Abstract
The standard oceanic Rossby wave modes are separable solutions of the primitive equations linearized around a resting, flat-bottom ocean whose stratification depends upon depth only. These waves have a modal structure in the vertical and a propagating horizontal part that satisfies the shallow water equations with an equivalent depth He that is different for each mode. These waves propagate independently of each other over a flat-bottom, but become everywhere coupled over topography. This coupling can be primarily interpreted as defining new dynamical wave modes, i.e. generalized topographic Rossby waves, which can be constructed explicitly by means of WKB theory under the usual scale separation assumption. WKB solutions may locally breakdown, however, when the wavenumbers and frequency of the mode considered approximately satisfy locally the dispersion relation of another wave mode supported by the system. In such a region, called a mode conversion point, the WKB solution becomes degenerate and can no longer be expressed in terms of a single wave mode. There, linear resonance occurs and energy can be exchanged between two different rays. This paper presents an application of mode conversion theory for Rossby waves in a two-layer ocean propagating over a mid-ocean Gaussian ridge varying with longitude only. This theory is shown to predict satisfactorily the location of mode conversion points, and the amount of energy exchanged between rays. In such a framework, wave creation thus occurs at points where WKB breaks down.
Highlights
There is strong observational evidence, e.g., [3], that mid-ocean ridges play a major role in creatinglamplifying incident long baroclinic Rossby waves
As explained in [15], the nature of this coupling can be twofold: a) it may result in new dynamical modes, which on may regard as generalized topographic Rossby wave modes; b) the new dynamical modes defined may themselves be coupled
The purpose of this paper is to describe a specific example of WKB mode coupling for two-layer long Rossby waves over a Gaussian ridge, by using linear mode conversion theory
Summary
There is strong observational evidence, e.g., [3], that mid-ocean ridges play a major role in creatinglamplifying incident long baroclinic Rossby waves. The JEBAR interpretation consists merely in stating that the standard barotropic and baroclinic modes, i.e., the modes defined for a flat-bottom reference ocean, are coupled over topography. Such a description, is not satisfactory because it is somehow largely tautological. Within the framework of WKB theory, wave creation can only occur in regions where the WKB approximation breaks down because by construction a ray conserves its energy as long as WKB remains valid To understand this issue, [6] investigated the validity of WKB theory in layered models of the ocean by comparing ray calculations with direct numerical simulations using a primitive equations model. The present discussion remains descriptive, and summarizes the detailed results which the interested reader may find in [16]
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