A simple model for self-sustained oscillations in homogeneous shear flow

Abstract

Generation of the large-scale coherent vortical structures in homogeneous shear flow couples dynamical processes of energy and enstrophy production. In the large rate of strain limit, the simple estimates of the contributions to the energy and enstrophy equations result in a dynamical system, describing experimentally and numerically observed self-sustained nonlinear oscillations of energy and enstrophy. It is shown that the period of these oscillations is independent of the box size and the energy and enstrophy fluctuations are strongly correlated.