Effect of enhanced dissipation by shear flows on transient relaxation and probability density function in two dimensions

Abstract

We report a non-perturbative study of the effects of shear flows on turbulence reduction in a decaying turbulence in two dimensions. By considering different initial power spectra and shear flows (zonal flows, streamers and zonal flows, and streamers combined), we demonstrate how shear flows rapidly generate small scales, leading to a fast damping of turbulence amplitude. In particular, a double exponential decrease in the turbulence amplitude is shown to occur due to an exponential increase in wavenumber. The scaling of the effective dissipation time scale τe, previously taken to be a hybrid time scale τe∝τΩ2/3τη, is shown to depend on types of shear flow as well as the initial power spectrum. Here, τΩ and τη are shearing and molecular diffusion times, respectively. Furthermore, we present time-dependent Probability Density Functions (PDFs) and discuss the effect of enhanced dissipation on PDFs and a dynamical time scale τ(t), which represents the time scale over which a system passes through statistically different states.