Interior Shelf Waves on an Equatorial β-Plane

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  • 1 School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia
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Abstract

In this note the properties of long-period waves on an interior exponential shelf on an equatorial β-plane are determined. When both the shelf and deep-sea region are in the same hemisphere the wave properties are similar to those of an exponential continental shelf. However, when the shelf and deep-sea regions are in opposite hemispheres a finite number of westward propagating modes may exist for a fixed wavenumber. All westward modes, except the fundamental mode, have a zero group velocity and a long-wave cutoff for trapping. The fundamental approaches the cutoff as the wavenumber decreases. When the shelf straddles the equator westward, eastward propagating modes may exist. In the case of the southern edge of the Melanesian Basin, the relevant resonant frequency at the zero group velocity in the fundamental mode is found to be between 25 and 33 days.

Abstract

In this note the properties of long-period waves on an interior exponential shelf on an equatorial β-plane are determined. When both the shelf and deep-sea region are in the same hemisphere the wave properties are similar to those of an exponential continental shelf. However, when the shelf and deep-sea regions are in opposite hemispheres a finite number of westward propagating modes may exist for a fixed wavenumber. All westward modes, except the fundamental mode, have a zero group velocity and a long-wave cutoff for trapping. The fundamental approaches the cutoff as the wavenumber decreases. When the shelf straddles the equator westward, eastward propagating modes may exist. In the case of the southern edge of the Melanesian Basin, the relevant resonant frequency at the zero group velocity in the fundamental mode is found to be between 25 and 33 days.

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