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We report a non-perturbative study of the effects of shear flows onturbulence reduction in a decaying turbulence in two dimensions. By consideringdifferent initial power spectra and shear flows (zonal flows, combined zonalflows and streamers), we demonstrate how shear flows rapidly generate smallscales, leading to a fast damping of turbulence amplitude. In particular, adouble exponential decrease in turbulence amplitude is shown to occur due to anexponential increase in wavenumber. The scaling of the effective dissipationtime 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 ofdepend 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 DensityFunctions (PDFs) and discuss the effect of enhanced dissipation on PDFs and adynamical time scale $\tau(t)$, which represents the time scale over which asystem passes through statistically different states.

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