A note on the surface quasi-geostrophic temperature variance cascade

TL;DR

This paper investigates the influence of inertial forces on surface temperature variance in rotating stratified flows, identifying conditions for a temperature variance cascade that aligns with SQG turbulence theories.

Contribution

It introduces a sufficient condition for a temperature variance cascade in strongly rotating flows with fractional dissipation, highlighting non-local effects.

Findings

Identifies a sufficient condition for temperature variance cascade.

Shows consistency with SQG turbulence theories.

Highlights the role of non-locality due to fractional dissipation.

Abstract

In this note we examine the dynamical role played by inertial forces on the surface temperature (or buoyancy) variance in strongly rotating, stratified flows with uniform potential vorticity fields. In particular, using a dynamic, multi-scale averaging process, we identify a sufficient condition for the existence of a direct temperature variance cascade across an inertial range. While the result is consistent with the physical and numerical theories of SQG turbulence, the condition which triggers the cascade is more exotic, a fact reflecting the non-locality introduced by fractional dissipation.