Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T23:37:38.304Z Has data issue: false hasContentIssue false
  • English
  • Français

Kelvin wave hydraulic control induced by interactions between vortices and topography

Published online by Cambridge University Press:  11 October 2011

Andrew McC. Hogg ,
William K. Dewar ,
Pavel Berloff  and
Marshall L. Ward
Andrew McC. Hogg*
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia
William K. Dewar
Affiliation:
Department of Oceanography, Florida State University, Tallahassee, FL 32306-4320, USA
Pavel Berloff
Affiliation:
Department of Mathematics and Grantham Institute for Climate Change, Imperial College, London SW7 2AZ, UK
Marshall L. Ward
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The interaction of a dipolar vortex with topography is examined using a combination of analytical solutions and idealized numerical models. It is shown that an anticyclonic vortex may generate along-topography flow with sufficient speeds to excite hydraulic control with respect to local Kelvin waves. A critical condition for Kelvin wave hydraulic control is found for the simplest case of a 1.5-layer shallow water model. It is proposed that in the continuously stratified case this mechanism may allow an interaction between low mode vortices and higher mode Kelvin waves, thereby generating rapidly converging isopycnals and hydraulic jumps. Thus, Kelvin wave hydraulic control may contribute to the flux of energy from mesoscale to smaller, unbalanced, scales of motion in the ocean.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Hydraulic control Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 194 - 208
Copyright
Copyright © Cambridge University Press 2011

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

1. Charney, J. G. 1971 Geostrophic turbulence. J. Atmos. Sci. 28 (6), 1087–1095.2.0.CO;2>CrossRefGoogle Scholar
2. Dewar, W. K. & Hogg, A. M. 2010 Topographic inviscid dissipation of balanced flow. Ocean Modell. 32 (1–2), 1–13.CrossRefGoogle Scholar
3. Ferrari, R. & Wunsch, C. 2009 Ocean circulation kinetic energy: reservoirs, sources, and sinks. Annu. Rev. Fluid Mech. 41 (1), 253–282.CrossRefGoogle Scholar
4. Hallberg, R. & Gnanadesikan, A. 2006 The role of eddies in determining the structure and response of the wind-driven Southern Hemisphere overturning: initial results from the Modelling Eddies in the Southern Ocean project. J. Phys. Oceanogr. 36, 3312–3330.CrossRefGoogle Scholar
5. Hughes, G. O., Hogg, A. M. & Griffiths, R. W. 2009 Available potential energy and irreversible mixing in the meridional overturning circulation. J. Phys. Oceanogr. 39, 3130–3146.CrossRefGoogle Scholar
6. Larichev, V. D. & Reznik, G. M. 1976 Strongly nonlinear two-dimensional solitary Rossby waves. Oceanology 16, 961–967.Google Scholar
7. Lin, S.-J., Chao, W. C., Sud, Y. C. & Walker, G. K. 1994 A class of the van Leer-type transport schemes and its application to the moisture transport in a general circulation model. Mon. Weath Rev. 122, 1575–1593.2.0.CO;2>CrossRefGoogle Scholar
8. Matsuno, T. 1966 Numerical integrations of the primitive equations by a simulated backward difference method. J. Meteor. Soc. Japan, Ser. II 44, 76–84.CrossRefGoogle Scholar
9. Molemaker, J. M., McWilliams, J. C. & Dewar, W. K. 2011 Submesoscale generation of mesoscale anticyclones in the California undercurrent. J. Phys. Oceanogr. (submitted).Google Scholar
10. Naveira Garabato, A. C., Polzin, K. L., King, B. A., Heywood, K. J. & Visbeck, M. 2004 Widespread intense turbulent mixing in the Southern Ocean. Science 303 (5655), 210–213.CrossRefGoogle Scholar
11. Nikurashin, M. & Ferrari, R. 2010 Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: theory. J. Phys. Oceanogr. 40 (5), 1055–1074.Google Scholar
12. Pratt, L. J. & Whitehead, J. A. 2008 Rotating Hydraulics: Nonlinear Topographic Effects in the Ocean and Atmosphere. Springer.Google Scholar
13. Sadourny, R. 1975 The dynamics of finite-difference models of the shallow-water equations. J. Atmos. Sci. 32, 680–689.2.0.CO;2>CrossRefGoogle Scholar
14. Wood, I. R. 1968 Selective withdrawal from a stably stratified fluid. J. Fluid Mech. 32, 209–223.CrossRefGoogle Scholar
15. Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314.CrossRefGoogle Scholar