Random shearing by zonal flows and transport reduction

The physics of random shearing by zonal flows and the consequent reduction of scalar field transport are studied. In contrast to mean shear flows, zonal flows have a finite autocorrelation time and can exhibit complex spatial structure. A random zonal flow with a finite correlation time ${\tau }_{\mathrm{ZF}}$ decorrelates two nearby fluid elements less efficiently than a mean shear flow does. The decorrelation time is ${\tau }_D{\mathrm{=(\tau }}_{\eta }{\mathrm{/\tau }}_{\mathrm{ZF}}{\Omega }_{\mathrm{rms}}^2{)}^{\text{1/2}}$ (${\tau }_{\eta }$ is the turbulent scattering time, and ${\Omega }_{\mathrm{rms}}$ is the rms shear), leading to larger scalar field amplitude with a slightly different scaling ${\mathrm{(\propto \tau }}_D{\mathrm{/\Omega }}_{\mathrm{rms}})$ , as compared to the case of coherent shearing. In the strong shear limit, the flux scales as ${\mathrm{\propto \Omega }}_{\mathrm{rms}}^{\text{−1}}$ .