Direct detection of linearized bursts in 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 behavior. Although the logarithmic layer of wall-bounded turbulence is used as the primary example, most conclusions should apply to other flows with linearly stable mean profiles that 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 statistical properties, such as the bursting time- and length-scales, the energy fluxes between components, and the mean inclination angles, are consistent in linear and nonlinear systems. The question addressed here is whether the individual structures predicted by the linearised solution can be detected in fully nonlinear simulations, and whether the linearized approximation can be used to predict their evolution. It is found that strong bursting of the largest scales is well described linearly, comprising about 65%–70% of the total time, but that weaker fluctuations are not. It is also found that adding an eddy viscosity does not substantially improve predictions.