The spatial relationships between dissipation and production rates and vortical structures in turbulent boundary and mixing layers

Abstract

A novel approach for studying the spatial relationship between the production and dissipation rates of turbulent kinetic energy and vortical structures is presented. Two turbulent flows were investigated: the zero pressure gradient boundary layer and the two-stream mixing layer. In both flows, a multisensor hot-wire probe was used to measure the velocity components in all three coordinate directions, as well as six components of the velocity gradient tensor. The remaining three velocity gradients were determined using Taylor’s hypothesis. With these data, the “instantaneous” production and dissipation rates, defined by P=−(∂U¯i∕∂xj)uiuj and D=−ν[(∂ui∕∂xj)2+(∂ui∕∂xj)(∂uj∕∂xi)], respectively, were determined. Cross-correlating the fluctuations of these two signals reveals that they are not randomly distributed in time with respect to each other; rather they display significant levels of correlation. Plotting the cross-correlation coefficients versus a dimensionless length scale, defined as L′=sgn(τ)∣τ∣∕νU¯, reveals an asymmetric pattern that persists at several cross-stream locations for both flows. Furthermore, correlating both the dissipation and production rates with a vortex identifier, ωxy=[(ωx)2+(ωy)2]1∕2, also reveals consistent cross-stream patterns. The magnitude of these correlations and their persistent shapes across the flows suggest that the spatial separation between regions of concentrated dissipation and production rates is associated with the presence of quasistreamwise vortices in both of these flows. More specifically, they imply that regions of concentrated rates of dissipation are primarily in the cores of the vortices, whereas regions of rates of production are more concentrated on their periphery.