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

TL;DR

This paper investigates how shear flows accelerate turbulence decay in two-dimensional systems, revealing rapid small-scale generation, double exponential damping, and the influence of flow type and initial conditions on dissipation times.

Contribution

It provides a non-perturbative analysis of shear flow effects on turbulence decay, highlighting the dependence of dissipation scaling on flow type and initial spectra, and explores PDF dynamics.

Findings

Shear flows cause rapid small-scale generation and turbulence damping.

Double exponential decrease in turbulence amplitude observed due to exponential wavenumber growth.

Dissipation time scale depends on shear flow type and initial power spectrum.

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, combined zonal flows and streamers), we demonstrate how shear flows rapidly generate small scales, leading to a fast damping of turbulence amplitude. In particular, a double exponential decrease in turbulence amplitude is shown to occur due to an exponential increase in wavenumber. The scaling of the effective dissipation time scale $\tau_{e}$, previously taken to be a hybrid time scale $\tau_{e} \propto \tau_{\Omega}^{{2/3}} \tau_{\eta}$, is shown to depend on types of depend on the type of shear flow as well as the initial power spectrum. Here, $\tau_{\Omega}$ and $\tau_{\eta}$ 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 $\tau(t)$, which represents the time scale over which a system passes through statistically different states.