HOM03 Direct numerical simulation of forced isotropic turbulence in a periodic box From: Jimenez, J., Wray, A.A., Saffman, P.G. & Rogallo, R.S., 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech., vol. 255, 65-90. Energy spectra, normalized in Kolmogorov variables: E(k)/(eps^(2/3)*eta^(5/3)) vs. k*eta Re_lambda=138.5 eta: Kolmogorov scale (Batchelor 1953). eps: energy dissipation rate. k: wavenumber E: Three-dimensional spectrum (sums to q^2/2) E11: One-dimensional longitudinal spectrum (normalized to sum u1^2) E22: One-dimensional transverse spectrum (normalized to sum u2^2) k*eta E(k) E11(k1) E22(k1) 0.0000000e+00 0.0000000e+00 1.3217660e+03 5.2365399e+02 1.2884500e-02 1.6304000e+03 9.3324628e+02 1.3120372e+03 2.3198000e-02 9.5745000e+02 3.5421356e+02 4.7735899e+02 3.4159000e-02 4.5888000e+02 1.7919398e+02 2.2942094e+02 4.3846500e-02 3.4153000e+02 1.1705030e+02 1.4870088e+02 5.5639500e-02 2.2517000e+02 7.9869637e+01 1.1035665e+02 6.7068500e-02 1.7397000e+02 5.6994270e+01 8.1685963e+01 7.7375500e-02 1.3932000e+02 4.2483122e+01 6.3228387e+01 8.8056500e-02 1.2495000e+02 3.2771958e+01 5.0734578e+01 9.9295000e-02 1.0290000e+02 2.5356926e+01 4.0367268e+01 1.1082000e-01 8.6635000e+01 2.0012968e+01 3.2911461e+01 1.2147500e-01 7.4097000e+01 1.5844457e+01 2.7044341e+01 1.3210500e-01 6.5145000e+01 1.2825603e+01 2.2604832e+01 1.4325500e-01 5.6687000e+01 1.0363378e+01 1.8806381e+01 1.5436500e-01 4.9986000e+01 8.4728311e+00 1.5877393e+01 1.6503500e-01 4.2819000e+01 7.0188691e+00 1.3441143e+01 1.7587500e-01 3.7334000e+01 5.8064906e+00 1.1448257e+01 1.8717000e-01 3.3513000e+01 4.8416557e+00 9.7534237e+00 1.9838000e-01 2.9206000e+01 4.0803597e+00 8.4295448e+00 2.0923000e-01 2.6801000e+01 3.4215155e+00 7.2419625e+00 2.2005000e-01 2.3405000e+01 2.8844544e+00 6.2358661e+00 2.3120000e-01 2.1157000e+01 2.4492820e+00 5.4190478e+00 2.4226000e-01 1.8345000e+01 2.0877707e+00 4.6898124e+00 2.5311000e-01 1.6577000e+01 1.7813561e+00 4.0786553e+00 2.6399500e-01 1.4723000e+01 1.5310477e+00 3.5583540e+00 2.7506000e-01 1.3035000e+01 1.3096295e+00 3.1153801e+00 2.8618500e-01 1.1621000e+01 1.1323066e+00 2.7337093e+00 2.9719000e-01 1.0429000e+01 9.7770291e-01 2.3922486e+00 3.0819500e-01 9.2976000e+00 8.4849939e-01 2.1027228e+00 3.1921500e-01 8.3736000e+00 7.3871655e-01 1.8567126e+00 3.3017000e-01 7.4963000e+00 6.4195476e-01 1.6362141e+00 3.4112000e-01 6.7292000e+00 5.5983111e-01 1.4455609e+00 3.5204500e-01 6.1079000e+00 4.8992264e-01 1.2834902e+00 3.6300000e-01 5.4774000e+00 4.2951115e-01 1.1426307e+00 3.7408000e-01 4.9568000e+00 3.7680701e-01 1.0134151e+00 3.8511500e-01 4.4543000e+00 3.3068754e-01 9.0039583e-01 3.9609000e-01 4.0477000e+00 2.9191701e-01 8.0399231e-01 4.0712500e-01 3.6541000e+00 2.5716224e-01 7.1838304e-01 4.1813500e-01 3.3280000e+00 2.2771991e-01 6.4230222e-01 4.2906000e-01 3.0054000e+00 2.0136912e-01 5.7479229e-01 4.4000500e-01 2.7268000e+00 1.7890844e-01 5.1641092e-01 4.5108500e-01 2.4848000e+00 1.5882030e-01 4.6344802e-01 4.6215500e-01 2.2527000e+00 1.4092821e-01 4.1558714e-01 4.7312000e-01 2.0541000e+00 1.2528917e-01 3.7388056e-01 4.8412000e-01 1.8685000e+00 1.1187899e-01 3.3727564e-01 4.9516000e-01 1.6986000e+00 9.9708937e-02 3.0425995e-01 5.0616000e-01 1.5565000e+00 8.9038639e-02 2.7375338e-01 5.1702000e-01 1.4197000e+00 7.9613210e-02 2.4693913e-01 5.2797500e-01 1.2991000e+00 7.1275397e-02 2.2318150e-01 5.3905000e-01 1.1880000e+00 6.3880455e-02 2.0224068e-01 5.5015000e-01 1.0849000e+00 5.7352926e-02 1.8326130e-01 5.6113000e-01 9.9781000e-01 5.1516184e-02 1.6584756e-01 5.7210500e-01 9.1097000e-01 4.6269216e-02 1.5071541e-01 5.8315000e-01 8.3667000e-01 4.1670682e-02 1.3689383e-01 5.9416000e-01 7.6580000e-01 3.7414092e-02 1.2407710e-01 6.0507500e-01 7.0357000e-01 3.3769221e-02 1.1294072e-01 6.1600000e-01 6.4439000e-01 3.0490520e-02 1.0263131e-01 6.2706000e-01 5.9253000e-01 2.7534054e-02 9.3437542e-02 6.3812000e-01 5.4436000e-01 2.4877650e-02 8.5249968e-02 6.4906000e-01 5.0135000e-01 2.2477054e-02 7.7642981e-02 6.6008000e-01 4.6288000e-01 2.0332577e-02 7.0931111e-02 6.7112000e-01 4.2436000e-01 1.8435877e-02 6.4742153e-02 6.8213500e-01 3.9091000e-01 1.6708235e-02 5.9081873e-02 6.9303500e-01 3.6127000e-01 1.5153353e-02 5.4022236e-02 7.0395500e-01 3.3377000e-01 1.3739671e-02 4.9338999e-02 7.1505500e-01 3.0799000e-01 1.2507493e-02 4.5202727e-02 7.2612000e-01 2.8356000e-01 1.1354102e-02 4.1387680e-02 7.3712000e-01 2.6162000e-01 1.0325593e-02 3.7940111e-02 7.4811000e-01 2.4144000e-01 9.4035908e-03 3.4791250e-02 7.5913000e-01 2.2381000e-01 8.5643456e-03 3.1866159e-02 7.7015500e-01 2.0681000e-01 7.8103127e-03 2.9246146e-02 7.8106500e-01 1.9140000e-01 7.1163317e-03 2.6868013e-02 7.9203500e-01 1.7732000e-01 6.4983229e-03 2.4684224e-02 8.0306500e-01 1.6360000e-01 5.9277807e-03 2.2667620e-02 8.1411500e-01 1.5163000e-01 5.4136354e-03 2.0844777e-02 8.2512500e-01 1.4058000e-01 4.9426897e-03 1.9164467e-02 8.3609500e-01 1.3012000e-01 4.5231439e-03 1.7645269e-02 8.4712500e-01 1.2060000e-01 4.1373381e-03 1.6243321e-02 8.5811000e-01 1.1171000e-01 3.7880963e-03 1.4979095e-02 8.6904500e-01 1.0400000e-01 3.4709723e-03 1.3792760e-02 8.8002500e-01 9.6673000e-02 3.1740494e-03 1.2701128e-02 8.9104500e-01 8.9619000e-02 2.9112287e-03 1.1741622e-02 9.0210000e-01 8.3440000e-02 2.6708142e-03 1.0819394e-02 9.1311000e-01 7.7416000e-02 2.4489203e-03 9.9936532e-03 9.2407500e-01 7.1843000e-02 2.2492199e-03 9.2348117e-03 9.3508000e-01 6.6948000e-02 2.0613405e-03 8.5101734e-03 9.4614000e-01 6.2187000e-02 1.8950366e-03 7.8728080e-03 9.5711000e-01 5.7831000e-02 1.7399322e-03 7.2760802e-03 9.6808000e-01 5.3855000e-02 1.5993007e-03 6.7242128e-03 9.7908000e-01 5.0131000e-02 1.4705240e-03 6.2249880e-03 9.9013500e-01 4.6640000e-02 1.3522174e-03 5.7520889e-03 1.0011700e+00 4.3427000e-02 1.2437364e-03 5.3243053e-03 1.0121500e+00 4.0518000e-02 1.1472412e-03 4.9348653e-03 1.0231500e+00 3.7737000e-02 1.0561339e-03 4.5634111e-03 1.0341000e+00 3.5201000e-02 9.7318077e-04 4.2298651e-03 1.0450500e+00 3.2844000e-02 8.9665659e-04 3.9175737e-03 1.0559500e+00 3.0656000e-02 8.2707127e-04 3.6361369e-03 1.0670000e+00 2.8539000e-02 7.6229113e-04 3.3708642e-03 1.0781000e+00 2.6607000e-02 7.0429062e-04 3.1289795e-03 1.0891500e+00 2.4888000e-02 6.4978558e-04 2.9042072e-03 1.1001500e+00 2.3238000e-02 6.0038493e-04 2.6947353e-03 1.1111000e+00 2.1697000e-02 5.5469915e-04 2.5026856e-03 1.1221000e+00 2.0250000e-02 5.1197129e-04 2.3226728e-03 1.1331500e+00 1.8892000e-02 4.7341918e-04 2.1587947e-03 1.1440500e+00 1.7670000e-02 4.3761290e-04 2.0055401e-03 1.1551000e+00 1.6535000e-02 4.0478515e-04 1.8646359e-03 1.1661000e+00 1.5455000e-02 3.7448291e-04 1.7323092e-03 1.1771000e+00 1.4434000e-02 3.4622656e-04 1.6087601e-03 1.1880500e+00 1.3514000e-02 3.2057350e-04 1.4988551e-03 1.1991000e+00 1.2631000e-02 2.9698903e-04 1.3925386e-03 1.2102000e+00 1.1809000e-02 2.7512834e-04 1.2985205e-03 1.2211000e+00 1.1049000e-02 2.5495380e-04 1.2083937e-03 1.2320500e+00 1.0341000e-02 2.3627931e-04 1.1249386e-03 1.2431000e+00 9.6884000e-03 2.1907876e-04 1.0477077e-03 1.2541000e+00 9.0619000e-03 2.0337285e-04 9.7666780e-04 1.2651000e+00 8.4789000e-03 1.8856591e-04 9.1034838e-04 1.2760500e+00 7.9476000e-03 1.7472288e-04 8.4776860e-04 1.2871500e+00 7.4377000e-03 1.6235456e-04 7.9090778e-04 1.2981500e+00 6.9733000e-03 1.5055489e-04 7.3694454e-04 1.3090500e+00 6.5258000e-03 1.3995511e-04 6.8791601e-04 1.3200500e+00 6.1120000e-03 1.2998164e-04 6.4247689e-04 1.3311000e+00 5.7393000e-03 1.2088671e-04 5.9966536e-04 1.3421000e+00 5.3750000e-03 1.1224656e-04 5.5959183e-04 1.3531500e+00 5.0365000e-03 1.0423297e-04 5.2219982e-04 1.3641000e+00 4.7343000e-03 9.6890337e-05 4.8797821e-04 1.3751000e+00 4.4401000e-03 9.0080756e-05 4.5574641e-04 1.3861500e+00 4.1617000e-03 8.3797806e-05 4.2630696e-04 1.3971500e+00 3.9031000e-03 7.7980002e-05 3.9821772e-04 1.4080500e+00 3.6616000e-03 7.2479131e-05 3.7232986e-04 1.4191000e+00 3.4326000e-03 6.7386650e-05 3.4808932e-04 1.4301500e+00 3.2243000e-03 6.2831957e-05 3.2589654e-04 1.4411500e+00 3.0260000e-03 5.8493444e-05 3.0508473e-04 1.4521000e+00 2.8409000e-03 5.4409738e-05 2.8567921e-04 1.4631000e+00 2.6681000e-03 5.0702619e-05 2.6777926e-04 1.4741500e+00 2.5103000e-03 4.7180327e-05 2.5066261e-04 1.4851500e+00 2.3566000e-03 4.3930555e-05 2.3472706e-04 1.4961000e+00 2.2155000e-03 4.0901773e-05 2.2005591e-04 1.5071500e+00 2.0808000e-03 3.8160266e-05 2.0650787e-04 1.5181500e+00 1.9541000e-03 3.5447970e-05 1.9364924e-04 1.5291500e+00 1.8395000e-03 3.2962142e-05 1.8151755e-04 1.5401000e+00 1.7321000e-03 3.0731573e-05 1.7047715e-04 1.5511000e+00 1.6289000e-03 2.8626416e-05 1.6005065e-04 1.5621500e+00 1.5316000e-03 2.6613289e-05 1.5022134e-04 1.5731500e+00 1.4395000e-03 2.4695594e-05 1.4106351e-04 1.5840500e+00 1.3566000e-03 2.3048434e-05 1.3254365e-04 1.5951000e+00 1.2771000e-03 2.1421442e-05 1.2470072e-04 1.6061000e+00 1.2012000e-03 1.9884599e-05 1.1719648e-04 1.6171500e+00 1.1313000e-03 1.8474688e-05 1.1026869e-04 1.6281500e+00 1.0667000e-03 1.7167242e-05 1.0379391e-04 1.6392000e+00 1.0048000e-03 1.5906484e-05 9.7640255e-05 1.6502000e+00 9.4651000e-04 1.4779528e-05 9.1982448e-05 1.6611500e+00 8.9136000e-04 1.3671004e-05 8.6619508e-05 1.6721000e+00 8.4191000e-04 1.2653206e-05 8.1610264e-05 1.6831000e+00 7.9426000e-04 1.1653907e-05 7.6935616e-05 1.6941500e+00 7.4978000e-04 1.0801106e-05 7.2648671e-05 1.7051500e+00 7.0892000e-04 9.9691969e-06 6.8539252e-05 1.7161000e+00 6.7143000e-04 9.1553015e-06 6.4635424e-05 1.7271500e+00 6.3445000e-04 8.4310737e-06 6.1037544e-05 1.7381500e+00 6.0111000e-04 7.7431327e-06 5.7637418e-05 1.7491000e+00 5.6902000e-04 7.0809485e-06 5.4395807e-05 1.7601000e+00 5.4117000e-04 6.4671037e-06 5.1354814e-05 1.7711500e+00 5.1392000e-04 5.8566061e-06 4.8396528e-05 1.7821500e+00 4.8972000e-04 5.3125557e-06 4.5668738e-05 1.7931500e+00 4.6653000e-04 4.7940165e-06 4.3088562e-05 1.8042000e+00 4.4678000e-04 4.3181402e-06 4.0689093e-05 1.8151500e+00 4.2918000e-04 3.8712529e-06 3.8406428e-05 1.8261500e+00 4.1375000e-04 3.4578440e-06 3.6190765e-05 1.8371500e+00 4.0009000e-04 3.0243375e-06 3.3882773e-05 1.8481500e+00 3.8940000e-04 2.6653760e-06 3.1890962e-05 1.8591500e+00 3.8130000e-04 2.3058540e-06 2.9839672e-05 1.8702000e+00 3.7604000e-04 1.9834257e-06 2.7921222e-05 1.8812000e+00 3.7213000e-04 1.6755701e-06 2.5919181e-05 1.8922000e+00 3.7260000e-04 1.3998022e-06 2.4025958e-05 1.9032500e+00 3.7699000e-04 1.1508382e-06 2.2217959e-05 1.9142500e+00 3.8601000e-04 9.0247300e-07 2.0144215e-05 1.9252500e+00 4.0127000e-04 7.0036791e-07 1.8237382e-05 1.9362000e+00 4.2596000e-04 5.0883107e-07 1.6065073e-05 1.9472500e+00 4.6069000e-04 3.4035274e-07 1.3663317e-05 1.9583000e+00 5.0757000e-04 2.0582298e-07 1.1172941e-05 1.9694000e+00 5.7935000e-04 9.9754911e-08 8.3442969e-06 1.9805000e+00 7.1262000e-04 2.7344142e-08 4.8448728e-06 1.9886500e+00 9.1100000e-04 9.6528584e-12 9.6962527e-08