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. Pdf of transversal velocity diferences at various separations = dx. Only positive part is included, using the symmetry of the pdf. Re_lambda=142. Field filtered with the Gaussian filter with transfer function F = exp(-k^2 H^2), H=8*eta eta: Kolmogorov scale (Batchelor 1953). L: integral scale (Batchelor 1953). u': one-component rms velocity du : velocity difference at centre of the histogram box pdfs ____________________________________________________________________________ du/u' dx/L =4/3 dx/L=4/6 dx/L=4/9 dx/L=4/12 dx/L=4/15 2.0000000e-002 3.1384995e-001 4.0670900e-001 4.9996505e-001 5.9128800e-001 6.8331850e-001 6.0000000e-002 3.1376095e-001 4.0590920e-001 4.9858200e-001 5.8871800e-001 6.7854250e-001 1.0000000e-001 3.1333015e-001 4.0390810e-001 4.9510835e-001 5.8290200e-001 6.6929100e-001 1.4000000e-001 3.1235110e-001 4.0098445e-001 4.9012160e-001 5.7354450e-001 6.5538950e-001 1.8000000e-001 3.1070510e-001 3.9763055e-001 4.8355685e-001 5.6168250e-001 6.3892100e-001 2.2000000e-001 3.0862110e-001 3.9343715e-001 4.7429965e-001 5.4816950e-001 6.1877550e-001 2.6000000e-001 3.0694385e-001 3.8823635e-001 4.6444455e-001 5.3336600e-001 5.9580800e-001 3.0000000e-001 3.0527545e-001 3.8210900e-001 4.5323740e-001 5.1626000e-001 5.7205850e-001 3.4000000e-001 3.0288970e-001 3.7535115e-001 4.4144175e-001 4.9784945e-001 5.4585100e-001 3.8000000e-001 2.9990395e-001 3.6760840e-001 4.2886280e-001 4.7788405e-001 5.1821050e-001 4.2000000e-001 2.9675660e-001 3.5971930e-001 4.1524575e-001 4.5821940e-001 4.9020675e-001 4.6000000e-001 2.9304185e-001 3.5152710e-001 4.0136025e-001 4.3775640e-001 4.6171345e-001 5.0000000e-001 2.8905425e-001 3.4267545e-001 3.8701670e-001 4.1714895e-001 4.3342960e-001 5.4000000e-001 2.8513695e-001 3.3351720e-001 3.7219565e-001 3.9626650e-001 4.0613000e-001 5.8000000e-001 2.8068330e-001 3.2404690e-001 3.5756340e-001 3.7577145e-001 3.8002275e-001 6.2000000e-001 2.7610130e-001 3.1444310e-001 3.4272785e-001 3.5535050e-001 3.5413735e-001 6.6000000e-001 2.7109805e-001 3.0465970e-001 3.2805780e-001 3.3492335e-001 3.2948860e-001 7.0000000e-001 2.6611665e-001 2.9503645e-001 3.1357145e-001 3.1533515e-001 3.0583850e-001 7.4000000e-001 2.6117755e-001 2.8532760e-001 2.9934580e-001 2.9641270e-001 2.8318215e-001 7.8000000e-001 2.5608550e-001 2.7572130e-001 2.8544785e-001 2.7820445e-001 2.6156465e-001 8.2000000e-001 2.5106380e-001 2.6638270e-001 2.7202950e-001 2.6089705e-001 2.4125325e-001 8.6000000e-001 2.4585950e-001 2.5706390e-001 2.5837280e-001 2.4414890e-001 2.2200910e-001 9.0000000e-001 2.4093730e-001 2.4811000e-001 2.4505300e-001 2.2820855e-001 2.0393010e-001 9.4000000e-001 2.3567515e-001 2.3917355e-001 2.3232790e-001 2.1313615e-001 1.8744970e-001 9.8000000e-001 2.3016060e-001 2.3033130e-001 2.1966390e-001 1.9853335e-001 1.7196600e-001 1.0200000e+000 2.2425205e-001 2.2175115e-001 2.0758390e-001 1.8477975e-001 1.5706405e-001 1.0600000e+000 2.1826950e-001 2.1329945e-001 1.9619525e-001 1.7152485e-001 1.4315815e-001 1.1000000e+000 2.1270865e-001 2.0479205e-001 1.8537575e-001 1.5902030e-001 1.3030440e-001 1.1400000e+000 2.0665860e-001 1.9657415e-001 1.7494050e-001 1.4753950e-001 1.1837505e-001 1.1800000e+000 2.0063030e-001 1.8837705e-001 1.6483015e-001 1.3678590e-001 1.0740835e-001 1.2200000e+000 1.9461480e-001 1.8030310e-001 1.5510830e-001 1.2641970e-001 9.7516850e-002 1.2600000e+000 1.8861000e-001 1.7261400e-001 1.4596335e-001 1.1631035e-001 8.8289700e-002 1.3000000e+000 1.8254085e-001 1.6526710e-001 1.3686125e-001 1.0680270e-001 7.9823750e-002 1.3400000e+000 1.7697105e-001 1.5781895e-001 1.2829945e-001 9.8016200e-002 7.2116100e-002 1.3800000e+000 1.7157650e-001 1.5038135e-001 1.2010485e-001 9.0014050e-002 6.5226850e-002 1.4200000e+000 1.6586900e-001 1.4329945e-001 1.1239585e-001 8.2667450e-002 5.8798600e-002 1.4600000e+000 1.6026590e-001 1.3631195e-001 1.0478425e-001 7.5870950e-002 5.2838800e-002 1.5000000e+000 1.5447715e-001 1.2971080e-001 9.7283500e-002 6.9646250e-002 4.7440735e-002 1.5400000e+000 1.4869245e-001 1.2331445e-001 9.0235100e-002 6.3892900e-002 4.2631505e-002 1.5800000e+000 1.4322150e-001 1.1682985e-001 8.3856200e-002 5.8345850e-002 3.8219000e-002 1.6200000e+000 1.3805575e-001 1.1033620e-001 7.8026350e-002 5.3052200e-002 3.4099105e-002 1.6600000e+000 1.3312965e-001 1.0403855e-001 7.2293350e-002 4.8153265e-002 3.0276080e-002 1.7000000e+000 1.2814165e-001 9.8178800e-002 6.6923350e-002 4.3683320e-002 2.6919775e-002 1.7400000e+000 1.2331450e-001 9.2868550e-002 6.1918650e-002 3.9665725e-002 2.3711280e-002 1.7800000e+000 1.1843225e-001 8.7725800e-002 5.7218700e-002 3.5907125e-002 2.0918950e-002 1.8200000e+000 1.1376160e-001 8.2796100e-002 5.2806100e-002 3.2427040e-002 1.8416730e-002 1.8600000e+000 1.0925510e-001 7.8067450e-002 4.8526825e-002 2.9295070e-002 1.6185765e-002 1.9000000e+000 1.0482195e-001 7.3448300e-002 4.4497290e-002 2.6434990e-002 1.4358585e-002 1.9400000e+000 1.0043530e-001 6.8986550e-002 4.1042300e-002 2.3844765e-002 1.2727590e-002 1.9800000e+000 9.6192400e-002 6.4729100e-002 3.7791480e-002 2.1378665e-002 1.1262775e-002 2.0200000e+000 9.1968050e-002 6.0835750e-002 3.4780660e-002 1.9227855e-002 9.9963850e-003 2.0600000e+000 8.7812350e-002 5.6926750e-002 3.1970055e-002 1.7227485e-002 8.8617600e-003 2.1000000e+000 8.3465400e-002 5.3177600e-002 2.9384425e-002 1.5452100e-002 7.8189750e-003 2.1400000e+000 7.9282450e-002 4.9666775e-002 2.6920365e-002 1.3787155e-002 6.9657250e-003 2.1800000e+000 7.5177700e-002 4.6328310e-002 2.4715040e-002 1.2333155e-002 6.1724800e-003 2.2200000e+000 7.1249050e-002 4.3198810e-002 2.2611855e-002 1.1072960e-002 5.4915150e-003 2.2600000e+000 6.7408450e-002 4.0213110e-002 2.0679070e-002 9.8713650e-003 4.8928545e-003 2.3000000e+000 6.3995400e-002 3.7358510e-002 1.8899050e-002 8.7658200e-003 4.3454000e-003 2.3400000e+000 6.0690700e-002 3.4489495e-002 1.7219830e-002 7.8584650e-003 3.8386005e-003 2.3800000e+000 5.7506600e-002 3.1860500e-002 1.5619140e-002 7.0716850e-003 3.3588325e-003 2.4200000e+000 5.4558500e-002 2.9564590e-002 1.4145975e-002 6.3349450e-003 2.9268700e-003 2.4600000e+000 5.1745400e-002 2.7394635e-002 1.2795535e-002 5.6768900e-003 2.5468970e-003 2.5000000e+000 4.8936995e-002 2.5346800e-002 1.1476310e-002 5.0622600e-003 2.2176850e-003 2.5400000e+000 4.6255635e-002 2.3405320e-002 1.0396105e-002 4.4901310e-003 1.9095315e-003 2.5800000e+000 4.3551875e-002 2.1720015e-002 9.4216900e-003 4.0131465e-003 1.6751360e-003 2.6200000e+000 4.0831680e-002 2.0194950e-002 8.5169400e-003 3.5859550e-003 1.4358095e-003 2.6600000e+000 3.8246215e-002 1.8704415e-002 7.6349500e-003 3.1587395e-003 1.2303330e-003 2.7000000e+000 3.5950675e-002 1.7099615e-002 6.8537000e-003 2.7674460e-003 1.0423700e-003 2.7400000e+000 3.3699700e-002 1.5646685e-002 6.1766350e-003 2.4545585e-003 9.1046700e-004 2.7800000e+000 3.1567600e-002 1.4202425e-002 5.5410500e-003 2.1397825e-003 7.8365400e-004 2.8200000e+000 2.9535010e-002 1.2788790e-002 4.9575245e-003 1.8738545e-003 6.8782050e-004 2.8600000e+000 2.7556320e-002 1.1526595e-002 4.3591230e-003 1.6300275e-003 6.0839650e-004 2.9000000e+000 2.5638230e-002 1.0395490e-002 3.8498955e-003 1.4322650e-003 5.2143000e-004 2.9400000e+000 2.3764385e-002 9.4071600e-003 3.3968145e-003 1.2505940e-003 4.5608590e-004 2.9800000e+000 2.1933615e-002 8.4199550e-003 3.0279405e-003 1.0989700e-003 3.9379540e-004 3.0200000e+000 2.0141110e-002 7.5347500e-003 2.7014270e-003 9.4934500e-004 3.4131630e-004 3.0600000e+000 1.8563410e-002 6.7275250e-003 2.3734545e-003 8.3404800e-004 3.0410630e-004 3.1000000e+000 1.7077430e-002 6.0443650e-003 2.0847275e-003 7.2909000e-004 2.6701900e-004 3.1400000e+000 1.5750270e-002 5.4189100e-003 1.8195480e-003 6.3892250e-004 2.3656665e-004 3.1800000e+000 1.4523800e-002 4.8335685e-003 1.5733785e-003 5.4889000e-004 2.0829740e-004 3.2200000e+000 1.3321110e-002 4.2857085e-003 1.3583115e-003 4.6835025e-004 1.7785730e-004 3.2600000e+000 1.2232015e-002 3.7975025e-003 1.1730830e-003 4.0191435e-004 1.4825125e-004 3.3000000e+000 1.1220735e-002 3.4057555e-003 1.0182830e-003 3.5047775e-004 1.1852250e-004 3.3400000e+000 1.0277460e-002 3.0635315e-003 8.6635250e-004 3.1254415e-004 9.7795750e-005 3.3800000e+000 9.3535250e-003 2.7572300e-003 7.3806750e-004 2.7218230e-004 8.3765350e-005 3.4200000e+000 8.5250600e-003 2.4828890e-003 6.3633500e-004 2.2805520e-004 6.3516950e-005 3.4600000e+000 7.7752150e-003 2.2519640e-003 5.5302300e-004 2.0151520e-004 5.3963050e-005 3.5000000e+000 7.0746800e-003 2.0174210e-003 4.8040605e-004 1.7372425e-004 4.7045965e-005 3.5400000e+000 6.3804100e-003 1.7778740e-003 3.9784260e-004 1.5909290e-004 3.9086420e-005 3.5800000e+000 5.7440700e-003 1.5648795e-003 3.3528225e-004 1.3097080e-004 3.5468440e-005 3.6200000e+000 5.1516450e-003 1.3622360e-003 2.9332600e-004 8.9774900e-005 3.2193870e-005 3.6600000e+000 4.6058200e-003 1.1822570e-003 2.5306220e-004 7.0838750e-005 2.1989945e-005 3.7000000e+000 4.0757560e-003 1.0197915e-003 2.2002210e-004 4.9854500e-005 1.4753990e-005 3.7400000e+000 3.6268690e-003 8.8527600e-004 1.8546120e-004 4.4911980e-005 1.2031310e-005 3.7800000e+000 3.2791260e-003 7.8656050e-004 1.5737590e-004 3.9785485e-005 8.4133300e-006 3.8200000e+000 3.0048470e-003 7.0039150e-004 1.4377475e-004 3.5370325e-005 6.0585800e-006 3.8600000e+000 2.6939580e-003 6.2023150e-004 1.2933960e-004 3.3555205e-005 5.2368700e-006 3.9000000e+000 2.3893980e-003 5.4517400e-004 1.0252980e-004 2.9900435e-005 4.2925155e-006 3.9400000e+000 2.1072205e-003 4.7377105e-004 9.1847550e-005 2.5252255e-005 3.5689200e-006 3.9800000e+000 1.8486395e-003 4.2029855e-004 8.0981350e-005 1.7035155e-005 2.4038090e-006 4.0200000e+000 1.6146110e-003 3.6600440e-004 6.6816050e-005 1.3932280e-005 7.7265300e-007 4.0600000e+000 1.4326700e-003 3.1752350e-004 5.6661200e-005 1.0952045e-005 5.0000000e-015 4.1000000e+000 1.2672980e-003 2.7495400e-004 4.8260135e-005 9.2718350e-006 5.0000000e-015 4.1400000e+000 1.1252525e-003 2.4889230e-004 4.3133650e-005 7.8369050e-006 5.0000000e-015 4.1800000e+000 1.0121260e-003 2.2902410e-004 3.7921310e-005 7.1623700e-006 5.0000000e-015 4.2200000e+000 9.1320200e-004 2.1305595e-004 3.2120280e-005 6.1689600e-006 5.0000000e-015 4.2600000e+000 8.0841550e-004 1.8623385e-004 2.3743745e-005 5.3104550e-006 5.0000000e-015 4.3000000e+000 7.1617550e-004 1.6559300e-004 1.8494610e-005 4.5255380e-006 5.0000000e-015 4.3400000e+000 6.3472800e-004 1.3671050e-004 1.6434200e-005 3.6057130e-006 5.0000000e-015 4.3800000e+000 5.6970250e-004 1.0649120e-004 1.4287945e-005 2.3792800e-006 5.0000000e-015 4.4200000e+000 5.2275500e-004 9.1246600e-005 1.2791695e-005 5.2736600e-007 5.0000000e-015 4.4600000e+000 4.8087210e-004 8.0613450e-005 1.1258655e-005 5.0000000e-015 5.0000000e-015 4.5000000e+000 4.3334780e-004 7.2028400e-005 1.0044485e-005 5.0000000e-015 5.0000000e-015 4.5400000e+000 3.6574680e-004 6.3038650e-005 8.5972950e-006 5.0000000e-015 5.0000000e-015 4.5800000e+000 3.2823030e-004 4.9449780e-005 7.4199200e-006 5.0000000e-015 5.0000000e-015 4.6200000e+000 3.0463370e-004 3.9049630e-005 5.9727300e-006 5.0000000e-015 5.0000000e-015 4.6600000e+000 2.8449570e-004 3.0673090e-005 4.4764805e-006 5.0000000e-015 5.0000000e-015 4.7000000e+000 2.6758315e-004 2.2357875e-005 2.7104170e-006 5.0000000e-015 5.0000000e-015 4.7400000e+000 2.5268200e-004 1.5906835e-005 8.5850300e-008 5.0000000e-015 5.0000000e-015 4.7800000e+000 2.3947330e-004 1.1626585e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 4.8200000e+000 2.2422875e-004 6.5614150e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 4.8600000e+000 2.0962195e-004 6.8680250e-007 5.0000000e-015 5.0000000e-015 5.0000000e-015 4.9000000e+000 1.9126220e-004 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 4.9400000e+000 1.6566655e-004 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 4.9800000e+000 1.4832480e-004 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0200000e+000 1.3520200e-004 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0600000e+000 1.1903760e-004 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.1000000e+000 1.0272600e-004 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.1400000e+000 8.9137150e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.1800000e+000 7.4456750e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.2200000e+000 6.5405650e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.2600000e+000 5.8917850e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.3000000e+000 5.0872450e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.3400000e+000 4.3673280e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.3800000e+000 3.3530680e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.4200000e+000 2.5423955e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.4600000e+000 2.1805980e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.5000000e+000 2.0788040e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.5400000e+000 1.9242735e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.5800000e+000 1.7390820e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.6200000e+000 1.6213445e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.6600000e+000 1.4263415e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.7000000e+000 1.2570940e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.7400000e+000 9.9218450e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.7800000e+000 6.3651850e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.8200000e+000 2.8207960e-007 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015