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Energy flux of edge waves travelling along a continental shelf. (English) Zbl 0612.76051

(Author’s summary.) Longuet-Higgins (1964) originally recognised that the energy flux defined by pressure work from the equations of motion was not the same as the mean energy density times group velocity for planetary waves on a beta-plane. This paper addresses a similar paradox for linear, long period edge waves on an arbitrary shaped (in the offshore direction) straight continental shelf. The approach is to first examine a wavetrain solution to the problem and then to use a multiple scale argument which results in a solution as a group of waves modulated about a central frequency \(\sigma\) and wavenumber k. The paradox is resolved in both instances by noting that a divergence free quantity J can be included in the energy conservation equation to establish an equivalence between the two definitions of mean energy flux. For the wavetrain solution \(J(x)=(1/8)g^ 2h[AA^*/\sigma)_{kx}-4\sigma^{-1}Re(A_ xA^*_ k)]\), where x is the offshore direction, h(x) is the depth, A(k,x) is the complex wave displacement, \(\sigma\) is the frequency and k is the wavenumber. For the modulated group, the quantity J is given by \(J(x,Y,T)=J(x)BB^*\), where \(B=B(Y,T)\) is part of the edge wave complex amplitude A(k,x)B(Y,T) and Y,T are the long longshore and time variables, respectively. We discuss which energy flux definition is preferable in a given situation.
Reviewer: H.S.Takhar

MSC:

76E20 Stability and instability of geophysical and astrophysical flows
86A05 Hydrology, hydrography, oceanography
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