Abstract

This presentation focuses on a model of temperature evolution at the ocean surface known as surface quasi-geostrophy (SQG). The resulting equations describe the two-dimensional transport of a scalar—-the surface temperature—-by a velocity field that is itself generated by the spatial distribution of that scalar. As such, the temperature in SQG is an active scalar and shares various mathematical, and physical, properties with the velocity in three-dimensional Navier–Stokes equations. In particular, it is well established that the kinetic energy cascades to smaller scales in SQG . Beyond its relevance to geophysics, the study of SQG flows thus falls within a more fundamental context—-the statistical study of hydrodynamical turbulence—-and may offer a valuable testbed for refined theories and statistical models.

We aim to substantiate, or challenge, this analogy by studying various aspects of SQG turbulence in the regime dominated by the direct energy cascade. Our approach relies on the systematic use of massively resolved direct numerical simulations, and their statistical analysis at both Eulerian and Lagrangian levels.