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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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Volume 29, issue 6
Ann. Geophys., 29, 997–1003, 2011
https://doi.org/10.5194/angeo-29-997-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.
Ann. Geophys., 29, 997–1003, 2011
https://doi.org/10.5194/angeo-29-997-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.

  15 Jun 2011

15 Jun 2011

Instability of combined gravity-inertial-Rossby waves in atmospheres and oceans

J. F. McKenzie J. F. McKenzie
  • Department of Mathematics, Statistics and Physics, Durban University of Technology, 4041, South Africa
  • Department of Physics, CSPAR, University of Alabama, AL, USA
  • School of Mathematical Sciences, University of KwaZulu-Natal, South Africa
  • Senior Member, King's College, University of Cambridge, UK

Abstract. The properties of the instability of combined gravity-inertial-Rossby waves on a β-plane are investigated. The wave-energy exchange equation shows that there is an exchange of energy with the background stratified medium. The energy source driving the instability lies in the background enthalpy released by the gravitational buoyancy force.

It is shown that if the phase speed of the westward propagating low frequency-long wavelength Rossby wave exceeds the Poincaré-Kelvin (or "equivalent" shallow water) wave speed, instability arises from the merging of Rossby and Poincaré modes. There are two key parameters in this instability condition; namely, the equatorial/rotational Mach (or Froude) number M and the latitude θ0 of the β-plane. In general waves equatorward of a critical latitude for given M can be driven unstable, with corresponding growth rates of the order of a day or so. Although these conclusions may only be safely drawn for short wavelengths corresponding to a JWKB wave packet propagating internally and located far from boundaries, nevertheless such a local instability may play a significant role in atmosphere-ocean dynamics.

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