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


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(|ϕ| < 45°) and (iii) Nmin = 4fh, both under nonlinear stability, where horizontal component fh = 2Ω cos ϕ at latitude ϕ. The Nmin are not in terms of inertial frequency f = 2Ω sin ϕ, 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.

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H. D. I. Abarbanel , D. D. Holm , J. E. Marsden & T. Ratiu 1984 Richardson number criterion for the nonlinear stability of three-dimensional stratified flow. Phys. Rev. Lett. 52, 23522355.

A. E. Gargett , P. J. Hendricks , T. B. Sanford , T. R. Osborn & A. J. Williams III 1981 A composite spectrum of vertical shear in the upper ocean. J. Phys. Oceanogr. 11, 12581271.

T. Gerkema & V. I. Shrira 2005 bNear-inertial waves on the ‘nontraditional’ β. plane. J. Geophys. Res. 110, C01003, doi:10.1029/2004JC002519.

K. D. Leaman & T. B. Sanford 1975 Vertical energy propagation of inertial waves: a vector spectral analysis of velocity profiles. J. Geophys. Res. 80, 19751978.

P. H. LeBlond & L. A. Mysak 1978 Waves in the Ocean. Elsevier.

J. Marshall & F. Schott 1999 Open-ocean convection: observations, theory, and models. Rev. Geophys. 37, 164.

C. Millot & M. Crépon 1981 Inertial oscillations on the continental shelf of the Gulf of Lions – Observations and theory. J. Phys. Oceanogr. 11, 639657.

B. Saint-Guily 1970 On internal waves. Effects of the horizontal component of the Earth's rotation and of a uniform current. D. Hyd. Z. 23, 1623.

F. Straneo , M. Kawase & S. C. Riser 2002 Idealized models of slantwise convection in a baroclinic flow. J. Phys. Oceanogr. 32, 558572.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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