# Fig. S1b: Mean streamwise velocity profiles in wall units # Validates that fibers do not significantly alter the mean flow (Re=5600, Re_tau~180). # All profiles symmetrized as (lower_half + flip(upper_half))/2 and scaled to wall units. # Columns (each pair is one curve): # yplus_reference : y+ for reference simulation (no fiber) [solid gray] # Uplus_reference : U+ for reference simulation (no fiber) # yplus_KMM1987 : y+ from Kim, Moin & Moser (1987) [gray circles] # Uplus_KMM1987 : U+ from Kim, Moin & Moser (1987) # yplus_fiber_h0p5 : y+ for fiber case h/H=0.5, rho_s/rho_f=1.08 [black dashed] # Uplus_fiber_h0p5 : U+ for fiber case h/H=0.5 # yplus_fiber_h0p25 : y+ for fiber case h/H=0.25, rho_s/rho_f=1.08 [black dash-dot] # Uplus_fiber_h0p25 : U+ for fiber case h/H=0.25 # yplus_fiber_h0p125 : y+ for fiber case h/H=0.125, rho_s/rho_f=1.08 [black dotted] # Uplus_fiber_h0p125 : U+ for fiber case h/H=0.125 # Vertical lines in figure (scalar values, not columns): # y+ = 180*0.51 = 91.8 -> fiber tip mean position, h/H=0.5 [dashed] # y+ = 180*0.28 = 50.4 -> fiber tip mean position, h/H=0.25 [dash-dot] # y+ = 180*0.145 = 26.1 -> fiber tip mean position, h/H=0.125 [dotted] # Rows beyond a series length are filled with NaN. # # yplus_reference Uplus_reference yplus_KMM1987 Uplus_KMM1987 yplus_fiber_h0p5 Uplus_fiber_h0p5 yplus_fiber_h0p25 Uplus_fiber_h0p25 yplus_fiber_h0p125 Uplus_fiber_h0p125 9.000000e-01 8.807118e-01 5.364800e-02 5.363900e-02 9.000000e-01 9.033918e-01 9.000000e-01 9.359454e-01 9.000000e-01 8.985198e-01 2.700000e+00 2.616469e+00 2.145600e-01 2.144300e-01 2.700000e+00 2.675954e+00 2.700000e+00 2.774503e+00 2.700000e+00 2.666630e+00 4.500000e+00 4.284750e+00 4.826300e-01 4.819700e-01 4.500000e+00 4.363938e+00 4.500000e+00 4.520519e+00 4.500000e+00 4.355714e+00 6.300000e+00 5.826730e+00 8.577100e-01 8.555500e-01 6.300000e+00 5.903920e+00 6.300000e+00 6.099328e+00 6.300000e+00 5.899427e+00 8.100000e+00 7.197875e+00 1.339600e+00 1.333900e+00 8.100000e+00 7.250696e+00 8.100000e+00 7.462647e+00 8.100000e+00 7.251811e+00 9.900000e+00 8.381576e+00 1.927900e+00 1.914800e+00 9.900000e+00 8.392361e+00 9.900000e+00 8.602500e+00 9.900000e+00 8.400314e+00 1.170000e+01 9.384593e+00 2.622400e+00 2.593900e+00 1.170000e+01 9.343104e+00 1.170000e+01 9.541229e+00 1.170000e+01 9.360471e+00 1.350000e+01 1.022659e+01 3.422600e+00 3.363200e+00 1.350000e+01 1.012874e+01 1.350000e+01 1.031106e+01 1.350000e+01 1.015918e+01 1.530000e+01 1.093156e+01 4.328000e+00 4.209500e+00 1.530000e+01 1.077879e+01 1.530000e+01 1.094446e+01 1.530000e+01 1.082630e+01 1.710000e+01 1.152296e+01 5.338100e+00 5.113300e+00 1.710000e+01 1.132042e+01 1.710000e+01 1.146955e+01 1.710000e+01 1.138851e+01 1.890000e+01 1.202151e+01 6.452300e+00 6.049300e+00 1.890000e+01 1.177707e+01 1.890000e+01 1.190891e+01 1.890000e+01 1.186670e+01 2.070000e+01 1.244469e+01 7.670000e+00 6.989200e+00 2.070000e+01 1.216463e+01 2.070000e+01 1.227991e+01 2.070000e+01 1.227633e+01 2.250000e+01 1.280682e+01 8.990200e+00 7.905200e+00 2.250000e+01 1.249609e+01 2.250000e+01 1.259622e+01 2.250000e+01 1.263020e+01 2.430000e+01 1.311951e+01 1.041200e+01 8.774100e+00 2.430000e+01 1.278266e+01 2.430000e+01 1.286866e+01 2.430000e+01 1.293640e+01 2.610000e+01 1.339198e+01 1.193600e+01 9.579000e+00 2.610000e+01 1.303341e+01 2.610000e+01 1.310604e+01 2.610000e+01 1.320397e+01 2.790000e+01 1.363155e+01 1.355900e+01 1.031100e+01 2.790000e+01 1.325588e+01 2.790000e+01 1.331516e+01 2.790000e+01 1.344183e+01 2.970000e+01 1.384398e+01 1.528100e+01 1.096700e+01 2.970000e+01 1.345618e+01 2.970000e+01 1.350186e+01 2.970000e+01 1.365104e+01 3.150000e+01 1.403384e+01 1.710200e+01 1.155000e+01 3.150000e+01 1.363901e+01 3.150000e+01 1.367118e+01 3.150000e+01 1.383430e+01 3.330000e+01 1.420479e+01 1.901900e+01 1.206600e+01 3.330000e+01 1.380745e+01 3.330000e+01 1.382734e+01 3.330000e+01 1.399771e+01 3.510000e+01 1.435980e+01 2.103300e+01 1.252000e+01 3.510000e+01 1.396329e+01 3.510000e+01 1.397346e+01 3.510000e+01 1.414560e+01 3.690000e+01 1.450134e+01 2.314100e+01 1.292100e+01 3.690000e+01 1.410733e+01 3.690000e+01 1.411222e+01 3.690000e+01 1.428093e+01 3.870000e+01 1.463142e+01 2.534200e+01 1.327600e+01 3.870000e+01 1.424041e+01 3.870000e+01 1.424486e+01 3.870000e+01 1.440605e+01 4.050000e+01 1.475179e+01 2.763500e+01 1.359000e+01 4.050000e+01 1.436364e+01 4.050000e+01 1.437262e+01 4.050000e+01 1.452290e+01 4.230000e+01 1.486387e+01 3.001900e+01 1.387000e+01 4.230000e+01 1.447801e+01 4.230000e+01 1.449578e+01 4.230000e+01 1.463296e+01 4.410000e+01 1.496886e+01 3.249200e+01 1.412100e+01 4.410000e+01 1.458523e+01 4.410000e+01 1.461482e+01 4.410000e+01 1.473732e+01 4.590000e+01 1.506775e+01 3.505300e+01 1.434900e+01 4.590000e+01 1.468627e+01 4.590000e+01 1.473091e+01 4.590000e+01 1.483681e+01 4.770000e+01 1.516135e+01 3.770100e+01 1.455700e+01 4.770000e+01 1.478249e+01 4.770000e+01 1.484425e+01 4.770000e+01 1.493211e+01 4.950000e+01 1.525036e+01 4.043200e+01 1.475000e+01 4.950000e+01 1.487488e+01 4.950000e+01 1.495510e+01 4.950000e+01 1.502387e+01 5.130000e+01 1.533533e+01 4.324700e+01 1.493100e+01 5.130000e+01 1.496419e+01 5.130000e+01 1.506188e+01 5.130000e+01 1.511274e+01 5.310000e+01 1.541674e+01 4.614300e+01 1.510100e+01 5.310000e+01 1.505125e+01 5.310000e+01 1.516156e+01 5.310000e+01 1.519934e+01 5.490000e+01 1.549498e+01 4.911800e+01 1.526400e+01 5.490000e+01 1.513569e+01 5.490000e+01 1.525488e+01 5.490000e+01 1.528412e+01 5.670000e+01 1.557035e+01 5.217100e+01 1.541900e+01 5.670000e+01 1.521704e+01 5.670000e+01 1.534327e+01 5.670000e+01 1.536725e+01 5.850000e+01 1.564313e+01 5.530000e+01 1.556900e+01 5.850000e+01 1.529542e+01 5.850000e+01 1.542732e+01 5.850000e+01 1.544860e+01 6.030000e+01 1.571355e+01 5.850300e+01 1.571400e+01 6.030000e+01 1.537180e+01 6.030000e+01 1.550769e+01 6.030000e+01 1.552788e+01 6.210000e+01 1.578177e+01 6.177800e+01 1.585500e+01 6.210000e+01 1.544576e+01 6.210000e+01 1.558510e+01 6.210000e+01 1.560485e+01 6.390000e+01 1.584795e+01 6.512300e+01 1.599300e+01 6.390000e+01 1.551748e+01 6.390000e+01 1.566023e+01 6.390000e+01 1.567942e+01 6.570000e+01 1.591224e+01 6.853600e+01 1.612800e+01 6.570000e+01 1.558742e+01 6.570000e+01 1.573363e+01 6.570000e+01 1.575165e+01 6.750000e+01 1.597477e+01 7.201600e+01 1.626000e+01 6.750000e+01 1.565610e+01 6.750000e+01 1.580571e+01 6.750000e+01 1.582166e+01 6.930000e+01 1.603570e+01 7.555900e+01 1.638900e+01 6.930000e+01 1.572384e+01 6.930000e+01 1.587675e+01 6.930000e+01 1.588965e+01 7.110000e+01 1.609514e+01 7.916400e+01 1.651500e+01 7.110000e+01 1.579080e+01 7.110000e+01 1.594696e+01 7.110000e+01 1.595592e+01 7.290000e+01 1.615322e+01 8.282800e+01 1.663700e+01 7.290000e+01 1.585785e+01 7.290000e+01 1.601645e+01 7.290000e+01 1.602075e+01 7.470000e+01 1.621006e+01 8.655000e+01 1.675600e+01 7.470000e+01 1.592489e+01 7.470000e+01 1.608524e+01 7.470000e+01 1.608439e+01 7.650000e+01 1.626574e+01 9.032700e+01 1.687200e+01 7.650000e+01 1.599265e+01 7.650000e+01 1.615327e+01 7.650000e+01 1.614706e+01 7.830000e+01 1.632034e+01 9.415700e+01 1.698500e+01 7.830000e+01 1.606108e+01 7.830000e+01 1.622046e+01 7.830000e+01 1.620901e+01 8.010000e+01 1.637391e+01 9.803700e+01 1.709400e+01 8.010000e+01 1.613106e+01 8.010000e+01 1.628679e+01 8.010000e+01 1.627047e+01 8.190000e+01 1.642651e+01 1.019700e+02 1.720000e+01 8.190000e+01 1.620251e+01 8.190000e+01 1.635228e+01 8.190000e+01 1.633155e+01 8.370000e+01 1.647817e+01 1.059400e+02 1.730200e+01 8.370000e+01 1.627606e+01 8.370000e+01 1.641692e+01 8.370000e+01 1.639221e+01 8.550000e+01 1.652896e+01 1.099600e+02 1.740000e+01 8.550000e+01 1.635200e+01 8.550000e+01 1.648065e+01 8.550000e+01 1.645232e+01 8.730000e+01 1.657892e+01 1.140200e+02 1.749400e+01 8.730000e+01 1.642892e+01 8.730000e+01 1.654342e+01 8.730000e+01 1.651178e+01 8.910000e+01 1.662811e+01 1.181200e+02 1.758500e+01 8.910000e+01 1.650599e+01 8.910000e+01 1.660525e+01 8.910000e+01 1.657053e+01 9.090000e+01 1.667656e+01 1.222500e+02 1.767200e+01 9.090000e+01 1.658387e+01 9.090000e+01 1.666616e+01 9.090000e+01 1.662863e+01 9.270000e+01 1.672431e+01 1.264200e+02 1.775600e+01 9.270000e+01 1.666115e+01 9.270000e+01 1.672621e+01 9.270000e+01 1.668616e+01 9.450000e+01 1.677137e+01 1.306200e+02 1.783500e+01 9.450000e+01 1.673792e+01 9.450000e+01 1.678540e+01 9.450000e+01 1.674322e+01 9.630000e+01 1.681777e+01 1.348400e+02 1.791100e+01 9.630000e+01 1.681195e+01 9.630000e+01 1.684374e+01 9.630000e+01 1.679994e+01 9.810000e+01 1.686352e+01 1.391000e+02 1.798100e+01 9.810000e+01 1.688354e+01 9.810000e+01 1.690114e+01 9.810000e+01 1.685641e+01 9.990000e+01 1.690863e+01 1.433700e+02 1.804500e+01 9.990000e+01 1.695261e+01 9.990000e+01 1.695748e+01 9.990000e+01 1.691264e+01 1.017000e+02 1.695310e+01 1.476700e+02 1.810300e+01 1.017000e+02 1.701994e+01 1.017000e+02 1.701254e+01 1.017000e+02 1.696856e+01 1.035000e+02 1.699696e+01 1.519900e+02 1.815400e+01 1.035000e+02 1.708548e+01 1.035000e+02 1.706617e+01 1.035000e+02 1.702405e+01 1.053000e+02 1.704020e+01 1.563200e+02 1.819800e+01 1.053000e+02 1.714914e+01 1.053000e+02 1.711832e+01 1.053000e+02 1.707891e+01 1.071000e+02 1.708281e+01 1.606600e+02 1.823500e+01 1.071000e+02 1.721071e+01 1.071000e+02 1.716904e+01 1.071000e+02 1.713292e+01 1.089000e+02 1.712477e+01 1.650200e+02 1.826400e+01 1.089000e+02 1.727003e+01 1.089000e+02 1.721850e+01 1.089000e+02 1.718590e+01 1.107000e+02 1.716609e+01 1.693800e+02 1.828500e+01 1.107000e+02 1.732701e+01 1.107000e+02 1.726682e+01 1.107000e+02 1.723773e+01 1.125000e+02 1.720674e+01 1.737500e+02 1.829700e+01 1.125000e+02 1.738170e+01 1.125000e+02 1.731413e+01 1.125000e+02 1.728834e+01 1.143000e+02 1.724671e+01 1.781200e+02 1.830100e+01 1.143000e+02 1.743429e+01 1.143000e+02 1.736048e+01 1.143000e+02 1.733767e+01 1.161000e+02 1.728596e+01 nan nan 1.161000e+02 1.748506e+01 1.161000e+02 1.740588e+01 1.161000e+02 1.738570e+01 1.179000e+02 1.732449e+01 nan nan 1.179000e+02 1.753435e+01 1.179000e+02 1.745026e+01 1.179000e+02 1.743238e+01 1.197000e+02 1.736227e+01 nan nan 1.197000e+02 1.758239e+01 1.197000e+02 1.749363e+01 1.197000e+02 1.747773e+01 1.215000e+02 1.739929e+01 nan nan 1.215000e+02 1.762930e+01 1.215000e+02 1.753604e+01 1.215000e+02 1.752178e+01 1.233000e+02 1.743554e+01 nan nan 1.233000e+02 1.767514e+01 1.233000e+02 1.757759e+01 1.233000e+02 1.756464e+01 1.251000e+02 1.747099e+01 nan nan 1.251000e+02 1.771988e+01 1.251000e+02 1.761838e+01 1.251000e+02 1.760642e+01 1.269000e+02 1.750565e+01 nan nan 1.269000e+02 1.776348e+01 1.269000e+02 1.765844e+01 1.269000e+02 1.764720e+01 1.287000e+02 1.753952e+01 nan nan 1.287000e+02 1.780596e+01 1.287000e+02 1.769771e+01 1.287000e+02 1.768700e+01 1.305000e+02 1.757259e+01 nan nan 1.305000e+02 1.784732e+01 1.305000e+02 1.773604e+01 1.305000e+02 1.772575e+01 1.323000e+02 1.760486e+01 nan nan 1.323000e+02 1.788763e+01 1.323000e+02 1.777334e+01 1.323000e+02 1.776336e+01 1.341000e+02 1.763632e+01 nan nan 1.341000e+02 1.792690e+01 1.341000e+02 1.780951e+01 1.341000e+02 1.779978e+01 1.359000e+02 1.766697e+01 nan nan 1.359000e+02 1.796519e+01 1.359000e+02 1.784457e+01 1.359000e+02 1.783502e+01 1.377000e+02 1.769678e+01 nan nan 1.377000e+02 1.800252e+01 1.377000e+02 1.787853e+01 1.377000e+02 1.786911e+01 1.395000e+02 1.772572e+01 nan nan 1.395000e+02 1.803890e+01 1.395000e+02 1.791139e+01 1.395000e+02 1.790207e+01 1.413000e+02 1.775378e+01 nan nan 1.413000e+02 1.807432e+01 1.413000e+02 1.794312e+01 1.413000e+02 1.793388e+01 1.431000e+02 1.778093e+01 nan nan 1.431000e+02 1.810876e+01 1.431000e+02 1.797366e+01 1.431000e+02 1.796454e+01 1.449000e+02 1.780712e+01 nan nan 1.449000e+02 1.814217e+01 1.449000e+02 1.800294e+01 1.449000e+02 1.799408e+01 1.467000e+02 1.783230e+01 nan nan 1.467000e+02 1.817450e+01 1.467000e+02 1.803085e+01 1.467000e+02 1.802248e+01 1.485000e+02 1.785645e+01 nan nan 1.485000e+02 1.820572e+01 1.485000e+02 1.805731e+01 1.485000e+02 1.804978e+01 1.503000e+02 1.787951e+01 nan nan 1.503000e+02 1.823577e+01 1.503000e+02 1.808224e+01 1.503000e+02 1.807596e+01 1.521000e+02 1.790144e+01 nan nan 1.521000e+02 1.826462e+01 1.521000e+02 1.810561e+01 1.521000e+02 1.810100e+01 1.539000e+02 1.792221e+01 nan nan 1.539000e+02 1.829222e+01 1.539000e+02 1.812744e+01 1.539000e+02 1.812485e+01 1.557000e+02 1.794177e+01 nan nan 1.557000e+02 1.831852e+01 1.557000e+02 1.814773e+01 1.557000e+02 1.814746e+01 1.575000e+02 1.796010e+01 nan nan 1.575000e+02 1.834341e+01 1.575000e+02 1.816648e+01 1.575000e+02 1.816877e+01 1.593000e+02 1.797716e+01 nan nan 1.593000e+02 1.836675e+01 1.593000e+02 1.818374e+01 1.593000e+02 1.818871e+01 1.611000e+02 1.799292e+01 nan nan 1.611000e+02 1.838841e+01 1.611000e+02 1.819954e+01 1.611000e+02 1.820724e+01 1.629000e+02 1.800736e+01 nan nan 1.629000e+02 1.840830e+01 1.629000e+02 1.821396e+01 1.629000e+02 1.822428e+01 1.647000e+02 1.802046e+01 nan nan 1.647000e+02 1.842638e+01 1.647000e+02 1.822707e+01 1.647000e+02 1.823973e+01 1.665000e+02 1.803219e+01 nan nan 1.665000e+02 1.844263e+01 1.665000e+02 1.823894e+01 1.665000e+02 1.825348e+01 1.683000e+02 1.804252e+01 nan nan 1.683000e+02 1.845701e+01 1.683000e+02 1.824959e+01 1.683000e+02 1.826542e+01 1.701000e+02 1.805142e+01 nan nan 1.701000e+02 1.846946e+01 1.701000e+02 1.825900e+01 1.701000e+02 1.827550e+01 1.719000e+02 1.805887e+01 nan nan 1.719000e+02 1.847991e+01 1.719000e+02 1.826710e+01 1.719000e+02 1.828374e+01 1.737000e+02 1.806484e+01 nan nan 1.737000e+02 1.848830e+01 1.737000e+02 1.827379e+01 1.737000e+02 1.829021e+01 1.755000e+02 1.806933e+01 nan nan 1.755000e+02 1.849461e+01 1.755000e+02 1.827895e+01 1.755000e+02 1.829499e+01 1.773000e+02 1.807233e+01 nan nan 1.773000e+02 1.849882e+01 1.773000e+02 1.828246e+01 1.773000e+02 1.829814e+01 1.791000e+02 1.807383e+01 nan nan 1.791000e+02 1.850094e+01 1.791000e+02 1.828424e+01 1.791000e+02 1.829971e+01