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The Scattering of Continental Shelf Waves by an Isolated Topographic Irregularity

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  • 1 Department of Marine Science and Engineering, North Carolina State University, Raleigh 27650
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Abstract

A model for the scattering of a continental shelf wave by a small, isolated and smooth topographic irregularity is developed. It is found that a wave of frequency ω, incident on a bump of a sufficiently small horizontal extent such that the solution for a delta-function bump will apply, will trigger all other allowable modes of the same frequency with the highest modes having the largest amplitudes. Further, the higher the mode of the incoming wave, the more strongly will it be scattered. Thus, for a continuous spectrum of continental shelf waves propagating over complicated and extended topography, one would expect a net cascading process toward the higher wavenumber end of the spectrum due solely to the effects of topography. It is noted, however, that if the solution is integrated over a bump of large horizontal extent, the behavior of the forward-scattered and backscattered waves could be entirely different from that of a delta function bump.

Abstract

A model for the scattering of a continental shelf wave by a small, isolated and smooth topographic irregularity is developed. It is found that a wave of frequency ω, incident on a bump of a sufficiently small horizontal extent such that the solution for a delta-function bump will apply, will trigger all other allowable modes of the same frequency with the highest modes having the largest amplitudes. Further, the higher the mode of the incoming wave, the more strongly will it be scattered. Thus, for a continuous spectrum of continental shelf waves propagating over complicated and extended topography, one would expect a net cascading process toward the higher wavenumber end of the spectrum due solely to the effects of topography. It is noted, however, that if the solution is integrated over a bump of large horizontal extent, the behavior of the forward-scattered and backscattered waves could be entirely different from that of a delta function bump.

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