A note on the surface quasi-geostrophic temperature variance cascade

Abstract

In this note we examine the dynamical role played by inertial forces on the surface tem- perature (or buoyancy) variance in strongly rotating, stratified flows with uniform potential vorticity fields and fractional dissipation. 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 turbu- lence, the condition triggering the cascade is more exotic, a fact reflecting the non-locality introduced by fractional dissipation. A comment regarding the scale-locality of the temperature variance flux is also included.