A study of surface semi-geostrophic turbulence: freely decaying dynamics

TL;DR

This paper characterizes surface semi-geostrophic turbulence through decaying simulations, revealing distinct dynamics from quasi-geostrophic flows, especially in the formation of fronts, filaments, and energy distribution at small scales.

Contribution

It provides a detailed numerical analysis of surface semi-geostrophic turbulence, highlighting differences from quasi-geostrophic models and emphasizing the role of fronts and small-scale structures.

Findings

Semi-geostrophic turbulence features prominent fronts and filaments.

Energy spectra are less steep with more small-scale energy at higher Rossby numbers.

Potential temperature distribution is skewed and peaked near the active boundary.

Abstract

In this study we give a characterization of semi-geostrophic turbulence by performing freely decaying simulations for the case of constant uniform potential vorticity, a set of equations known as surface semi-geostrophic approximation. The equations are formulated as conservation laws for potential temperature and potential vorticity, with a nonlinear Monge-Amp\'{e}re type inversion equation for the streamfunction, expressed in a transformed coordinate system that follows the geostrophic flow. We perform model studies of turbulent surface semi-geostrophic flows in a doubly-periodic domain in the horizontal limited in the vertical by two rigid lids, allowing for variations of potential temperature at one of the boundaries, and we compare them with the corresponding surface quasi-geostrophic case. Results show that, while surface quasi-geostrophic dynamics is dominated by a symmetric population of cyclones-anticyclones, surface semi-geostrophic dynamics features a more prominent role of fronts and filaments. The resulting distribution of potential temperature is strongly skewed and peaked at non-zero values at and close to the active boundary, while symmetry is restored in the interior of the domain, where small-scale frontal structures do not penetrate. In surface semi-geostrophic turbulence energy spectra are less steep than in the surface quasi-geostrophic case, with more energy concentrated at small scales for increasing Rossby number. Energy connected to frontal structures, lateral strain rate and vertical velocities are largest close to the active boundary. These results show that the semi-geostrophic model could be of interest for studying the lateral mixing of properties in geophysical flows.