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=170.2 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 2.1253310e+03 1.0850784e+03 1.0180000e-02 2.6487000e+03 1.5175400e+03 1.7879106e+03 1.7864500e-02 1.5463000e+03 5.1825805e+02 8.0863394e+02 2.5663500e-02 6.7193000e+02 2.9529249e+02 3.5743434e+02 3.3341500e-02 4.8177000e+02 1.8410631e+02 2.4471828e+02 4.1929500e-02 3.7935000e+02 1.3134819e+02 1.7296718e+02 5.0566500e-02 2.7757000e+02 9.8768087e+01 1.3403776e+02 5.8298000e-02 2.2243000e+02 7.5376977e+01 1.0808890e+02 6.6481500e-02 1.9762000e+02 5.7996746e+01 8.4651927e+01 7.4811000e-02 1.6417000e+02 4.5641009e+01 6.9247622e+01 8.3610500e-02 1.3538000e+02 3.7279400e+01 5.7575969e+01 9.1749000e-02 1.2438000e+02 3.0416618e+01 4.8148615e+01 9.9749000e-02 1.0858000e+02 2.5210354e+01 4.0571616e+01 1.0808000e-01 9.3571000e+01 2.0947147e+01 3.5122902e+01 1.1657000e-01 8.4873000e+01 1.7902722e+01 3.0160260e+01 1.2459500e-01 7.4121000e+01 1.4806343e+01 2.5615285e+01 1.3277500e-01 6.4587000e+01 1.2769108e+01 2.2662367e+01 1.4135000e-01 5.8323000e+01 1.0951762e+01 1.9715831e+01 1.4981500e-01 5.2736000e+01 9.2642908e+00 1.7348298e+01 1.5800000e-01 4.7700000e+01 7.8906068e+00 1.5167362e+01 1.6613500e-01 4.2672000e+01 6.8397381e+00 1.3365500e+01 1.7458500e-01 3.9616000e+01 5.9810128e+00 1.1815311e+01 1.8293000e-01 3.5366000e+01 5.1796761e+00 1.0523083e+01 1.9112000e-01 3.2172000e+01 4.5077631e+00 9.2634688e+00 1.9934000e-01 2.9383000e+01 3.9591611e+00 8.3932392e+00 2.0769500e-01 2.6628000e+01 3.4749700e+00 7.3745106e+00 2.1610500e-01 2.4280000e+01 3.0358059e+00 6.6232259e+00 2.2441500e-01 2.2293000e+01 2.6838396e+00 5.8930302e+00 2.3273000e-01 2.0224000e+01 2.3659621e+00 5.2395570e+00 2.4103500e-01 1.8362000e+01 2.0976454e+00 4.7374066e+00 2.4930500e-01 1.6848000e+01 1.8574634e+00 4.2432000e+00 2.5755500e-01 1.5433000e+01 1.6456760e+00 3.8287509e+00 2.6581000e-01 1.4102000e+01 1.4653063e+00 3.4593388e+00 2.7406500e-01 1.2906000e+01 1.3049866e+00 3.1286116e+00 2.8244000e-01 1.1858000e+01 1.1735514e+00 2.8193695e+00 2.9079500e-01 1.0919000e+01 1.0480216e+00 2.5563451e+00 2.9905500e-01 1.0002000e+01 9.3417910e-01 2.3064673e+00 3.0741000e-01 9.1999000e+00 8.3743248e-01 2.0918669e+00 3.1571500e-01 8.4368000e+00 7.5603106e-01 1.8979010e+00 3.2395500e-01 7.7401000e+00 6.7823570e-01 1.7381344e+00 3.3223500e-01 7.2360000e+00 6.1205740e-01 1.5794868e+00 3.4058500e-01 6.5928000e+00 5.5307897e-01 1.4418879e+00 3.4895500e-01 6.1212000e+00 4.9855889e-01 1.3165258e+00 3.5724000e-01 5.6370000e+00 4.5010740e-01 1.1946550e+00 3.6553000e-01 5.2117000e+00 4.0876622e-01 1.0987211e+00 3.7386500e-01 4.7948000e+00 3.6974275e-01 1.0011536e+00 3.8216000e-01 4.4666000e+00 3.3511458e-01 9.1646986e-01 3.9037500e-01 4.1076000e+00 3.0576862e-01 8.4072578e-01 3.9864500e-01 3.8149000e+00 2.7710181e-01 7.7086210e-01 4.0702000e-01 3.5384000e+00 2.5283481e-01 7.0740951e-01 4.1539000e-01 3.2665000e+00 2.2842023e-01 6.4932365e-01 4.2368000e-01 3.0485000e+00 2.0914218e-01 5.9610228e-01 4.3196500e-01 2.8115000e+00 1.9158706e-01 5.5102096e-01 4.4031000e-01 2.6156000e+00 1.7453210e-01 5.0810510e-01 4.4861000e-01 2.4460000e+00 1.5929116e-01 4.6494956e-01 4.5686500e-01 2.2811000e+00 1.4506458e-01 4.2987565e-01 4.6510000e-01 2.1228000e+00 1.3298735e-01 3.9488175e-01 4.7346500e-01 1.9757000e+00 1.2186310e-01 3.6625352e-01 4.8181000e-01 1.8338000e+00 1.1165180e-01 3.3637402e-01 4.9007500e-01 1.7036000e+00 1.0242905e-01 3.1064926e-01 4.9837500e-01 1.5913000e+00 9.4011095e-02 2.8779923e-01 5.0672500e-01 1.4801000e+00 8.6859465e-02 2.6739175e-01 5.1505000e-01 1.3888000e+00 7.9718798e-02 2.4716242e-01 5.2327500e-01 1.2931000e+00 7.3127539e-02 2.2881349e-01 5.3152000e-01 1.2101000e+00 6.7267143e-02 2.1209397e-01 5.3991000e-01 1.1235000e+00 6.2147602e-02 1.9665173e-01 5.4824000e-01 1.0528000e+00 5.7046515e-02 1.8245571e-01 5.5656000e-01 9.8153000e-01 5.2853992e-02 1.6988442e-01 5.6486000e-01 9.2082000e-01 4.8762091e-02 1.5741568e-01 5.7317500e-01 8.5980000e-01 4.4939074e-02 1.4619993e-01 5.8150000e-01 8.0508000e-01 4.1587502e-02 1.3580066e-01 5.8973500e-01 7.5659000e-01 3.8470995e-02 1.2648015e-01 5.9802500e-01 7.0848000e-01 3.5687084e-02 1.1762176e-01 6.0634500e-01 6.6106000e-01 3.2974985e-02 1.0928188e-01 6.1469000e-01 6.2063000e-01 3.0472548e-02 1.0169895e-01 6.2301000e-01 5.8478000e-01 2.8151020e-02 9.4997313e-02 6.3129000e-01 5.4572000e-01 2.6145313e-02 8.8630113e-02 6.3962000e-01 5.1400000e-01 2.4257394e-02 8.2301573e-02 6.4792000e-01 4.8170000e-01 2.2457258e-02 7.7106758e-02 6.5616500e-01 4.5214000e-01 2.0864764e-02 7.1892192e-02 6.6445500e-01 4.2478000e-01 1.9363583e-02 6.7001176e-02 6.7278500e-01 3.9826000e-01 1.8000989e-02 6.2690762e-02 6.8112500e-01 3.7543000e-01 1.6710567e-02 5.8741923e-02 6.8945500e-01 3.5274000e-01 1.5487810e-02 5.4749457e-02 6.9772500e-01 3.3193000e-01 1.4422248e-02 5.1179247e-02 7.0603000e-01 3.1193000e-01 1.3425725e-02 4.7812975e-02 7.1438000e-01 2.9382000e-01 1.2509752e-02 4.4815969e-02 7.2267000e-01 2.7571000e-01 1.1652593e-02 4.1927475e-02 7.3094500e-01 2.6048000e-01 1.0819167e-02 3.9148191e-02 7.3926000e-01 2.4514000e-01 1.0098182e-02 3.6846128e-02 7.4760000e-01 2.3127000e-01 9.4055068e-03 3.4456541e-02 7.5592500e-01 2.1755000e-01 8.7534915e-03 3.2305596e-02 7.6422500e-01 2.0509000e-01 8.1645598e-03 3.0282429e-02 7.7252500e-01 1.9346000e-01 7.6078216e-03 2.8379590e-02 7.8080000e-01 1.8234000e-01 7.1073298e-03 2.6638513e-02 7.8906000e-01 1.7254000e-01 6.6356442e-03 2.4969949e-02 7.9733000e-01 1.6279000e-01 6.2010957e-03 2.3477682e-02 8.0565500e-01 1.5365000e-01 5.8069696e-03 2.2039242e-02 8.1404500e-01 1.4487000e-01 5.4196382e-03 2.0699391e-02 8.2237000e-01 1.3671000e-01 5.0680614e-03 1.9475810e-02 8.3064000e-01 1.2924000e-01 4.7257359e-03 1.8293831e-02 8.3895000e-01 1.2218000e-01 4.4279014e-03 1.7180600e-02 8.4727000e-01 1.1538000e-01 4.1340432e-03 1.6104008e-02 8.5559500e-01 1.0883000e-01 3.8672430e-03 1.5223824e-02 8.6383500e-01 1.0312000e-01 3.6172802e-03 1.4265133e-02 8.7215500e-01 9.7667000e-02 3.3883358e-03 1.3420930e-02 8.8050500e-01 9.2208000e-02 3.1680192e-03 1.2610994e-02 8.8879000e-01 8.7360000e-02 2.9661999e-03 1.1870521e-02 8.9707500e-01 8.2429000e-02 2.7787297e-03 1.1195229e-02 9.0540500e-01 7.8190000e-02 2.5994469e-03 1.0518182e-02 9.1375000e-01 7.3923000e-02 2.4380812e-03 9.9305254e-03 9.2201000e-01 7.0057000e-02 2.2865833e-03 9.3357366e-03 9.3028000e-01 6.6328000e-02 2.1490065e-03 8.7988772e-03 9.3860000e-01 6.2827000e-02 2.0159715e-03 8.2845355e-03 9.4693500e-01 5.9387000e-02 1.8883562e-03 7.8026132e-03 9.5523500e-01 5.6322000e-02 1.7742929e-03 7.3735279e-03 9.6352500e-01 5.3347000e-02 1.6634748e-03 6.9361995e-03 9.7187500e-01 5.0584000e-02 1.5625227e-03 6.5499668e-03 9.8017500e-01 4.7992000e-02 1.4685557e-03 6.1825979e-03 9.8843000e-01 4.5473000e-02 1.3755734e-03 5.8178119e-03 9.9673000e-01 4.3009000e-02 1.2954897e-03 5.4985402e-03 1.0051000e+00 4.0860000e-02 1.2149585e-03 5.1962260e-03 1.0134000e+00 3.8681000e-02 1.1411916e-03 4.8934484e-03 1.0217000e+00 3.6656000e-02 1.0765653e-03 4.6341715e-03 1.0300000e+00 3.4842000e-02 1.0118740e-03 4.3740606e-03 1.0383000e+00 3.2970000e-02 9.4976490e-04 4.1291757e-03 1.0466500e+00 3.1309000e-02 8.9432126e-04 3.9025855e-03 1.0549000e+00 2.9736000e-02 8.3952146e-04 3.6795339e-03 1.0632000e+00 2.8185000e-02 7.8917177e-04 3.4790745e-03 1.0715000e+00 2.6750000e-02 7.4553607e-04 3.2915549e-03 1.0798500e+00 2.5419000e-02 7.0068442e-04 3.1063990e-03 1.0881000e+00 2.4146000e-02 6.6011948e-04 2.9363261e-03 1.0964500e+00 2.2902000e-02 6.2279587e-04 2.7771996e-03 1.1047500e+00 2.1728000e-02 5.8665975e-04 2.6272861e-03 1.1131000e+00 2.0659000e-02 5.5277098e-04 2.4883269e-03 1.1213500e+00 1.9622000e-02 5.1980277e-04 2.3548514e-03 1.1296500e+00 1.8625000e-02 4.9021179e-04 2.2229813e-03 1.1380000e+00 1.7676000e-02 4.6137728e-04 2.1027329e-03 1.1463000e+00 1.6834000e-02 4.3462528e-04 1.9884379e-03 1.1546000e+00 1.6000000e-02 4.1104423e-04 1.8864352e-03 1.1628500e+00 1.5204000e-02 3.8751716e-04 1.7835746e-03 1.1712000e+00 1.4431000e-02 3.6551086e-04 1.6921343e-03 1.1795000e+00 1.3752000e-02 3.4504747e-04 1.6022259e-03 1.1878000e+00 1.3060000e-02 3.2531755e-04 1.5169424e-03 1.1960500e+00 1.2407000e-02 3.0744015e-04 1.4386394e-03 1.2044000e+00 1.1814000e-02 2.8969455e-04 1.3626082e-03 1.2127000e+00 1.1233000e-02 2.7351007e-04 1.2894440e-03 1.2210500e+00 1.0678000e-02 2.5868761e-04 1.2241019e-03 1.2293500e+00 1.0162000e-02 2.4465915e-04 1.1602327e-03 1.2376500e+00 9.6831000e-03 2.3075539e-04 1.0995496e-03 1.2460000e+00 9.1900000e-03 2.1784644e-04 1.0412624e-03 1.2542500e+00 8.7546000e-03 2.0621426e-04 9.8845710e-04 1.2625500e+00 8.3327000e-03 1.9438377e-04 9.3641667e-04 1.2708500e+00 7.9274000e-03 1.8380671e-04 8.8767352e-04 1.2792000e+00 7.5449000e-03 1.7430866e-04 8.4586675e-04 1.2875000e+00 7.1847000e-03 1.6459618e-04 8.0115680e-04 1.2957500e+00 6.8379000e-03 1.5564816e-04 7.6025092e-04 1.3040500e+00 6.5155000e-03 1.4713120e-04 7.2116585e-04 1.3124500e+00 6.2047000e-03 1.3913124e-04 6.8481689e-04 1.3206500e+00 5.9128000e-03 1.3187443e-04 6.5081542e-04 1.3289500e+00 5.6311000e-03 1.2470769e-04 6.1756737e-04 1.3373500e+00 5.3585000e-03 1.1801980e-04 5.8709229e-04 1.3456500e+00 5.1134000e-03 1.1160115e-04 5.5665195e-04 1.3539500e+00 4.8697000e-03 1.0600862e-04 5.3042940e-04 1.3622500e+00 4.6377000e-03 1.0019624e-04 5.0301856e-04 1.3705500e+00 4.4219000e-03 9.4875160e-05 4.7836812e-04 1.3788500e+00 4.2110000e-03 8.9791278e-05 4.5415006e-04 1.3871500e+00 4.0143000e-03 8.4856994e-05 4.3167039e-04 1.3954500e+00 3.8242000e-03 8.0378416e-05 4.1077136e-04 1.4037500e+00 3.6437000e-03 7.6246068e-05 3.9079520e-04 1.4120500e+00 3.4749000e-03 7.2163304e-05 3.7089564e-04 1.4204000e+00 3.3178000e-03 6.8407805e-05 3.5334094e-04 1.4286500e+00 3.1666000e-03 6.4771859e-05 3.3589088e-04 1.4369500e+00 3.0183000e-03 6.1318036e-05 3.1954470e-04 1.4453000e+00 2.8742000e-03 5.8220178e-05 3.0445136e-04 1.4536000e+00 2.7466000e-03 5.5184314e-05 2.8992276e-04 1.4618500e+00 2.6176000e-03 5.2280734e-05 2.7630574e-04 1.4701500e+00 2.4957000e-03 4.9552342e-05 2.6266587e-04 1.4785000e+00 2.3834000e-03 4.7037802e-05 2.5037620e-04 1.4868000e+00 2.2748000e-03 4.4537784e-05 2.3830570e-04 1.4951000e+00 2.1719000e-03 4.2270625e-05 2.2745244e-04 1.5034500e+00 2.0744000e-03 4.0072115e-05 2.1661945e-04 1.5117500e+00 1.9803000e-03 3.8031495e-05 2.0646874e-04 1.5200500e+00 1.8891000e-03 3.6074403e-05 1.9689345e-04 1.5283500e+00 1.8035000e-03 3.4123809e-05 1.8758798e-04 1.5366500e+00 1.7222000e-03 3.2339563e-05 1.7902991e-04 1.5449500e+00 1.6433000e-03 3.0674765e-05 1.7072054e-04 1.5532500e+00 1.5725000e-03 2.9062547e-05 1.6277408e-04 1.5616000e+00 1.5028000e-03 2.7535936e-05 1.5521976e-04 1.5699000e+00 1.4332000e-03 2.6082447e-05 1.4836402e-04 1.5781500e+00 1.3703000e-03 2.4743317e-05 1.4168427e-04 1.5864500e+00 1.3092000e-03 2.3448027e-05 1.3494481e-04 1.5948000e+00 1.2510000e-03 2.2244723e-05 1.2916780e-04 1.6030500e+00 1.1951000e-03 2.1060542e-05 1.2330411e-04 1.6114000e+00 1.1426000e-03 1.9955614e-05 1.1783517e-04 1.6197000e+00 1.0923000e-03 1.8897121e-05 1.1253649e-04 1.6280000e+00 1.0439000e-03 1.7828043e-05 1.0746637e-04 1.6363000e+00 9.9734000e-04 1.6936704e-05 1.0283077e-04 1.6446000e+00 9.5581000e-04 1.5958561e-05 9.8213247e-05 1.6529000e+00 9.1350000e-04 1.5169000e-05 9.4089875e-05 1.6612000e+00 8.7411000e-04 1.4317005e-05 9.0036634e-05 1.6695000e+00 8.3636000e-04 1.3500827e-05 8.6141524e-05 1.6778500e+00 8.0149000e-04 1.2782556e-05 8.2371684e-05 1.6861500e+00 7.6636000e-04 1.2097529e-05 7.8929335e-05 1.6944000e+00 7.3540000e-04 1.1328097e-05 7.5361438e-05 1.7028000e+00 7.0343000e-04 1.0714025e-05 7.2345411e-05 1.7111000e+00 6.7421000e-04 1.0098816e-05 6.9248560e-05 1.7193500e+00 6.4681000e-04 9.5244238e-06 6.6402245e-05 1.7277000e+00 6.2049000e-04 8.9698121e-06 6.3663994e-05 1.7360000e+00 5.9562000e-04 8.4189973e-06 6.0927741e-05 1.7443000e+00 5.7222000e-04 7.9020058e-06 5.8411292e-05 1.7526000e+00 5.4866000e-04 7.4302500e-06 5.6125359e-05 1.7609000e+00 5.2796000e-04 6.9485614e-06 5.3784257e-05 1.7692000e+00 5.0861000e-04 6.4865796e-06 5.1493795e-05 1.7775000e+00 4.8952000e-04 6.0764755e-06 4.9410190e-05 1.7858000e+00 4.7211000e-04 5.6600032e-06 4.7456511e-05 1.7941000e+00 4.5536000e-04 5.2762296e-06 4.5444898e-05 1.8024000e+00 4.4016000e-04 4.8955822e-06 4.3620364e-05 1.8107000e+00 4.2579000e-04 4.5459031e-06 4.1874661e-05 1.8190000e+00 4.1211000e-04 4.2132296e-06 4.0231952e-05 1.8273500e+00 3.9961000e-04 3.8660725e-06 3.8459310e-05 1.8357000e+00 3.8879000e-04 3.5707876e-06 3.6974396e-05 1.8440000e+00 3.7894000e-04 3.2664804e-06 3.5393484e-05 1.8523000e+00 3.6997000e-04 2.9765493e-06 3.3867190e-05 1.8605500e+00 3.6327000e-04 2.7045611e-06 3.2313078e-05 1.8689000e+00 3.5735000e-04 2.4585865e-06 3.0971566e-05 1.8772000e+00 3.5290000e-04 2.2041926e-06 2.9539556e-05 1.8855000e+00 3.4983000e-04 1.9628576e-06 2.8076076e-05 1.8938000e+00 3.4838000e-04 1.7376589e-06 2.6650911e-05 1.9021500e+00 3.4876000e-04 1.5201767e-06 2.5282503e-05 1.9104500e+00 3.5084000e-04 1.3187931e-06 2.3876198e-05 1.9187500e+00 3.5498000e-04 1.1284476e-06 2.2353566e-05 1.9270500e+00 3.6144000e-04 9.5685903e-07 2.0939419e-05 1.9353500e+00 3.7139000e-04 7.9162392e-07 1.9458148e-05 1.9437000e+00 3.8500000e-04 6.3732064e-07 1.7852907e-05 1.9520000e+00 4.0243000e-04 5.0191777e-07 1.6204727e-05 1.9603000e+00 4.2568000e-04 3.7515349e-07 1.4435771e-05 1.9686500e+00 4.5823000e-04 2.6386966e-07 1.2565499e-05 1.9769500e+00 5.0359000e-04 1.6695907e-07 1.0405352e-05 1.9852500e+00 5.7476000e-04 8.7933325e-08 8.0217749e-06 1.9936000e+00 6.8206000e-04 3.0462476e-08 5.1017307e-06 2.0014000e+00 9.2487000e-04 2.2337162e-09 1.4646737e-06