Linearised Structures in Shear Turbulence

Abstract

The relevance of linear transitional mechanisms in fully turbulent shear flows, and in particular of the Orr-like inviscid transient amplification of disturbances, is explored in the context of the prediction of bursting behaviour. Although the logarithmic layer of wall-bounded turbulence is used as the primary example, most conclusions also apply to turbulent flows with a uniform shear, as well as probably to other flows with linearly stable mean profiles. They are dominated by large-scale streamwise-velocity streaks and intermittent bursts of the cross-shear velocity. When the linearised problem is solved in the limit of small viscosity, it has previously been shown that many properties, such as the bursting time and length scales, the energy fluxes between components, and the mean inclination angles, agree well between linear and nonlinear systems. The question addressed here is whether the structures predicted by the linearised solution can be traced in fully nonlinear simulations. It is found that the largest scales of strong bursts are well described linearly, but that the weaker fluctuations are not.