0.420000D+02 0.188854D-10 0.430000D+02 0.126663D-10 0.440000D+02 0.896347D-11 0.450000D+02 0.722703D-11 0.460000D+02 0.535594D-11 0.470000D+02 0.505562D-11 5. References 5.1 Iida, O., and Kasagi, N., "Direct Numerical Simulation of Homogeneous Isotropic Turbulence with Scalar Transport," Preprint of the 69th JSME Ann. Meeting, Nagoya, 1991, Vol. B, pp. 425-427. 5.2 Iida, O., and Kasagi, N., "Plandtl Number Effect on Scalar Transport in Homogeneous Isotropic Turbulence," Proc. of the 5th Symposium of Numeical Fluid Dynamics, Tokyo, 1991, pp. 307-310. (EOF)