*** LDV-data of Christoffer Norberg (1998) *** Source: C. Norberg, LDV-measurements in the near wake of a circular cylinder. In Advances in Understanding of Bluff Body wakes and Flow-Induced Vibration, Proc. 1998 ASME Fluids Engineering Division, Washington DC, USA, June 1998 (eds. C. H. K. Williamson & P. W. Bearman), pages 1-12, New York: ASME, 1998 (FEDSM98-5202). Abbreviations (scaling with cylinder diameter and free-stream velocity): x - streamwise distance from cylinder centre y - cross-stream distance from cylinder centre um - time-mean streamwise velocity up - streamwise RMS velocity wp - spanwise RMS velocity su - skewness of streamwise velocity fluctuations Re - Reynolds number N - number of positions in each data-set Note: In the above paper, the data for y<0 at x=const. has been folded. I. y=0 (a) Re=1.5E+03 N=49 x um up wp su .5167 -.0016 .0100 .0870 -2.310 .5667 -.0140 .0574 .1249 -1.889 .6167 -.0286 .0899 .1213 -1.485 .6667 -.0377 .1106 .1208 -1.451 .7150 -.0483 .1213 .1242 -1.223 .7650 -.0616 .1384 .1275 -1.210 .8150 -.0631 .1470 .1384 -1.190 .8650 -.0769 .1577 .1522 -.980 .9150 -.0829 .1704 .1530 -.945 .9650 -.0917 .1842 .1582 -.858 1.0150 -.1005 .1964 .1745 -.770 1.0650 -.1138 .2078 .1865 -.696 1.1150 -.1286 .2203 .1901 -.564 1.1650 -.1545 .2387 .2031 -.451 1.2150 -.1644 .2470 .2148 -.343 1.2650 -.1982 .2647 .2192 -.259 1.3167 -.2218 .2774 .2397 -.095 1.3667 -.2423 .2855 .2400 -.043 1.4167 -.2805 .2948 .2642 .104 1.4667 -.3010 .2979 .2792 .198 1.5167 -.3255 .3018 .2771 .283 1.5667 -.3496 .2977 .2964 .429 1.6167 -.3714 .2966 .3081 .554 1.6667 -.3852 .2925 .3288 .612 1.7167 -.3899 .2891 .3356 .649 1.7500 -.4016 .2782 .3332 .726 1.7667 -.3982 .2855 .3416 .736 1.8167 -.3940 .2790 .3491 .698 1.8667 -.3743 .2868 .3496 .721 1.9167 -.3655 .2834 .3527 .701 1.9667 -.3332 .2868 .3491 .744 2.0167 -.2938 .2995 .3587 .496 2.0650 -.2569 .3088 .3655 .450 2.1333 -.1751 .3171 .3608 .286 2.2167 -.0790 .3184 .3569 .070 2.3000 .0257 .3192 .3481 -.089 2.4167 .1421 .2982 .3442 -.407 2.5167 .2421 .2797 .3083 -.592 2.6667 .3436 .2558 .2852 -.697 2.8333 .4332 .2288 .2545 -.818 3.0000 .5031 .2083 .2405 -.662 3.1667 .5751 .1935 .2203 -.491 3.3333 .6075 .1951 .1974 -.693 3.5000 .6382 .1855 .1862 -.489 3.8333 .6930 .1787 .1797 -.595 4.6667 .7486 .1777 .1629 -.351 5.5000 .7662 .1805 .1636 -.154 6.3333 .7709 .1756 .1592 -.041 7.1667 .7740 .1719 .1610 .044 --- (b) Re=3.0E+03 N=49 x um up wp su .5167 -.0036 .0206 .1338 -1.813 .5667 -.0205 .0812 .1545 -1.346 .6167 -.0412 .1160 .1414 -1.193 .6667 -.0509 .1377 .1453 -1.172 .7150 -.0627 .1535 .1542 -1.098 .7650 -.0729 .1662 .1529 -1.032 .8150 -.0839 .1796 .1605 -.975 .8650 -.0917 .1908 .1713 -.897 .9150 -.1056 .2056 .1851 -.803 .9650 -.1210 .2231 .1981 -.724 1.0150 -.1435 .2439 .2136 -.617 1.0650 -.1544 .2545 .2274 -.551 1.1150 -.1770 .2673 .2388 -.377 1.1650 -.2058 .2874 .2481 -.267 1.2150 -.2312 .3001 .2594 -.136 1.2650 -.2656 .3161 .2786 -.021 1.3167 -.2966 .3183 .2927 .084 1.3667 -.3265 .3209 .2952 .186 1.4167 -.3660 .3283 .3130 .341 1.4667 -.3949 .3286 .3349 .417 1.5167 -.4070 .3261 .3525 .497 1.5667 -.4199 .3208 .3621 .609 1.6167 -.4438 .3131 .3753 .601 1.6667 -.4343 .3126 .3761 .665 1.7167 -.4325 .3066 .3808 .693 1.7500 -.4173 .3051 .3913 .643 1.7667 -.4165 .3056 .3705 .615 1.8167 -.3810 .3109 .3878 .589 1.8667 -.3470 .3153 .3942 .545 1.9167 -.2973 .3192 .3919 .474 1.9583 -.2590 .3252 .3862 .369 2.0000 -.1983 .3342 .3848 .257 2.0833 -.1096 .3336 .3757 .078 2.1667 .0175 .3303 .3609 -.233 2.2500 .1268 .3221 .3491 -.386 2.3333 .2043 .3032 .3422 -.545 2.4167 .2756 .2801 .3099 -.672 2.5000 .3532 .2513 .2916 -.804 2.6667 .4427 .2312 .2522 -.865 2.8333 .5165 .2044 .2340 -.674 3.0000 .5769 .1945 .2234 -.647 3.1667 .6234 .1826 .2070 -.554 3.3333 .6518 .1778 .2029 -.485 3.5000 .6773 .1771 .1918 -.527 3.8333 .7142 .1740 .1861 -.347 4.6667 .7536 .1816 .1773 -.252 5.5000 .7712 .1801 .1729 -.122 6.3333 .7823 .1765 .1675 .045 7.1667 .7905 .1725 .1666 .055 --- (c) Re=5.0E+03 N=49 x um up wp su .5167 -.0048 .0279 .1548 -2.205 .5667 -.0309 .1278 .1952 -1.087 .6167 -.0610 .1765 .1811 -.865 .6667 -.0863 .2000 .1809 -.779 .7150 -.1072 .2185 .1892 -.761 .7650 -.1219 .2363 .1974 -.636 .8150 -.1439 .2525 .2020 -.585 .8650 -.1639 .2671 .2202 -.509 .9150 -.1865 .2842 .2376 -.396 .9650 -.2085 .3044 .2458 -.342 1.0150 -.2412 .3161 .2613 -.204 1.0650 -.2718 .3294 .2813 -.074 1.1150 -.3058 .3333 .2864 .045 1.1650 -.3394 .3449 .3060 .191 1.2150 -.3776 .3524 .3218 .237 1.2650 -.4058 .3454 .3378 .372 1.3167 -.4338 .3444 .3580 .499 1.3667 -.4466 .3364 .3585 .525 1.4167 -.4495 .3345 .3731 .572 1.4667 -.4454 .3295 .3825 .595 1.5167 -.4307 .3318 .3802 .608 1.5667 -.4028 .3282 .3897 .515 1.6167 -.3611 .3369 .3900 .477 1.6667 -.3049 .3478 .3907 .426 1.7167 -.2611 .3530 .3841 .309 1.7500 -.2161 .3584 .3804 .270 1.7667 -.2073 .3571 .3724 .239 1.8167 -.1186 .3636 .3679 .041 1.8667 -.0367 .3608 .3584 -.126 1.9167 .0185 .3559 .3517 -.189 1.9583 .1036 .3496 .3380 -.436 2.0000 .1423 .3329 .3345 -.502 2.0833 .2166 .3161 .3167 -.641 2.1667 .3128 .2793 .2904 -.805 2.2500 .3737 .2643 .2785 -.871 2.3333 .4286 .2467 .2591 -.856 2.4167 .4691 .2304 .2486 -.880 2.5000 .5125 .2175 .2382 -.882 2.6667 .5764 .2005 .2209 -.837 2.8333 .6233 .1880 .2005 -.834 3.0000 .6511 .1838 .1929 -.713 3.1667 .6759 .1778 .1849 -.635 3.3333 .7028 .1778 .1921 -.523 3.5000 .7252 .1733 .1835 -.381 3.8333 .7417 .1843 .1811 -.312 4.6667 .7672 .1865 .1749 -.075 5.5000 .7854 .1885 .1770 .001 6.3333 .7932 .1844 .1677 .100 7.1667 .7989 .1790 .1708 .137 --- (d) Re=8.0E+03 N=42 x um up wp su .5250 -.0312 .1265 .2579 -1.145 .5750 -.0647 .1949 .2349 -.804 .6250 -.1040 .2444 .2227 -.610 .6750 -.1502 .2829 .2338 -.524 .7233 -.1765 .3027 .2520 -.431 .7733 -.2038 .3201 .2614 -.426 .8233 -.2145 .3344 .2701 -.373 .8733 -.2479 .3449 .2864 -.230 .9233 -.2749 .3535 .3087 -.092 .9733 -.2990 .3748 .3305 .023 1.0233 -.3199 .3729 .3419 .089 1.0733 -.3385 .3786 .3499 .271 1.1233 -.3365 .3750 .3534 .315 1.1733 -.3520 .3793 .3622 .372 1.2233 -.3465 .3887 .3761 .449 1.2733 -.3088 .4136 .3860 .477 1.3250 -.3511 .3916 .3729 .538 1.3750 -.2945 .4153 .3833 .444 1.4500 -.2479 .4274 .3856 .407 1.5500 -.1589 .4448 .3830 .223 1.6500 -.0148 .4472 .3737 -.086 1.7528 .1108 .4314 .3461 -.376 1.8250 .1703 .4207 .3335 -.514 1.9000 .2204 .3963 .3200 -.621 1.9875 .3302 .3534 .2865 -.871 2.0917 .3957 .3157 .2847 -.950 2.1750 .4486 .2908 .2698 -1.019 2.2583 .4819 .2693 .2581 -.968 2.3417 .5533 .2404 .2463 -.950 2.4250 .5628 .2321 .2339 -.970 2.5083 .6018 .2156 .2228 -.949 2.6750 .6373 .1972 .2191 -.833 2.8417 .6508 .1928 .2093 -.745 3.0083 .6750 .1859 .2058 -.671 3.1750 .6962 .1816 .1970 -.712 3.3417 .7197 .1804 .1905 -.680 3.5083 .7243 .1790 .1894 -.658 3.8417 .7414 .1804 .1935 -.627 4.6750 .7627 .1813 .1909 -.466 5.5083 .7632 .1818 .1836 -.344 6.3417 .7777 .1809 .1803 -.307 7.1750 .7840 .1754 .1796 -.302 --- (e) Re=1.0E+04 N=39 x um up wp su .5167 -.0205 .1021 .2742 -1.528 .6000 -.1230 .2773 .2475 -.371 .6833 -.2102 .3253 .2571 -.235 .7667 -.2547 .3461 .2979 -.081 .8483 -.3129 .3598 .3170 .059 .9317 -.3564 .3706 .3452 .209 1.0150 -.3836 .3657 .3537 .355 1.0983 -.3815 .3729 .3731 .477 1.1667 -.3454 .3779 .3731 .423 1.2167 -.3381 .3849 .3767 .459 1.2650 -.3004 .3869 .3859 .383 1.3167 -.2373 .4025 .3741 .264 1.3650 -.1972 .4131 .3719 .189 1.4167 -.1688 .4253 .3600 .158 1.4667 -.0507 .4296 .3484 -.140 1.5150 .0106 .4275 .3452 -.282 1.5667 .0465 .4269 .3355 -.332 1.6150 .1101 .4141 .3253 -.509 1.6667 .1874 .3960 .3159 -.697 1.7167 .2478 .3728 .3047 -.882 1.7650 .2688 .3663 .2934 -.884 1.8167 .3120 .3518 .2870 -1.004 1.8650 .3777 .3166 .2767 -1.146 1.9167 .3958 .3034 .2767 -1.131 1.9667 .4278 .2897 .2654 -1.300 2.0167 .4553 .2756 .2544 -1.167 2.0650 .4761 .2727 .2498 -1.152 2.1150 .4807 .2611 .2449 -1.137 2.1667 .5314 .2334 .2389 -1.115 2.3333 .5776 .2153 .2241 -1.042 2.5000 .6159 .1987 .2231 -.997 2.6667 .6445 .1929 .2060 -.783 2.8333 .6710 .1899 .2087 -.663 3.0000 .6890 .1892 .2048 -.699 3.4167 .7166 .1882 .1895 -.614 3.8333 .7198 .1959 .2032 -.504 4.6667 .7383 .1951 .1902 -.352 5.5000 .7480 .1910 .1940 -.234 6.3333 .7564 .1853 .1866 -.230 --- II. x=0.6 (a) Re=3.0E+03 (1) N=30 y um up wp su -.6007 .6348 .3454 .0590 -.107 -.5857 .4373 .3195 .0760 .411 -.5690 .2394 .2416 .0947 .763 -.5507 .0930 .1691 .1111 .367 -.5023 -.0366 .1062 .1251 -.954 -.3357 -.0426 .1062 .1242 -1.208 -.1690 -.0372 .1116 .1300 -1.206 -.0190 -.0326 .1100 .1355 -1.133 .0143 -.0346 .1107 .1347 -1.276 .1643 -.0409 .1133 .1298 -1.335 .3310 -.0383 .1037 .1239 -1.281 .4143 -.0481 .0988 .1263 -1.151 .4810 -.0487 .1006 .1225 -.987 .4977 -.0432 .1046 .1264 -.930 .5127 -.0305 .1104 .1200 -.719 .5310 .0035 .1237 .1102 -.109 .5460 .0606 .1547 .0964 .372 .5643 .1899 .2235 .0818 .995 .5727 .2649 .2640 .0696 .960 .5810 .3635 .3066 .0581 .809 .5877 .4554 .3380 .0506 .555 .5960 .5849 .3584 .0443 .235 .6060 .7350 .3617 .0363 -.176 .6143 .8432 .3460 .0315 -.475 .6293 1.0209 .2946 .0222 -1.044 .6643 1.2473 .1355 .0162 -2.306 .7477 1.3076 .0230 .0135 -.150 .8310 1.2829 .0218 .0125 -.114 .9977 1.2467 .0197 .0108 -.286 1.3310 1.1828 .0193 .0093 -.222 --- (b) Re=3.0E+03 (2) N=8 y um up wp su .6060 .7581 .3741 .0340 -.275 .6143 .8578 .3571 .0293 -.554 .6227 .9650 .3295 .0257 -.886 .6293 1.0226 .3026 .0230 -1.086 .6477 1.1673 .2144 .0182 -1.697 .6643 1.2396 .1438 .0173 -2.216 .6960 1.3066 .0483 .0149 -2.847 .7477 1.3086 .0234 .0138 -.286 --- (c) Re=5.0E+03 (1) N=42 y um up wp su -1.3360 1.1709 .0286 .0125 .034 -1.0027 1.2540 .0326 .0146 .010 -.8360 1.2923 .0350 .0168 .111 -.7527 1.3280 .0391 .0197 .099 -.7010 1.3443 .0443 .0238 -2.124 -.6693 1.3275 .0796 .0272 -4.412 -.6527 1.2889 .1344 .0292 -3.690 -.6343 1.2144 .2308 .0395 -2.633 -.6193 1.0946 .3284 .0551 -1.647 -.6010 .8873 .4434 .0862 -.693 -.5860 .6370 .4770 .1189 .097 -.5693 .3313 .4036 .1406 1.028 -.5510 .1196 .2622 .1515 1.509 -.5360 .0540 .1981 .1523 1.040 -.5027 -.0183 .1415 .1551 -.726 -.4677 -.0272 .1385 .1560 -.908 -.4193 -.0350 .1409 .1502 -1.029 -.3360 -.0429 .1543 .1586 -1.020 -.1693 -.0590 .1663 .1738 -.959 -.0860 -.0662 .1745 .1780 -.892 -.0193 -.0601 .1692 .1740 -.906 .0140 -.0611 .1712 .1754 -.965 .0807 -.0611 .1684 .1736 -.945 .1640 -.0585 .1693 .1680 -.925 .3307 -.0437 .1541 .1587 -1.097 .4140 -.0310 .1403 .1529 -.956 .4623 -.0305 .1375 .1507 -.927 .4973 -.0199 .1406 .1537 -.753 .5307 .0273 .1777 .1508 .679 .5457 .0901 .2288 .1363 1.499 .5640 .2499 .3595 .1150 1.419 .5807 .5083 .4826 .0889 .563 .5957 .7931 .4947 .0639 -.266 .6140 1.0657 .3898 .0450 -1.281 .6290 1.2146 .2687 .0317 -2.251 .6473 1.2945 .1673 .0271 -3.593 .6640 1.3300 .1054 .0266 -5.426 .6957 1.3365 .0415 .0214 -1.627 .7473 1.3124 .0334 .0193 .090 .8307 1.2907 .0304 .0173 .095 .9973 1.2475 .0283 .0151 -.042 1.3307 1.1781 .0252 .0134 -.071 --- (d) Re=5.0E+03 (2) N=14 y um up wp su -.6190 1.0904 .3338 .0512 -1.568 -.6107 1.0116 .3855 .0659 -1.161 -.6007 .8900 .4491 .0860 -.679 -.5923 .7430 .4752 .1016 -.233 -.5857 .6169 .4766 .1142 .147 -.5773 .4647 .4463 .1219 .603 -.5690 .3280 .3974 .1348 1.014 .5643 .2608 .3666 .1109 1.353 .5727 .3792 .4310 .0953 .990 .5810 .5268 .4781 .0834 .513 .5893 .7008 .5003 .0683 .001 .5977 .8526 .4798 .0581 -.432 .6060 .9714 .4330 .0481 -.883 .6143 1.0666 .3882 .0432 -1.282 --- (e) Re=8.0E+03 N=30 y um up wp su -.6026 1.1221 .4657 .1161 -1.423 -.5876 .9261 .5695 .1475 -.629 -.5709 .7008 .6171 .1711 .019 -.5526 .4563 .5866 .1864 .668 -.5042 .0687 .2909 .2056 1.554 -.3376 -.0506 .2330 .2118 -.880 -.1709 -.1008 .2423 .2179 -.703 -.0209 -.1021 .2487 .2236 -.585 .0124 -.1142 .2503 .2255 -.507 .1624 -.0909 .2338 .2156 -.761 .3291 -.0559 .2235 .2035 -.900 .4124 -.0166 .2223 .2030 -.788 .4791 .0272 .2317 .2025 .463 .4958 .0412 .2551 .2047 .915 .5107 .0903 .3250 .1977 1.714 .5291 .2000 .4414 .1906 1.580 .5441 .3198 .5274 .1785 1.179 .5624 .5767 .6263 .1578 .390 .5707 .7040 .6267 .1401 .054 .5791 .7920 .6132 .1258 -.222 .5857 .9612 .5834 .1074 -.689 .5941 1.0143 .5514 .0983 -.893 .6041 1.1216 .4803 .0822 -1.347 .6124 1.1849 .4160 .0741 -1.776 .6274 1.2889 .2836 .0594 -2.876 .6624 1.3528 .1096 .0395 -6.522 .7458 1.3348 .0402 .0272 -.446 .8291 1.3089 .0357 .0220 -.183 .9958 1.2521 .0306 .0177 -.307 1.3291 1.1773 .0256 .0142 -.582 --- III. x=1.0 (a) Re=3.0E+03 N=70 y um up wp su -2.5158 1.0816 .0203 .0052 -.177 -1.6825 1.1435 .0243 .0066 -.132 -1.2658 1.2014 .0281 .0084 -.129 -.8492 1.2930 .0342 .0142 -.080 -.6825 1.2457 .1349 .0332 -2.569 -.5158 .0169 .2032 .1666 -.336 -.1825 -.0997 .2196 .1917 -.682 -.0992 -.1203 .2264 .1939 -.685 -.0158 -.1309 .2288 .1951 -.635 .0258 -.1288 .2274 .1964 -.653 .0675 -.1282 .2305 .1951 -.636 .1092 -.1206 .2266 .1982 -.663 .1508 -.1134 .2260 .1903 -.687 .1842 -.1038 .2255 .1903 -.692 .2158 -.0996 .2244 .1917 -.731 .2508 -.0838 .2196 .1831 -.717 .2842 -.0778 .2170 .1844 -.721 .3008 -.0743 .2173 .1826 -.751 .3175 -.0629 .2138 .1796 -.713 .3342 -.0660 .2160 .1795 -.748 .3508 -.0595 .2090 .1835 -.670 .3675 -.0604 .2077 .1764 -.681 .3842 -.0506 .2003 .1783 -.645 .4008 -.0501 .1992 .1743 -.701 .4175 -.0461 .2027 .1743 -.685 .4342 -.0397 .1974 .1740 -.715 .4508 -.0394 .1913 .1690 -.651 .4675 -.0288 .1942 .1706 -.630 .4842 -.0252 .1943 .1668 -.505 .5008 -.0112 .1930 .1714 -.572 .5175 .0104 .1990 .1657 -.416 .5342 .0510 .2118 .1608 -.201 .5508 .1147 .2370 .1483 .049 .5675 .2156 .2709 .1312 .520 .5842 .3574 .3200 .1025 .525 .6008 .5551 .3660 .0861 .190 .6175 .7535 .3622 .0701 -.227 .6342 .9375 .3309 .0514 -.701 .6508 1.0758 .2751 .0403 -1.176 .6675 1.1758 .2109 .0295 -1.591 .6842 1.2500 .1518 .0286 -2.025 .7008 1.3004 .0973 .0248 -2.980 .7175 1.3209 .0623 .0210 -2.864 .7342 1.3287 .0425 .0201 -3.505 .7508 1.3226 .0317 .0179 -.945 .7675 1.3165 .0299 .0174 -1.204 .7842 1.3114 .0277 .0169 -.761 .8008 1.3052 .0279 .0155 -1.449 .8175 1.3068 .0256 .0148 -.391 .8342 1.2997 .0240 .0143 -.306 .8508 1.2951 .0242 .0135 -.303 .8675 1.2914 .0244 .0134 -.271 .8842 1.2895 .0234 .0127 -.303 .9008 1.2831 .0234 .0125 -.340 .9175 1.2783 .0222 .0122 -.326 .9342 1.2739 .0225 .0122 -.379 .9508 1.2674 .0223 .0118 -.407 .9675 1.2669 .0225 .0122 -.417 .9842 1.2623 .0217 .0110 -.388 1.0008 1.2608 .0217 .0112 -.366 1.0258 1.2504 .0219 .0108 -.296 1.0675 1.2342 .0219 .0104 -.226 1.1508 1.2264 .0208 .0104 -.283 1.2342 1.2126 .0201 .0088 -.397 1.3175 1.1971 .0201 .0087 -.269 1.4842 1.1692 .0190 .0088 -.354 1.6508 1.1496 .0188 .0066 -.290 1.9842 1.1162 .0168 .0057 -.474 2.4842 1.0816 .0188 .0053 -1.231 2.4842 1.0853 .0177 .0055 -.295 --- (b) Re=5.0E+03 (1) N=69 y um up wp su -2.5592 1.0658 .0213 .0107 -.458 -1.7258 1.1228 .0272 .0118 -.284 -1.3092 1.1765 .0325 .0131 -.279 -.8925 1.2775 .0410 .0187 -.380 -.7258 1.3287 .0677 .0334 -2.416 -.5925 .8695 .4847 .1586 -.626 -.5742 .6504 .5019 .1787 -.024 -.5592 .5022 .4883 .2017 .331 -.5592 .4526 .4744 .1951 .212 -.5425 .3352 .4301 .2108 .440 -.2258 -.1487 .3435 .2568 -.390 -.0592 -.2254 .3139 .2584 -.249 -.0175 -.2369 .3128 .2601 -.191 .0242 -.2305 .3152 .2566 -.236 .0658 -.2213 .3102 .2526 -.212 .1075 -.2167 .3204 .2547 -.209 .1408 -.1941 .3248 .2594 -.270 .1725 -.1819 .3318 .2580 -.246 .2075 -.1630 .3402 .2556 -.288 .2408 -.1361 .3485 .2515 -.370 .2575 -.1247 .3509 .2495 -.357 .2742 -.1121 .3474 .2403 -.417 .2908 -.1015 .3545 .2508 -.395 .3075 -.0793 .3492 .2543 -.478 .3242 -.0670 .3587 .2427 -.464 .3408 -.0499 .3526 .2397 -.516 .3575 -.0457 .3522 .2403 -.592 .3742 -.0313 .3540 .2370 -.562 .3908 -.0169 .3474 .2268 -.592 .4075 .0067 .3474 .2304 -.629 .4242 .0147 .3439 .2353 -.611 .4408 .0369 .3371 .2199 -.606 .4408 .0404 .3424 .2286 -.615 .4558 .0546 .3347 .2230 -.529 .4742 .0781 .3360 .2249 -.459 .4892 .1060 .3411 .2192 -.316 .5075 .1460 .3462 .2155 -.008 .5242 .2207 .3934 .2116 .330 .5392 .2974 .4185 .2001 .507 .5575 .4117 .4607 .1801 .453 .5725 .6328 .5206 .1609 .035 .5908 .8623 .5025 .1331 -.530 .6075 1.0382 .4353 .1043 -1.059 .6225 1.1299 .3565 .0882 -1.566 .6392 1.2364 .2695 .0648 -2.361 .6575 1.2854 .1978 .0556 -2.965 .6742 1.3158 .1325 .0504 -3.564 .6908 1.3269 .0966 .0406 -4.035 .7058 1.3369 .0742 .0374 -3.581 .7225 1.3379 .0617 .0314 -3.188 .7408 1.3168 .0519 .0304 -2.430 .7575 1.3097 .0454 .0267 -1.653 .7742 1.3145 .0461 .0249 -4.500 .7892 1.3114 .0407 .0240 -.700 .8058 1.3061 .0365 .0225 -.529 .8408 1.2980 .0370 .0205 -.674 .8725 1.2787 .0337 .0190 -.582 .9075 1.2705 .0325 .0182 -.507 .9408 1.2613 .0317 .0176 -.663 .9825 1.2526 .0293 .0170 -.639 1.0242 1.2402 .0392 .0165 -23.432 1.1075 1.2130 .0301 .0157 -.560 1.1908 1.1988 .0297 .0152 -.421 1.2742 1.1873 .0285 .0142 -.414 1.4408 1.1600 .0257 .0138 -.336 1.6075 1.1385 .0237 .0129 -.310 1.9408 1.1135 .0208 .0128 -.303 2.4408 1.0747 .0186 .0122 -.357 2.4408 1.0709 .0199 .0106 -.450 --- (c) Re=5.0E+03 (2) N=20 y um up wp su -1.6750 1.1433 .0270 .0130 -.304 -.7900 1.3099 .0477 .0247 -.345 -.7417 1.3283 .0575 .0358 -1.332 -.6900 1.3305 .1034 .0551 -3.731 -.6400 1.2140 .2678 .0829 -2.192 -.5917 .8212 .4947 .1595 -.491 -.5417 .3122 .4174 .2101 .395 -.0917 -.2266 .3245 .2639 -.230 -.0083 -.2425 .3136 .2594 -.222 .0750 -.2291 .3186 .2601 -.249 .1583 -.1951 .3324 .2577 -.289 .1583 -.1994 .3305 .2509 -.288 .4733 .0759 .3446 .2257 -.496 .5233 .1933 .3723 .2098 .185 .5733 .6228 .5207 .1625 .106 .6233 1.1235 .3726 .0964 -1.512 .6733 1.3064 .1496 .0589 -3.639 .7233 1.3346 .0662 .0340 -3.041 .7733 1.3202 .0474 .0275 -1.461 1.6583 1.1426 .0240 .0143 -.317 --- (d) Re=8.0E+03 N=70 y um up wp su -2.5725 1.0649 .0431 .0086 -8.859 -1.7392 1.1232 .0535 .0114 -11.253 -1.3225 1.1710 .0508 .0152 -.415 -.9058 1.2638 .0785 .0268 -3.395 -.7392 1.3250 .0870 .0453 -2.012 -.5725 .9592 .5442 .1953 -.896 -.2392 -.1377 .4352 .3177 -.053 -.1558 -.2268 .4021 .3172 .149 -.0725 -.2876 .3585 .3218 .026 -.0308 -.3000 .3415 .3185 -.029 .0108 -.2880 .3430 .3222 -.063 .0525 -.2850 .3494 .3195 -.052 .0942 -.2662 .3672 .3134 -.014 .1275 -.2545 .3700 .3199 .028 .1592 -.2210 .3935 .3108 .044 .1942 -.2006 .4083 .3063 .040 .2275 -.1606 .4300 .3073 .012 .2442 -.1444 .4300 .2966 -.064 .2608 -.1269 .4414 .2941 -.040 .2775 -.1030 .4441 .2987 -.081 .2942 -.0810 .4577 .2983 -.125 .3108 -.0649 .4531 .2947 -.082 .3275 -.0411 .4315 .2930 -.216 .3442 -.0121 .4394 .2890 -.222 .3608 .0069 .4493 .2792 -.236 .3775 .0400 .4508 .2802 -.212 .3942 .0864 .4805 .2816 -.192 .4108 .0997 .4768 .2737 -.104 .4275 .1414 .4855 .2747 -.048 .4442 .1774 .4987 .2634 .087 .4608 .2417 .5246 .2572 .210 .4775 .2993 .5426 .2520 .244 .4942 .3933 .5782 .2404 .230 .5108 .5086 .6045 .2298 .103 .5275 .6315 .6260 .2177 -.134 .5442 .7668 .6207 .1981 -.400 .5608 .8804 .5930 .1737 -.633 .5775 1.0008 .5464 .1563 -.991 .5942 1.0893 .4849 .1417 -1.285 .6108 1.1643 .4256 .1218 -1.677 .6275 1.2457 .3329 .1014 -2.436 .6442 1.2975 .2499 .0832 -2.984 .6608 1.3109 .1987 .0750 -3.492 .6775 1.3264 .1600 .0680 -3.697 .6942 1.3269 .1262 .0597 -2.855 .7108 1.3244 .1182 .0527 -3.582 .7275 1.3140 .0981 .0438 -3.940 .7442 1.3244 .0920 .0431 -2.940 .7608 1.3150 .0859 .0420 -1.847 .7775 1.3081 .0836 .0339 -4.456 .7942 1.2982 .0832 .0338 -2.908 .8108 1.2949 .0733 .0301 -1.684 .8275 1.2962 .0709 .0319 -3.828 .8442 1.2850 .0728 .0311 -1.686 .8608 1.2715 .0747 .0274 -3.194 .8775 1.2753 .0681 .0248 -3.639 .8942 1.2744 .0640 .0248 -.894 .9108 1.2550 .0750 .0256 -3.957 .9275 1.2636 .0633 .0237 -1.664 .9442 1.2489 .0645 .0232 -.815 .9692 1.2454 .0633 .0210 -1.646 1.0108 1.2419 .0636 .0207 -3.456 1.0942 1.2135 .0627 .0191 -2.019 1.1775 1.2018 .0544 .0173 -.521 1.2608 1.1794 .0567 .0162 -4.831 1.4275 1.1607 .0516 .0140 -3.730 1.5942 1.1343 .0526 .0127 -6.854 1.9275 1.1084 .0534 .0111 -11.970 2.4275 1.0771 .0463 .0095 -8.645 2.4275 1.0838 .0386 .0083 -.620 --- IV. x=2.0 (a) Re=3.5E+03 N=40 y um up wp su -.1850 .0801 .4502 .3234 -.100 -.1350 -.0310 .4196 .3420 .057 -.0850 -.1042 .3826 .3389 .167 -.0350 -.1298 .3547 .3491 .145 .0150 -.1433 .3468 .3526 .179 .0633 -.1281 .3644 .3531 .167 .1133 -.0606 .3977 .3437 .124 .1633 .0286 .4340 .3401 -.027 .2133 .1388 .4667 .3317 -.192 .2633 .2598 .4803 .3148 -.429 .3133 .3798 .4729 .3018 -.652 .3633 .5164 .4422 .2841 -.873 .4133 .6215 .4220 .2626 -.965 .4633 .7322 .4017 .2419 -.987 .5133 .8212 .3736 .2173 -.966 .5150 .8286 .3831 .2233 -1.082 .5633 .9159 .3575 .2048 -1.094 .6133 .9880 .3110 .1776 -1.163 .6633 1.0367 .2727 .1443 -1.162 .6817 1.0519 .2657 .1425 -1.275 .7133 1.0659 .2404 .1275 -1.219 .7633 1.0825 .2049 .1070 -1.013 .8133 1.0873 .1826 .0933 -1.091 .8483 1.0882 .1644 .0767 -.899 .8633 1.0922 .1530 .0694 -.760 .9133 1.0905 .1385 .0615 -.814 .9633 1.0857 .1227 .0533 -.649 1.0133 1.0859 .1099 .0424 -.475 1.0150 1.0871 .1107 .0443 -.497 1.0633 1.0844 .0977 .0363 -.369 1.1133 1.0870 .0885 .0302 -.364 1.1633 1.0837 .0815 .0256 -.357 1.2483 1.0883 .0700 .0222 -.315 1.3483 1.0847 .0596 .0196 -.305 1.5150 1.0801 .0461 .0210 -.215 1.6817 1.0761 .0383 .0287 -.164 2.0150 1.0650 .0273 .0261 -.091 2.5150 1.0562 .0209 .0205 .003 3.3483 1.0381 .0177 .0125 -.003 3.3483 1.0406 .0200 .0120 .000 --- (b) Re=5.0E+03 N=40 y um up wp su -.3017 .4743 .4380 .2823 -.697 -.2517 .3961 .4264 .2895 -.601 -.2017 .3062 .4116 .3088 -.510 -.1517 .2340 .3910 .3106 -.463 -.1017 .1650 .3649 .3168 -.383 -.0517 .1540 .3452 .3207 -.474 -.0033 .1374 .3359 .3206 -.534 .0467 .1493 .3366 .3147 -.480 .0967 .1807 .3533 .3148 -.404 .1467 .2239 .3845 .3136 -.430 .1967 .2862 .4147 .3102 -.477 .2467 .3844 .4212 .2948 -.585 .2967 .4679 .4352 .2804 -.646 .3467 .5624 .4305 .2668 -.707 .3967 .6522 .4274 .2564 -.803 .4467 .7374 .4177 .2522 -.779 .4967 .8184 .3999 .2300 -.878 .5467 .8862 .3734 .2143 -.887 .5967 .9163 .3531 .2016 -.898 .6150 .9506 .3329 .1890 -.987 .6467 .9653 .3187 .1799 -1.025 .6967 1.0180 .2879 .1501 -1.071 .7467 1.0360 .2543 .1336 -1.081 .7817 1.0436 .2360 .1298 -1.087 .7967 1.0467 .2257 .1143 -1.068 .8467 1.0588 .2040 .0944 -1.048 .8967 1.0589 .1746 .0880 -.794 .9467 1.0638 .1535 .0684 -.685 .9483 1.0654 .1525 .0699 -.771 .9967 1.0680 .1381 .0547 -.630 1.0467 1.0716 .1236 .0493 -.656 1.0967 1.0686 .1120 .0368 -.467 1.1817 1.0655 .0932 .0307 -.325 1.2817 1.0719 .0798 .0250 -.233 1.4483 1.0694 .0609 .0176 -.217 1.6150 1.0599 .0482 .0141 -.189 1.9483 1.0702 .0347 .0105 -.189 2.4483 1.0550 .0255 .0083 -.259 3.2817 1.0466 .0218 .0078 -.363 3.2817 1.0409 .0208 .0068 -.458 --- (c) Re=8.1E+03 N=40 y um up wp su -.2600 .5045 .3837 .2787 -.825 -.2100 .4480 .3795 .2913 -.810 -.1600 .3782 .3727 .2909 -.744 -.1100 .3862 .3481 .2852 -.913 -.0600 .3256 .3548 .2902 -.859 -.0100 .3263 .3378 .2891 -.946 .0383 .3322 .3399 .2825 -.923 .0883 .3537 .3482 .2852 -.910 .1383 .4025 .3411 .2802 -.864 .1883 .4224 .3683 .2893 -.797 .2383 .4692 .3881 .2796 -.725 .2883 .5353 .3833 .2838 -.773 .3383 .5938 .3913 .2722 -.764 .3883 .6690 .3763 .2602 -.814 .4383 .7187 .3763 .2520 -.804 .4883 .7847 .3614 .2468 -.810 .5383 .8348 .3615 .2254 -.890 .5883 .8789 .3400 .2195 -.823 .6383 .9215 .3202 .1968 -.845 .6567 .9274 .3215 .2010 -.922 .6883 .9514 .3066 .1799 -.939 .7383 .9714 .2832 .1749 -.880 .7883 .9874 .2653 .1573 -.959 .8233 1.0105 .2402 .1396 -1.062 .8383 1.0111 .2350 .1392 -.983 .8883 1.0112 .2152 .1241 -1.051 .9383 1.0227 .1945 .1002 -.988 .9883 1.0324 .1791 .1000 -1.094 .9900 1.0339 .1714 .0847 -1.047 1.0383 1.0307 .1638 .0865 -.973 1.0883 1.0420 .1390 .0621 -.740 1.1383 1.0446 .1272 .0608 -.669 1.2233 1.0419 .1082 .0479 -.807 1.3233 1.0450 .0892 .0362 -.449 1.4900 1.0439 .0690 .0278 -.285 1.6567 1.0460 .0539 .0195 -.330 1.9900 1.0428 .0353 .0133 -.308 2.4900 1.0395 .0225 .0098 -.265 3.3233 1.0325 .0163 .0086 -.354 3.3233 1.0306 .0170 .0077 -.454 --- C. Norberg, Department of Energy Sciences, Lund Institute of Technology, P.O. Box 118, SE-22100, Lund, Sweden. Tel.+46-46-2228606 Christoffer.Norberg@energy.lth.se ---