Communications in Mathematical Sciences

Volume 13 (2015)

Number 2

A note on the surface quasi-geostrophic temperature variance cascade

Pages: 557 – 564



Zachary Bradshaw (Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada)

Zoran Grujić (Department of Mathematics, University of Virginia, Charlottesville, Va., U.S.A.)


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 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 turbulence, 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.


surface quasi-geostrophic equations, turbulence, surface temperature cascade, inertial range

2010 Mathematics Subject Classification

35Q35, 35Q86, 35S10, 76F02, 76F45

Published 3 December 2014