Data from direct numerical simulations have been correlated to examine the effects of Reynolds number on vorticity fluctuation profiles. Three different scalings are found: two in the inner region and the third in the outer region. In the inner region a two-term asymptotic expansion is required to represent the mean square vorticity profiles;
〈ωω〉# = 〈ωω〉0#+〈ωω〉1+u∗/U0. The first scaling
〈ωω〉0# = 〈ωω〉0/(u∗3U0/ν2) is for inactive motions that do not generate Reynolds shear stress. It applies to the streamwise and spanwise components. However, the zero-order term is zero for the normal vorticity component. The scrubbing of the inactive motions over the wall generates vorticity, which is a maximum at the wall, and diffuses out to about
y+ = 50 before it decays. The fluctuating viscous wall shear stress is due entirely to this motion, and as a result the stress ratio (rms/mean)
τ′/τ0 = C
depends on the Reynolds number. The second scaling
〈ωω〉1+ = 〈ωω〉1/(u∗4/ν2), the same scaling as the Reynolds shear stress, is active motions. All three components participate in these motions, which are zero at the wall, rise to a peak at about
y+ = 13–20, and fall to zero at about
y+ = 400. This is consistent with the fact that the Reynolds shear stress is identically zero at the wall. The third scaling correlates data in the outer region using the Kolmogorov time scale
〈ωω〉/(u∗3/hν). Matching between the inner and outer regions has a common part (the equivalent of the log law) of
∼ C/y+ or
∼ C/Y for all three components. All components decrease further and become isotropic as the centerline is approached. Scaling with the Kolmogorov scale implies that dissipation is the important activity. The correlated data are fitted to simplified equations that can be formed into composite expansions to predict profiles at any Reynolds number.
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