Surface quasi-geostrophic dynamics

TLDR

Quasi‑geostrophic flow with uniform potential vorticity reduces to buoyancy evolution on horizontal boundaries, resembling two‑dimensional flow but with distinct flow‑scalar relationships that generate secondary instabilities, finite‑time collapse, and make it a useful testbed for turbulence theories. The authors illustrate these distinctive features through examples of elliptical vortex evolution, mountain‑shed vortex start‑up, temperature filament instability, edge‑wave critical layers, and mixing in overturning edge waves. They describe how tracer variance cascades directly to small scales in homogeneous turbulence while energy undergoes an inverse cascade.

Abstract

The dynamics of quasi-geostrophic flow with uniform potential vorticity reduces to the evolution of buoyancy, or potential temperature, on horizontal boundaries. There is a formal resemblance to two-dimensional flow, with surface temperature playing the role of vorticity, but a different relationship between the flow and the advected scalar creates several distinctive features. A series of examples are described which highlight some of these features: the evolution of an elliptical vortex; the start-up vortex shed by flow over a mountain; the instability of temperature filaments; the ‘edge wave’ critical layer; and mixing in an overturning edge wave. Characteristics of the direct cascade of the tracer variance to small scales in homogeneous turbulence, as well as the inverse energy cascade, are also described. In addition to its geophysical relevance, the ubiquitous generation of secondary instabilities and the possibility of finite-time collapse make this system a potentially important, numerically tractable, testbed for turbulence theories.