Fluctuating interfaces in barotropic beta-plane turbulence

TL;DR

This paper develops a method to analyze and characterize the complex, fluctuating vorticity interfaces in barotropic beta-plane turbulence, revealing their scale-invariant, heavy-tailed, and multifractal properties.

Contribution

It introduces an algorithm to track vorticity interfaces and systematically investigates their spatio-temporal behavior and fractal nature in turbulent flows.

Findings

Interfacial height fluctuations are sub-Gaussian.

Fluctuation speeds have heavy-tailed distributions.

Interfaces exhibit multifractal, scale-invariant features.

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.