Journal of Fluid Mechanics


Abrupt transitions between gyroscopic and internal gravity waves: the mid-latitude case


a1 Royal Netherlands Institute for Sea Research (NIOZ), PO Box 59, 1790 AB Den Burg, The Netherlands


The large-scale vertical density stratification, represented by buoyancy frequency N, is generally very stable in the upper half of the ocean, and relatively weak in the lower half. However, closer inspection of density profiles demonstrates steps rather than a smooth increase with depth. As is demonstrated here using Richardson number, geostrophic balance and slantwise convective mixing arguments, these layers have a limited set of minimum, weak stratification, N-values Nmin indicating the transition between stably stratified and convective ‘homogeneous’ layers. Adopting the viewpoint that the transition occurs for neutral stability in the direction of Earth's rotation Ω instead of gravity g, three discrete states are hypothesized for mid-latitudes: (i) Nmin = 2fh under linear stability conditions, (ii) Nmin = fh(|xs03D5| < 45°) and (iii) Nmin = 4fh, both under nonlinear stability, where horizontal component fh = 2Ω cos xs03D5 at latitude xs03D5. The Nmin are not in terms of inertial frequency f = 2Ω sin xs03D5, because the effect of fh is the tilting of vortex tubes away from the local vertical in the direction of Ω. The above explains very well deep-ocean North-Atlantic and Mediterranean observations on transitions in conductivity-temperature with depth profiles, inertial polarization and near-inertial shear. The latter peaks at sub-inertial 0.97f, which is associated with the lower inertio-gravity wave limit for Nmin = 4fh, thereby stressing the importance of fh for the dominant physics associated with mixing in the ocean.

(Received June 21 2007)

(Revised October 25 2007)