Instabilities on density-driven boundary currents and fronts

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Abstract
It is shown that a coastal density current in a rotating system is unstable to downstream wave disturbances when the mean potential vorticity increases towards the (vertically-walled) coast and when the mean current vanishes there. Other new instability modes are also found which do not require the potential vorticity extremum of quasi-geostrophic theory. All the instabilities in our equivalent one-layer model release mean kinetic energy and most of them release mean potential energy, but an increase of the latter can occur under certain circumstances. Specifically, it is shown (a) that mean flows close to uniform potential vorticity can be unstable to disturbances of infinite wavelength (and hence also for finite wavelengths) even for monotonic potential vorticity distributions, and (b) that all mean flows which vanish at the wall and for which the potential vorticity has a maximum but not an extremum at the wall are unstable to waves of finite length. A logical extension shows that the second half of the latter criterion may be relaxed, in fact. The paper concludes with a discussion of the applications to recent laboratory experiments.

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