The scattering of Rossby waves from finite abrupt topography

Owen, G. W. and Willmott, A. J. and Abrahams, David and Mansley, H. (2005) The scattering of Rossby waves from finite abrupt topography. Geophysical and Astrophysical Fluid Dynamics, 99 (3). pp. 219-239. ISSN 1029-0419

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Abstract

The scattering of first mode linear baroclinic Rossby waves by a top-hat ridge in a continuously stratified ocean, with Brunt-Väisälä frequency that decays exponentially with depth below a surface mixed layer, is the subject of this study. A numerical mode matching technique is used to calculate the transmission coefficients for the propagating modes over the ridge. It is found that the scattered field depends crucially upon the stratification. For example, when the majority of the density variation is confined to a thin thermocline, corresponding to a small e-folding scale, gamma -1, for the Brunt-Väisälä frequency, a large amount of the incident wave energy is reflected by a small amplitude ridge. Appreciable energy conversion between the propagating barotropic and baroclinic modes takes place in this case. An asymptotic analysis for a small amplitude ridge is presented that confirms these numerical results. In the limit gamma -1? 0, it is demonstrated that the scattered field in the continuously stratified ocean model differs markedly from the two-layer solution. The latter does not exhibit appreciable reflection of the incident wave energy for a small amplitude ridge. In conclusion, the application of a two-layer ocean model to describe Rossby wave scattering by ridges in place of a continuously stratified model cannot be recommended.

Item Type:	Article
Uncontrolled Keywords:	Rossby wave, Continuous stratification, Abrupt topography
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 45 Integral equations MSC 2010, the AMS's Mathematics Subject Classification > 47 Operator theory
Depositing User:	Ms Lucy van Russelt
Date Deposited:	04 Jan 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/686

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