Fluctuating interfaces in barotropic beta-plane turbulence

Abstract: Zonal jets manifest themselves as bands with sharp interfaces in the vorticity configuration. We develop an algorithm to track these fluctuating vorticity interfaces and systematically investigate their characteristic spatio-temporal behavior. While the interfacial height fluctuations are typically sub-Gaussian, the corresponding $\textit{fluctuation speeds}$ exhibit wider, heavy-tailed distributions reflecting the influence of lateral dispersion induced by the zonal velocity profile along the interfacial contours. The temporal evolution of these fluctuations is further characterized through their power spectrum displaying scale invariance in the frequency domain. The sharp, dense, shock-like features present in the time series of the $\textit{height}$ field suggest a possible lacking of differentiability. We confirm this by calculating the moments of the time-increments of the interfacial height fluctuations. Finally, the fractal nature of these boundaries is investigated systematically through a multifractal approach, revealing the non-trivial, complex statistics of interfaces in such geophysical, turbulent flows.