The buoyancy staircase limit in surface quasigeostrophic turbulence

TL;DR

This paper investigates how surface quasigeostrophic turbulence leads to buoyancy staircases, revealing how vertical stratification influences jet structure, wave behavior, and flow interaction ranges in the resulting meridional buoyancy profiles.

Contribution

It demonstrates the emergence of buoyancy staircases in surface quasigeostrophic turbulence and elucidates how vertical stratification affects jet morphology and wave dynamics.

Findings

Over decreasing stratification, flows have longer interaction ranges and highly dispersive Rossby waves.

Over increasing stratification, jets are more sinuous with large meanders and less dispersive waves.

Jets are closer together over increasing stratification for a given Rhines wavenumber.

Abstract

Surface buoyancy gradients over a quasigeostrophic fluid permit the existence of surface-trapped Rossby waves. The interplay of these Rossby waves with surface quasigeostrophic turbulence results in latitudinally inhomogeneous mixing that, under certain conditions, culminates in a surface buoyancy staircase: a meridional buoyancy profile consisting of mixed-zones punctuated by sharp buoyancy gradients, with eastward jets centred at the sharp gradients and weaker westward flows in between. In this article, we investigate the emergence of this buoyancy staircase limit in surface quasigeostrophic turbulence and we examine the dependence of the resulting dynamics on the vertical stratification. Over decreasing stratification [$\mathrm{d}N(z)/\mathrm{d}z\leq0$, where $N(z)$ is the buoyancy frequency], we obtain flows with a longer interaction range (than in uniform stratification) and highly dispersive Rossby waves. In the staircase limit, we find straight jets that are perturbed by eastward propagating along jet waves, similar to two-dimensional barotropic $\beta$-plane turbulence. In contrast, over increasing stratification [$\mathrm{d}N(z)/\mathrm{d}z\geq0$], we obtain flows with shorter interaction range and weakly dispersive Rossby waves. In the staircase limit, we find sinuous jets with large latitudinal meanders whose shape evolves in time due to the westward propagation of weakly dispersive along jet waves. These along jet waves have larger amplitudes over increasing stratification than over decreasing stratification, and, as a result, the ratio of domain-averaged zonal to meridional speeds is two to three times smaller over increasing stratification than over decreasing stratification. Finally, we find that, for a given Rhines wavenumber, jets over increasing stratification are closer together than jets over decreasing stratification.