On the application of quasi-Lagrangian coordinates to random shear flows

Abstract

An ensemble of homogeneous random shear flows with steady linear mean velocity profiles is considered from a purely kinematical point of view. Quasi-Lagrangian coordinates (advected by the mean flow) are used so that a proper orthogonal decomposition of the fluctuation velocity field is possible and periodic boundary conditions can be imposed. The conditions of stationarity in time and incompressibility take on special forms when applied to wave-vector moments. A simple application of the methodology is presented in the construction of a two-dimensional random shear flow.