Number of lines to skip, then number of lines to read, format 2I3 81 18 CCCCCCCCCCCCCCCCCCCCCCCCCCCC DESCRIPTIONCCCCCCCCCCCCCCCCCCCCCCCCC C THIS IS EXPERIMENTAL DATA FROM A NEARLY HOMOGENEOUS CURVED C SHEAR FLOW AT THE UNIVERSITY OF OTTAWA, CANADA. THESE DATA C HAVE NOT YET BEEN PUBLISHED, HOWEVER, A COMPREHENSIVE MANUSCRIPT C DESCRIBING THIS EXPERIMENT, "THE EFFECTS OF CURVATURE ON C SHEARED TURBULENCE" BY A.G.L. HOLLOWAY AND S. TAVOULARIS C HAS BEEN SUBMITTED TO THE JOURNAL OF FLUID MECHANICS FOR C PUBLICATION. Contact authors before using their results in a paper! C There are six cases: 1, 3, 5 stabilized and 2,4 6 destabilized. C NOMENCLATURE C S --- THE DISTANCE ALONG THE WINDTUNNEL CENTERLINE; S IS ZERO C AT THE START OF CURVATURE C H --- HEIGHT OF THE CURVED WINDTUNNEL TEST SECTION (240 mm) C (NOTICE THAT THE STRAIGHT SECTION HEIGHT IS 305mm) C N --- THE TRANSVERSE COORDINATE; N IS ZERO ON THE CENTERLINE AND C POSITIVE OUTWARDS C UC --- STREAMWISE COMPONENT OF THE MEAN VELOCITY ON THE C WINDTUNNEL CENTERLINE (APPROX. 10 M/S) C A --- =DU/DN, THE TRANSVERSE DERIVATIVE OF THE STREAMWISE C COMPONENT OF THE MEAN VELOCITY C RC --- THE RADIUS OF CURVATURE OF THE WINDTUNNEL CENTERLINE C SBIG --- =UC/(A*RC) CURVATURE PARAMETER C TAU --- =S*A/UC, DIMENSIONLESS TOTAL STRAIN, ZERO AT THE START OF C WINDTUNNEL CURVATURE C U --- STREAMWISE VELOCITY FLUCTUATION (M/S) C V --- TRANSVERSE VELOCITY FLUCTUATION (M/S) C W --- SPANWISE VELOCITY FLUCTUATION (M/S) C Q2 ---=UU+VV+WW (TWICE THE KINETIC ENERGY PER UNIT MASS)(M2/S2) C KUU --- =UU/Q2 C KVV --- = VV/Q2 C KWW --- = WW/Q2 C KUV --- = UV/Q2 C LUU ---STREAMWISE INTEGRAL LENGTH SCALE OF THE STREAMWISE C VELOCITY FLUCTUATIONS (MM) C LVV --- STREAMWISE INTEGRAL LENGTH SCALE OF THE TRANSVERSE C VELOCITY FLUCTUATIONS (MM) C LWW --- STREAMWISE INTEGRAL LENGTH SCALE OF THE SPANWISE C VELOCITY FLUCTUATIONS (MM) C LMDAUU --- STREAMWISE TAYLOR MICROSCALE FOR THE STREAMWISE C VELOCITY FLUCTUATION (MM) C LMDAVV --- STREAMWISE TAYLOR MICROSCALE FOR THE TRANSVERSE C VELOCITY FLUCTUATIONS (MM) C LMDAWW --- STREAMWISE TAYLOR MICROSCALE FOR THE SPANWISE C VELOCITY FLUCTUATIONS (MM) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCCCCCCCCCCCCCCCC HOW TO START THE CALCULATIONS CCCCCCCCCCCCCC C EACH OF THESE FLOWS WERE ALLOWED TO DEVELOP AN EQUILIBRIUM C STRUCTURE IN A STRAIGHT TUNNEL BEFORE THE BEGINNING OF C WINDTUNNEL CURVATURE AT TAU=0. THE LAST MEASUREMENTS TAKEN IN C THIS STRAIGHT SECTION WERE 178 MM BEFORE THE START OF TUNNEL C CURVATURE (THE VALUE OF TAU WOULD BE NEGATIVE AND C WILL DEPEND ON THE SHEAR RATE AND UC). C C A CONVENIENT APPROACH C WOULD BE TO START THE CALCULATION WITH THE LAST MEASUREMENT C IN THE STRAIGHT SECTION AND CONTINUE THE COMPUTATION WITHOUT C CURVATURE EFFECTS UP TO TAU=0. THEN "TURN ON" THE CURVATURE C AND PROCEED WITH THE COMPUTATION THROUGH THE CURVED TUNNEL. C IT IS PROBABLE THAT THE FLOW CURVATURE WOULD EXPERIENCE A C GRADUAL TRANSITION, ALTHOUGH C THE LENGTH OF THIS TRANSITION REGION IS RELATIVELY SHORT. C THE FIRST MEASUREMENTS IN THE CURVED SECTION SHOW THAT THE C TRANSVERSE C AND SPANWISE COMPONENTS OF THE MEAN VELOCITY ARE SMALL C IN COMPARISON TO THE STREAMWISE COMPONENT, SUGGESTING THAT C THE MEAN STREAMLINES ARE APPROXIMATELY CONCENTRIC CIRCLES. C C FOR EACH SET OF DATA, THE LAST MEASUREMENT IN THE STRAIGHT C TUNNEL IS GIVEN FIRST (IT WOULD CORRESPOND TO SBIG=0.0) C IN THE STRAIGHT TUNNEL, S/H IS NOT GIVEN TO AVOID CONFUSION C DUE TO DIFFERENT TUNNEL HEIGHTS C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Case 1 STABILIZED SHEAR FLOW (RC = 5 METERS; A=64 1/SECOND) C %% MEANS, VARIANCES AND SHEAR STRESS %%%%%%%%%%% SBIG S/H TAU U V W UUQ2 VV/Q2 WW/Q2 UV/Q2 UW/Q2 Q2 .0 .0 -1.19 10.012 -.222 .044 .498 .202 .300 -.135 .055 1.454584 .03 0.42 0.67 9.961 -0.139 -0.030 0.503 0.195 0.302 -0.124 -0.031 1.658981 .03 1.25 2.00 10.055 -0.170 0.017 0.513 0.198 0.289 -0.124 -0.032 1.766546 .03 2.08 3.33 10.040 -0.159 0.050 0.523 0.201 0.276 -0.122 -0.051 1.793158 .03 2.92 4.66 9.868 -0.003 0.066 0.501 0.198 0.302 -0.110 -0.013 1.794372 .03 3.75 5.99 10.098 -0.151 0.120 0.504 0.204 0.292 -0.127 -0.020 1.857193 .03 4.58 7.33 9.746 -0.075 0.071 0.494 0.200 0.306 -0.119 -0.023 1.817850 .03 5.42 8.66 9.766 -0.064 0.107 0.493 0.202 0.306 -0.122 -0.011 1.906667 .03 6.25 9.99 9.627 0.175 0.067 0.490 0.193 0.317 -0.109 -0.010 1.953402 5 18 C %%%%%%% LENGTH SCALES %%%%%%%%%%%%%%%%%%%%%% SBIG S/H LUU LVV LWW LMDAUU LMDAVV LMDWW .0 .0 39.9 12.0 14.2 5.4 2.8 3.1 .03 0.42 39.3 11.2 15.0 5.3 2.6 3.1 .03 1.25 38.1 11.5 15.6 5.4 2.6 3.1 .03 2.08 34.6 10.9 16.1 5.3 2.6 3.9 .03 2.92 33.5 11.1 16.0 5.3 2.6 3.2 .03 3.75 35.6 12.1 16.4 5.4 2.8 3.1 .03 4.58 35.1 12.1 17.3 5.3 2.7 3.2 .03 5.42 37.6 13.2 18.4 5.3 2.8 3.3 .03 6.25 37.3 12.8 19.6 5.3 2.7 3.4 9 18 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Case 2 DESTABILIZED SHEAR FLOW (RC= 5 M,A=-61 1/S) %%%%%% C %% MEANS, VARIANCES AND SHEAR STRESS %%%%%%%%%%% SBIG S/H TAU U V W UU/Q2 VV/Q2 WW/Q2 UV/Q2 UW/Q2 Q2 .0 .0 -1.11 10.229 .185 .073 .495 .201 .304 .143 .002 1.243994 -.03 0.42 0.67 10.249 0.230 -0.065 0.492 0.208 0.300 0.148 0.008 1.422473 -.03 1.25 2.00 10.531 0.142 -0.004 0.491 0.205 0.304 0.150 0.019 1.640954 -.03 2.08 3.33 10.590 0.118 0.015 0.500 0.203 0.297 0.155 0.016 1.970502 -.03 2.92 4.67 10.522 0.153 0.064 0.511 0.203 0.287 0.148 0.045 2.345715 -.03 3.75 6.00 10.615 0.172 0.097 0.520 0.202 0.278 0.153 0.037 2.822464 -.03 4.58 7.34 10.634 0.284 0.076 0.505 0.206 0.289 0.153 0.019 3.270374 -.03 5.42 8.67 10.711 0.387 0.196 0.532 0.218 0.251 0.164 0.047 3.480301 -.03 6.25 10.00 10.742 0.610 0.067 0.501 0.217 0.283 0.167 0.030 4.308477 5 18 C %%%%% LENGTH SCALES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SBIG S/H LUU LVV LWW LMDAUU LMDAVV LMDWW .0 .0 37. 11.8 14.0 5.4 2.8 3.2 -.03 0.42 41.7 13.5 15.5 5.3 2.8 3.2 -.03 1.25 47.4 16.3 16.7 5.4 2.8 3.3 -.03 2.08 52.9 19.2 17.9 5.6 2.9 3.3 -.03 2.92 61.7 21.4 18.2 5.6 2.9 3.4 -.03 3.75 66.8 24.3 19.4 5.9 3.0 3.4 -.03 4.58 68.5 26.3 20.5 5.7 3.0 3.5 -.03 5.42 74.0 29.3 21.1 5.9 3.1 3.5 -.03 6.25 80.6 35.9 23.0 5.9 3.2 3.7 9 16 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Case 3 STABILIZED SHEAR FLOW (RC = 2 M, A=65 1/S) %%%%%% C %% MEANS, VARIANCES AND SHEAR STRESS %%%%%%%%%%% SBIG S/H TAU U V W UU/Q2 VV/Q2 WW/Q2 UV/Q2 UW/Q2 Q2 .0 .0 -1.19 10.012 -.222 .044 .498 .202 .300 -.135 .055 1.454584 .08 0.42 0.62 10.372 -0.183 -0.050 0.517 0.188 0.295 -0.125 -0.030 1.834792 .08 1.28 1.92 10.082 -0.124 -0.276 0.519 0.191 0.290 -0.102 -0.004 1.674759 .08 2.15 3.22 9.978 -0.139 -0.332 0.500 0.199 0.301 -0.102 -0.013 1.530697 .08 3.01 4.52 9.907 -0.221 -0.343 0.480 0.206 0.314 -0.108 -0.022 1.377271 .08 3.88 5.81 9.911 -0.145 -0.448 0.460 0.201 0.339 -0.109 -0.033 1.292068 .08 4.74 7.11 10.115 -0.018 -0.426 0.466 0.200 0.334 -0.104 -0.037 1.271311 .08 5.61 8.41 10.377 -0.042 -0.480 0.467 0.198 0.335 -0.106 -0.044 1.216584 5 16 C %%%%%%% LENGTH SCALES %%%%%%%%%%%%%% SBIG S/H LUU LVV LWW LMDAUU LMDAVV LMDWW .0 .0 39.9 12.0 14.2 5.4 2.8 3.1 .08 0.42 39.4 11.2 14.8 5.6 2.7 3.2 .08 1.28 31.5 9.6 14.7 5.3 2.6 3.1 .08 2.15 28.5 9.4 14.8 5.2 2.6 3.1 .08 3.01 27.3 10.1 15.6 5.0 2.6 3.1 .08 3.88 27.8 10.5 17.0 5.1 2.7 3.3 .08 4.74 29.5 11.1 18.4 5.3 2.8 3.5 .08 5.61 30.5 11.4 19.0 5.4 2.8 3.5 9 16 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Case 4 DESTABILIZED SHEAR FLOW (RC = 2 M,A=-64 1/S) %%%%%% C %% MEANS, VARIANCES AND SHEAR STRESS %%%%%%%%%%% SBIG S/H TAU U V W UU/Q2 VV/Q2 WW/Q2 UV/Q2 UW/Q2 Q2 .0 .0 -1.11 10.229 .185 .073 .495 .201 .304 .143 .002 1.243994 -.08 0.42 0.62 10.092 0.138 -0.104 0.481 0.211 0.308 0.148 0.008 1.620561 -.08 1.28 1.92 9.949 0.211 -0.276 0.478 0.219 0.303 0.160 -0.034 1.888343 -.08 2.15 3.22 10.271 0.230 -0.245 0.483 0.223 0.294 0.166 -0.026 2.561214 -.08 3.01 4.52 10.408 0.234 -0.357 0.490 0.221 0.289 0.164 -0.029 3.448072 -.08 3.88 5.81 10.662 0.388 -0.352 0.472 0.225 0.303 0.164 -0.030 4.523287 -.08 4.74 7.11 11.247 0.753 -0.380 0.477 0.243 0.280 0.185 -0.031 5.971560 -.08 5.61 8.41 11.764 0.892 -0.368 0.466 0.255 0.280 0.186 -0.031 7.384706 5 16 C %%%%% LENGTH SCALES%%%%%%%%%%%%%%%%%%%%%%% SBIG S/H LUU LVV LWW LMDAUU LMDAVV LMDWW .0 .0 37.0 11.8 14.0 5.4 2.8 3.2 -.08 0.42 44.7 15.7 17.7 5.5 2.9 3.4 -.08 1.28 55.6 22.7 18.5 5.6 3.0 3.4 -.08 2.15 59.3 30.6 20.7 5.8 3.1 3.5 -.08 3.01 71.4 36.6 22.1 5.7 3.1 3.6 -.08 3.88 79.4 44.3 24.8 5.9 3.3 3.8 -.08 4.74 89.6 56.1 26.1 6.1 3.6 3.9 -.08 5.61 103.1 63.3 28.4 6.3 3.9 4.1 9 16 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Case 5 STABILIZED SHEAR FLOW (RC=2M, A=30 1/S) C %% MEANS, VARIANCES AND SHEAR STRESS %%%%%%%%%%% SBIG S/H TAU U V W UU/Q2 VV/Q2 WW/Q2 UV/Q2 UW/Q2 Q2 .0 .0 -.485 11.0 -.145 -.042 .459 .218 .323 -.133 .016 0.202079 .18 0.42 0.28 11.256 -0.175 -0.092 0.487 0.197 0.316 -0.134 -0.049 0.234052 .18 1.28 0.85 11.040 -0.050 -0.297 0.516 0.188 0.296 -0.094 0.048 0.236580 .18 2.15 1.43 11.003 -0.008 -0.360 0.496 0.193 0.311 -0.073 0.037 0.223049 .18 3.01 2.00 10.805 -0.038 -0.389 0.472 0.204 0.324 -0.064 0.023 0.203793 .18 3.88 2.58 10.722 0.070 -0.499 0.433 0.206 0.361 -0.056 -0.029 0.194750 .18 4.74 3.15 10.986 0.234 -0.478 0.454 0.228 0.318 -0.059 0.004 0.171061 .18 5.61 3.73 10.971 0.234 -0.509 0.446 0.235 0.319 -0.069 -0.009 0.154169 5 16 C%%%%LENGTH SCALES %%%%%%%%%%%%%%%%%%%% SBIG S/H LUU LVV LWW LMDAUU LMDAVV LMDWW .0 .0 22.9 8.9 9.6 6.7 3.8 4.0 .18 0.42 24.7 8.7 10.3 6.8 3.5 4.0 .18 1.28 20.6 7.1 9.5 6.7 3.3 3.8 .18 2.15 18.2 6.6 11.2 6.3 3.2 3.7 .18 3.01 18.6 6.7 10.1 5.9 3.1 3.7 .18 3.88 20.8 7.1 11.1 5.7 3.1 3.7 .18 4.74 20.1 8.0 10.2 5.7 3.2 3.6 .18 5.61 19.6 8.0 10.9 5.8 3.3 3.7 9 16 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Case 6 DESTABILIZED SHEAR FLOW (RC=2M, A=-31 1/S) C %% MEANS, VARIANCES AND SHEAR STRESS %%%%%%%%%%% SBIG S/H TAU U V W UU/Q2 VV/Q2 WW/Q2 UV/Q2 UW/Q2 Q2 .0 .0 -.57 10.176 .115 .046 .463 .203 .333 .147 .021 .160303 -.15 0.42 0.33 9.919 0.052 -0.093 0.448 0.218 0.334 0.150 -0.008 0.184891 -.15 1.28 1.03 9.608 0.022 -0.279 0.432 0.239 0.329 0.172 0.025 0.202486 -.15 2.15 1.71 9.930 -0.001 -0.302 0.420 0.254 0.326 0.184 0.029 0.246620 -.15 3.01 2.41 9.974 -0.054 -0.285 0.416 0.254 0.330 0.185 0.033 0.299075 -.15 3.88 3.10 10.051 -0.043 -0.293 0.412 0.256 0.332 0.186 0.025 0.389095 -.15 4.74 3.79 10.675 0.205 -0.275 0.439 0.273 0.288 0.208 0.018 0.550771 -.15 5.61 4.48 10.900 0.291 -0.260 0.433 0.278 0.289 0.203 0.009 0.696258 5 16 C%%%%LENGTH SCALES %%%%%%%%%%%%%%%%%%%%% SBIG S/H LUU LVV LWW LMDAUU LMDAVV LMDWW .0 .0 22.9 9.2 9.6 7.0 3.9 4.3 -.15 0.42 25.5 10.2 10.5 7.0 4.0 4.3 -.15 1.28 27.8 13.3 11.2 6.9 4.1 4.3 -.15 2.15 30.8 17.0 12.2 6.9 4.3 4.4 -.15 3.01 33.0 19.5 13.0 6.7 4.2 4.4 -.15 3.88 35.8 22.6 14.5 6.7 4.2 4.5 -.15 4.74 45.4 28.9 15.0 7.1 4.4 4.2 -.15 5.61 49.7 32.4 16.5 6.9 4.3 4.2