Journal of Fluid Mechanics

Surface quasi-geostrophic dynamics

Isaac M.  Held a1, Raymond T.  Pierrehumbert a2, Stephen T.  Garner a1 and Kyle L.  Swanson a2
a1 Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University, Princeton, NJ 08542, USA
a2 Department of Geophysical Sciences, University of Chicago, Chicago, IL 60637, USA

Article author query
held im   [Google Scholar] 
pierrehumbert rt   [Google Scholar] 
garner st   [Google Scholar] 
swanson kl   [Google Scholar] 


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.

(Published Online April 26 2006)
(Received March 2 1994)
(Revised July 14 1994)