Hydraulic Jump and Undular Bore Formation on a Shelf Break

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  • 1 Department of Applied Mathematics, University of New South Wales, Kensington, N.S.W., Australia
  • | 2 Department of Geography and Oceanography, University College, University of New South Wales, Australian Defense Force Academy, Canberra, Australia
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Abstract

The evolution of the semidiurnal internal tide as it propagates across the Australian North West Shelf is discussed analytically. As the tide is of long wavelength and small amplitude, this evolution is described by a perturbed extended Korteweg-de Vries equation. It is found that the flow is dominated by nonlinearity, and hence is hydraulic, except in the neighborhood of any shocks predicted by hydraulic theory. Hydraulic theory predicts the formation of two shocks in each period of the tide. The inclusion of dispersion in boundary layers around the shocks results in one of these shocks breaking up into an undular bore. Good agreement is found with observations by Holloway of the semidiurnal internal tide on the Australian North West Shelf.

Abstract

The evolution of the semidiurnal internal tide as it propagates across the Australian North West Shelf is discussed analytically. As the tide is of long wavelength and small amplitude, this evolution is described by a perturbed extended Korteweg-de Vries equation. It is found that the flow is dominated by nonlinearity, and hence is hydraulic, except in the neighborhood of any shocks predicted by hydraulic theory. Hydraulic theory predicts the formation of two shocks in each period of the tide. The inclusion of dispersion in boundary layers around the shocks results in one of these shocks breaking up into an undular bore. Good agreement is found with observations by Holloway of the semidiurnal internal tide on the Australian North West Shelf.

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