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

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.