Cascades in Wall-Bounded Turbulence

Abstract

The kinematics and dynamics of wall-bounded turbulence are surveyed, with emphasis on the multiscale processes associated with the logarithmic layer and with its interactions with the wall. It is shown that the logarithmic law reflects a momentum cascade and that its structure agrees reasonably well with Townsend's (1961) model of a self-similar family of attached eddies, each of which contains, on average, a sweep-ejection pair, a segment of a large velocity streak, and disorganized vorticity. Those logarithmic eddies are themselves turbulent objects and can be studied in minimal simulation boxes that are much larger than those in the buffer layer. It is argued that, near the wall, the logarithmic eddies are probably the same as the vortex packets identified by experiments, but that their dynamics does not appear to be especially linked to the buffer layer. Further from the wall, they align into longer superstreaks, although the mechanism remains unclear.