! This file contains data for 5 basis functions for the 3-pt 3rd-order correlation T_{ijk} in homogeneous, isotropic, stationary turbulence. ! These functions are specifically 2nd order asymptotic forms for small s. ! This file is organized as follows: for each basis function we list its norm, followed by its 14 tensor components. ! For each tensor component, we list the number of terms, followed by row vectors of coefficients, g powers, and s powers of the terms. ! Tensor components are denoted as three characters: ! rrr = r_i*r_j*r_k ! rrs = r_i*r_j*s_k ! rsr = r_i*s_j*r_k ! srr = s_i*r_j*r_k ! sss = s_i*s_j*s_k ! ssr = s_i*s_j*r_k ! srs = s_i*r_j*s_k ! rss = r_i*s_j*s_k ! rdd = r_i*DELTA_jk ! drd = r_j*DELTA_ik ! ddr = r_k*DELTA_ij ! sdd = s_i*DELTA_jk ! dsd = s_j*DELTA_ik ! dds = s_k*DELTA_ij ! base1 norm 1920 ! rrr 6 960 -384 2016 -576 1536 -1440 0 0 1 2 2 3 1 2 2 1 2 2 ! rrs 6 792 -192 -1152 -2448 768 2040 0 1 1 2 3 4 1 0 1 1 0 1 ! rsr 4 768 -2496 4992 -3456 0 1 1 2 1 0 1 1 ! srr 6 -1560 -192 -1152 144 768 1800 0 1 1 2 3 4 1 0 1 1 0 1 ! sss 5 -648 288 720 -96 -72 0 1 2 3 4 -1 -2 -1 -2 -1 ! ssr 5 288 -1152 1440 96 -864 0 0 1 2 3 -1 0 0 -1 0 ! srs 7 432 768 1464 -1056 -2064 -144 -360 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! rss 5 288 -1152 1344 96 384 0 0 1 2 3 -1 0 0 -1 0 ! rdd 7 -192 -288 1152 -3456 1056 -2304 2304 0 0 0 1 2 2 3 0 1 2 2 1 2 2 ! drd 9 128 -528 -768 -936 672 1536 2832 -912 -2280 0 0 0 1 2 2 3 4 5 0 1 2 2 1 2 2 1 2 ! ddr 7 -192 -288 1152 1056 1056 -2304 864 0 0 0 1 2 2 3 0 1 2 2 1 2 2 ! sdd 7 256 1704 -864 768 -2544 416 1224 0 0 1 1 2 3 4 0 1 0 1 1 0 1 ! dsd 7 -64 -552 1632 -1536 1392 -608 -456 0 0 1 1 2 3 4 0 1 0 1 1 0 1 ! dds 7 -64 -552 -864 768 -624 416 24 0 0 1 1 2 3 4 0 1 0 1 1 0 1 ! base2 norm 1155840 ! rrr 8 285600 -33600 690480 -262080 698880 -957600 151200 529200 0 0 1 2 2 3 4 5 1 2 2 1 2 2 1 2 ! rrs 8 158760 -36960 -362880 27720 127680 600600 -90720 -370440 0 1 1 2 3 4 5 6 1 0 1 1 0 1 0 1 ! rsr 6 -28560 -228480 -248640 -272160 40320 25200 0 1 1 2 3 4 1 0 1 1 0 1 ! srr 8 -407400 -36960 -362880 -259560 127680 340200 -90720 -264600 0 1 1 2 3 4 5 6 1 0 1 1 0 1 0 1 ! sss 7 -37800 -10080 63000 -33600 -63000 30240 37800 0 1 2 3 4 5 6 -1 -2 -1 -2 -1 -2 -1 ! ssr 7 -30240 20160 -15120 33600 50400 -30240 -15120 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! srs 9 146160 188160 212520 -102480 -150360 -65520 -299880 75600 264600 0 0 1 2 3 4 5 6 7 -1 0 0 -1 0 -1 0 -1 0 ! rss 7 -30240 20160 183120 33600 3360 -30240 -45360 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! rdd 9 -115584 171360 -70560 -498960 47040 211680 -252000 10080 45360 0 0 0 1 2 2 3 4 5 0 1 2 2 1 2 2 1 2 ! drd 11 77056 -260400 -147840 -390600 260400 154560 1119720 -364560-1319640 136080 476280 0 0 0 1 2 2 3 4 5 6 7 0 1 2 2 1 2 2 1 2 1 2 ! ddr 9 -115584 171360 -70560 576240 47040 211680 352800 10080 5040 0 0 0 1 2 2 3 4 5 0 1 2 2 1 2 2 1 2 ! sdd 9 154112 125160 -110880 -114240 241080 38080 12600 -6048 -22680 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! dsd 9 -38528 41160 178080 288960 177240 -145600 -172200 54432 68040 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! dds 9 -38528 -185640 -110880 -114240 -513240 38080 121800 -6048 -7560 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! base3 norm 1257600 ! rrr 8 301680 -16320 353160 99360 99840 236400 6000 21000 0 0 1 2 2 3 4 5 1 2 2 1 2 2 1 2 ! rrs 8 -26940 -480 -382080 -551700 59520 219900 7200 18900 0 1 1 2 3 4 5 6 1 0 1 1 0 1 0 1 ! rsr 6 9480 -320640 60480 -494640 -24000 -63000 0 1 1 2 3 4 1 0 1 1 0 1 ! srr 8 -274260 -480 -382080 272340 59520 35700 7200 31500 0 1 1 2 3 4 5 6 1 0 1 1 0 1 0 1 ! sss 7 -67980 -69840 20460 24960 43020 3600 4500 0 1 2 3 4 5 6 -1 -2 -1 -2 -1 -2 -1 ! ssr 7 107520 -98880 190920 1440 -191760 -7200 33480 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! srs 9 -9240 357120 184380 -188520 -312780 -14760 -71100 9000 31500 0 0 1 2 3 4 5 6 7 -1 0 0 -1 0 -1 0 -1 0 ! rss 7 107520 -98880 234840 1440 189360 -7200 -76680 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! rdd 9 -125760 141360 11040 -243000 181440 -17760 765360 13200 -29880 0 0 0 1 2 2 3 4 5 0 1 2 2 1 2 2 1 2 ! drd 11 83840 -15960 -433920 262380 -270360 859200 -309780 -47880 -114300 -1800 -6300 0 0 0 1 2 2 3 4 5 6 7 0 1 2 2 1 2 2 1 2 1 2 ! ddr 9 -125760 141360 11040 21480 181440 -17760 -273840 13200 95880 0 0 0 1 2 2 3 4 5 0 1 2 2 1 2 2 1 2 ! sdd 9 167680 -52380 -63360 -79680 -730620 38240 315660 10080 -28980 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! dsd 9 -41920 133380 -250800 411840 46260 -24320 -10740 -720 -900 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! dds 9 -41920 -25620 -63360 -79680 371100 38240 -264540 10080 79380 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! base4 norm 462720 ! rrr 8 107904 -15936 58752 103104 -9216 286560 -14400 -50400 0 0 1 2 2 3 4 5 1 2 2 1 2 2 1 2 ! rrs 8 -76968 25248 -200448 -420192 9408 45240 21600 75600 0 1 1 2 3 4 5 6 1 0 1 1 0 1 0 1 ! rsr 6 7776 -123456 32448 -184896 -34560 -79200 0 1 1 2 3 4 1 0 1 1 0 1 ! srr 8 -56184 25248 -200448 364608 9408 -91800 21600 75600 0 1 1 2 3 4 5 6 1 0 1 1 0 1 0 1 ! sss 5 -20856 -57120 -33072 25824 53928 0 1 2 3 4 -1 -2 -1 -2 -1 ! ssr 7 83328 -57408 94080 5856 -121824 -4320 21600 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! srs 7 -67824 202752 21000 -80160 -86160 -21744 -75960 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! rss 7 83328 -57408 75744 5856 181824 -4320 -64800 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! rdd 9 -46272 46176 4128 31968 78816 -17376 581184 14400 -21600 0 0 0 1 2 2 3 4 5 0 1 2 2 1 2 2 1 2 ! drd 11 30848 81840 -254592 265560 -224640 527424 -386976 25008 127320 -21600 -75600 0 0 0 1 2 2 3 4 5 6 7 0 1 2 2 1 2 2 1 2 1 2 ! ddr 9 -46272 46176 4128 -143424 78816 -17376 -402336 14400 93600 0 0 0 1 2 2 3 4 5 0 1 2 2 1 2 2 1 2 ! sdd 9 61696 -97752 13056 -43968 -558336 2336 202824 12960 -10800 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! dsd 9 -15424 87096 -256032 246336 -33504 11872 26904 -8640 -10800 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! dds 9 -15424 38520 13056 -43968 485568 2336 -275016 12960 75600 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! base5 norm 10684800 ! rrr 8 2343600 -100800 2517480 997920 1128960 2242800 126000 441000 0 0 1 2 2 3 4 5 1 2 2 1 2 2 1 2 ! rrs 8 -520380 110880-3427200-4600260 282240 1215900 151200 396900 0 1 1 2 3 4 5 6 1 0 1 1 0 1 0 1 ! rsr 6 -284760-1774080-1874880-2404080 -504000-1323000 0 1 1 2 3 4 1 0 1 1 0 1 ! srr 8 -1934100 110880-3427200 3088260 282240 -686700 151200 661500 0 1 1 2 3 4 5 6 1 0 1 1 0 1 0 1 ! sss 7 -233100 -922320 -628740 342720 767340 75600 94500 0 1 2 3 4 5 6 -1 -2 -1 -2 -1 -2 -1 ! ssr 7 866880 -383040 682920 211680 -821520 -151200 -22680 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! srs 9 -345240 3144960 832860-1116360 -792540 -582120-2173500 189000 661500 0 0 1 2 3 4 5 6 7 -1 0 0 -1 0 -1 0 -1 0 ! rss 7 866880 -383040 1423800 211680 2283120 -151200 -884520 0 0 1 2 3 4 5 -1 0 0 -1 0 -1 0 ! rdd 9 -1068480 1456560 -493920 -748440 967680 1078560 5911920 277200 98280 0 0 0 1 2 2 3 4 5 0 1 2 2 1 2 2 1 2 ! drd 11 712320 118440-3790080 2531340-2472120 7398720-3088260 -309960 -661500 -37800 -132300 0 0 0 1 2 2 3 4 5 6 7 0 1 2 2 1 2 2 1 2 1 2 ! ddr 9 -1068480 1456560 -493920 269640 967680 1078560-4117680 277200 1287720 0 0 0 1 2 2 3 4 5 0 1 2 2 1 2 2 1 2 ! sdd 9 1424640-1266300 -60480-1189440-5394060 -23520 1684620 211680 117180 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! dsd 9 -356160 1515780-3150000 4777920 -268380 -47040 122220 -15120 -18900 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1 ! dds 9 -356160 -129780 -60480-1189440 4436460 -23520-3090780 211680 941220 0 0 1 1 2 3 4 5 6 0 1 0 1 1 0 1 0 1