Fluctuating Vorticity in Turbulent Wall Layers

DNS data for the correlations of fluctuating vorticity in the streamwise $<\omega _{x}\omega _{x}>$, spanwise $<\omega _{z}\omega _{z}>$, and normal $<\omega _{y}\omega _{y}>$ directions is given in the various papers of Del Alamo, Jimenez, Zandonade, Moser, and Hoyas (PofF \textbf{15}, L-41; JFM, \textbf{500},p135, PofF, \textbf{18}, 011702 at four Reynolds numbers. Previously, APS Bulletin \textbf{53,} 18, 2008 EA.00004, the inner wall region was considered. It was shown that the normal component profiles at different Reynolds numbers collapse together when scaled as $<\omega _{y}\omega _{y}>$ / ($ u_{\ast}^{4}/\nu ^{2})$. However, the other components, $<\omega _{x}\omega _{x}>$ and $<\omega _{z}\omega _{z}>$, require a two-term expansion of the form \textit{F$\sim $F}$_{0}+F_{1}{\cdot}u_{\ast }/U$. The first term scaling as $<\omega \omega >_{0}$ / (($ u_{\ast }/\nu )^{2} u_{\ast}U)$ and the second scaling as $<\omega \omega >_{1}$ / ($ u_{\ast}^{4}/\nu ^{2})$. In the outer region a completely different scaling is required. An analysis of the matching behavior between the two regions shows that the common part is a function that decreases as $1/y$. This implies that in the outer region the proper scaling is $<\omega \omega >$ / [$ u_{\ast}^{3}/(h\nu )$]. Indeed, profiles of all three components collapse in the outer region in this variable. Furthermore, all three components show a marked tendency toward the same level and isotropic behavior.