Satellite observations reveal a mesoscale oceanic circulation dominated by turbulence that is correlated, in most cases, with local baroclinicity. Linear baroclinic instability theory has proved useful in understanding the time and space scales of atmospheric eddies. The question addressed here is, to what degree can the observed oceanic eddy activity be understood through a local, linear stability analysis? This question is addressed as follows. A local quasigeostrophic linear stability calculation is performed on a grid of wavenumbers, ranging in magnitude about the local deformation wavenumber, for each vertical profile in a dataset of neutral density for the world's oceans. The initial results show that nearly the entire ocean is unstable, but in many places, particularly in low latitudes, the instability is dominated by surface intensified modes, resulting in very small-scale, quickly growing waves. At higher latitudes, the primary instabilities are due to thermocline depth shears and have a broader vertical structure. For each unstable wave, at each location, the mean-to-eddy energy conversion rate is also calculated and used to select the growing waves that are both fast and have significant energetic conversion potential. This procedure removes most of the surface-instabilities, which cannot lead to significant energy conversion, and reveals the slower but more powerful thermocline-level instabilities where they exist. The time and space scales of these growing waves are compared to estimates of the Eady growth rate and deformation scale, respectively. It is found that while the timescale is well-approximated by the Eady-estimate, the spatial scales are uniformly smaller than the deformation scale, typically by a factor of 4. The zonally averaged spatial scales are then compared to observed eddy scales. The spatial scales of maximum growth are everywhere significantly smaller than the observed eddy scales. In the Antarctic Circumpolar Current, for example, the scale of maximum growth is about 5 km, much smaller than the observed eddy scales, estimates of which range from 30–100 km. A possible, and unsurprising conclusion is that the observed eddy scales are the result of an inverse cascade, and cannot be understood by linear theory alone.
Smith, K. S.. 2007. "The geography of linear baroclinic instability in Earth’s oceans." Journal of Marine Research 65, (5). https://elischolar.library.yale.edu/journal_of_marine_research/179