The Baroclinic Response of Straits and Bays to Coastal-Trapped Wave Scattering

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  • 1 School of Mathematics, University of New South Wales, Kensington, New South Wales, Australia
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Abstract

A result for the conservation of bottom pressure along coastal isobaths is used to show how coastal-trapped wave (CTW) energy may be scattered into baroclinic and barotropic motions within straits and bays. Central to this scattering problem is the decoupling of CTWs and internal Kelvin waves (IKWs) for broad flat shelves where the former are shown to be either barotropic at the coast or trapped out on the shelf slope and break. In this case, the horizontal gradients of incident CTW bottom pressure that map into vertical gradients at the strait or bay mouth may be represented as a set of IKWs. A pair of decoupled long-wave equations are derived to describe the approximate baroclinic and barotropic response of the strait or bay to forcing by these IKWs as well as the scattered CTWs on the adjacent shelf. The results are applied to Bass Strait where about 1% of the energy of a mode 1 incident CTW is shown to force a 10-day period IKW, with temperature and velocity oscillations of about 1°C and 20 cm s−1. For the relatively narrow shelf adjacent to Jervis Bay, the CTWs and IKWs do not decouple and the scattering of energy in the bay is described by a forced CTW equation that is not easily solved. However, approximate results obtained suggest that observed 10-day period fluctuations of temperature (0.6°C) and velocity (5 cm s−1) in the bay may result from the scattering of a CTW on the shelf.

Abstract

A result for the conservation of bottom pressure along coastal isobaths is used to show how coastal-trapped wave (CTW) energy may be scattered into baroclinic and barotropic motions within straits and bays. Central to this scattering problem is the decoupling of CTWs and internal Kelvin waves (IKWs) for broad flat shelves where the former are shown to be either barotropic at the coast or trapped out on the shelf slope and break. In this case, the horizontal gradients of incident CTW bottom pressure that map into vertical gradients at the strait or bay mouth may be represented as a set of IKWs. A pair of decoupled long-wave equations are derived to describe the approximate baroclinic and barotropic response of the strait or bay to forcing by these IKWs as well as the scattered CTWs on the adjacent shelf. The results are applied to Bass Strait where about 1% of the energy of a mode 1 incident CTW is shown to force a 10-day period IKW, with temperature and velocity oscillations of about 1°C and 20 cm s−1. For the relatively narrow shelf adjacent to Jervis Bay, the CTWs and IKWs do not decouple and the scattering of energy in the bay is described by a forced CTW equation that is not easily solved. However, approximate results obtained suggest that observed 10-day period fluctuations of temperature (0.6°C) and velocity (5 cm s−1) in the bay may result from the scattering of a CTW on the shelf.

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