A Numerical Study of Topographic Wave Reflection in Semi-Infinite Channels

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  • 1 Eidgenössische Technische Hochschute, Zürich, Switzerland
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Abstract

The Potential vorticity equation describing topographic waves is approximately solved using the channel method of Stocker and Hutter. The domain of integration is a semi-infinite channel and models an estuary, the bathymetry of which is varied through a transverse and a longitudinal topography parameter. It is shown that in this domain the spectrum of topographic waves consists of a discrete and a continuous part. The former exhibits wave modes trapped at the closed end of the channel; these waves correspond to the bay modes in a rectangular basin. Resonances with a similar bay-trapped structure also occur in the continuous spectrum. Their dependence on the bay geometry is studied. A consistent explanation of the three topographic wave types found earlier in an enclosed basin is given in terms of topographic wave reflections.

Abstract

The Potential vorticity equation describing topographic waves is approximately solved using the channel method of Stocker and Hutter. The domain of integration is a semi-infinite channel and models an estuary, the bathymetry of which is varied through a transverse and a longitudinal topography parameter. It is shown that in this domain the spectrum of topographic waves consists of a discrete and a continuous part. The former exhibits wave modes trapped at the closed end of the channel; these waves correspond to the bay modes in a rectangular basin. Resonances with a similar bay-trapped structure also occur in the continuous spectrum. Their dependence on the bay geometry is studied. A consistent explanation of the three topographic wave types found earlier in an enclosed basin is given in terms of topographic wave reflections.

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