I have been interested in the physical mechanism by which unstable baroclinic flows equilibrate, or stabilize, due to wave growth and subsequent nonlinear feedback on the mean flow. The mechanism is fundamental to the maintenance and behaviour of geophysical flows such as the tropospheric jet streams and ocean currents such as the Gulf stream and Antarctic circumpolar current. In the animation below, waves develop on an unstable jet in the upper layer of a two-layer flow, leading to stirring and mixing on the jet flanks and across a wide region in the lower layer. Analogous processes are observed to occur in observed flows. The quantity contoured is potential vorticity, but any tracer with a latitudinal gradient in each layer would evolve similarly.

One aim of our work has been to investigate the extent to which physical constraints, such as momentum conservation and (near) conservation of total energy, can be used to determine the end state of such flows.

Another line of investigation has been the re-examination of some even simpler flows for which analytical solutions exist. The animation below shows the evolution of a Rossby wave critical layer in the lower layer of a channel flow like the one above. The solution (by Warn and Gauthier, based on earlier work by Pedlosky) is an exact mathematical description of the lower layer mixing behaviour in the somewhat more realistic jet flow above.

The effect is quite mesmerising!