Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-19T05:48:34.576Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  25 February 2008

HANS VAN HAREN
HANS VAN HAREN*
Affiliation:
Royal Netherlands Institute for Sea Research (NIOZ), PO Box 59, 1790 AB Den Burg, The [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 598 , 10 March 2008 , pp. 67 - 80
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abarbanel, H. D. I., Holm, D. D., Marsden, J. E. & Ratiu, T. 1984 Richardson number criterion for the nonlinear stability of three-dimensional stratified flow. Phys. Rev. Lett. 52, 2352–2355.CrossRefGoogle Scholar
Colinde Verdière, A. de Verdière, A. & Schopp, R. 1994 Flows in a rotating spherical shell: the equatorial case. J. Fluid Mech. 276, 233–260.Google Scholar
Gargett, A. E., Hendricks, P. J., Sanford, T. B., Osborn, T. R. & Williams, A. J. III 1981 A composite spectrum of vertical shear in the upper ocean. J. Phys. Oceanogr. 11, 1258–1271.2.0.CO;2>CrossRefGoogle Scholar
Gerkema, T. & Shrira, V. I. 2005 a Near-inertial waves in the ocean: beyond the ‘traditional approximation’. J. Fluid Mech. 529, 195–219.CrossRefGoogle Scholar
Gerkema, T. & Shrira, V. I. 2005 b Near-inertial waves on the ‘nontraditional’ β. plane. J. Geophys. Res. 110, C01003, doi:10.1029/2004JC002519.Google Scholar
Gill, A. E. 1982 Atmosphere–Ocean Dynamics. Academic.Google Scholar
vanHaren, H. Haren, H. 2006 Asymmetric vertical internal wave propagation. Geophys. Res. Lett. 33, L06618, doi:10.1029/2005GL025499.Google Scholar
vanHaren, H. Haren, H. & Millot, C. 2004 Rectilinear and circular inertial motions in the Western Mediterranean Sea. Deep-Sea Res. I 51, 1441–1455.Google Scholar
vanHaren, H. Haren, H. & Millot, C. 2006 Determination of buoyancy frequency in weakly stable waters. J. Geophys. Res. 111, C03014, doi:10.1029/2005JC003065.Google Scholar
Howard, L. N. 1961 Note on a paper of John W. Miles. J. Fluid Mech. 10, 509–512.CrossRefGoogle Scholar
Leaman, K. D. & Sanford, T. B. 1975 Vertical energy propagation of inertial waves: a vector spectral analysis of velocity profiles. J. Geophys. Res. 80, 1975–1978.CrossRefGoogle Scholar
LeBlond, P. H. & Mysak, L. A. 1978 Waves in the Ocean. Elsevier.Google Scholar
Marshall, J. & Schott, F. 1999 Open-ocean convection: observations, theory, and models. Rev. Geophys. 37, 1–64.CrossRefGoogle Scholar
Miles, J. W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 10, 496–508.CrossRefGoogle Scholar
Millot, C. & Crépon, M. 1981 Inertial oscillations on the continental shelf of the Gulf of Lions – Observations and theory. J. Phys. Oceanogr. 11, 639–657.2.0.CO;2>CrossRefGoogle Scholar
Saint-Guily, B. 1970 On internal waves. Effects of the horizontal component of the Earth's rotation and of a uniform current. D. Hyd. Z. 23, 16–23.CrossRefGoogle Scholar
Sheremet, V. A. 2004 Laboratory experiments with tilted convective plumes on a centrifuge: a finite angle between the buoyancy and the axis of rotation. J. Fluid Mech. 506, 217–244.CrossRefGoogle Scholar
Straneo, F., Kawase, M. & Riser, S. C. 2002 Idealized models of slantwise convection in a baroclinic flow. J. Phys. Oceanogr. 32, 558–572.2.0.CO;2>CrossRefGoogle Scholar