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Zbl 0848.76010
Porter, D.; Staziker, D.J.
Extensions of the mild-slope equation. (English)
[J] J. Fluid Mech. 300, 367-382 (1995). ISSN 0022-1120; ISSN 1469-7645/e

Summary: The use of the mild-slope approximation, which is invoked to simplify the problem of linear water wave diffraction-refraction by bed undulations, is reassessed by using a variational method. It is found that smooth approximations to the free surface elevation obtained by using the long-standing mild-slope equation are not consistent with the continuity of mass flow at locations where the bed slope is discontinuous. The use of interfacial jump conditions at such locations significantly improves the accuracy of approximations generated by the mild-slope equation and by the recently derived modified mild-slope equation. The variational principle is also used to produce a generalization of these equations and of the associated jump condition. Numerical results are presented to illustrate the main points of the theory.

MSC 2000:: *76B15 Wave motions (fluid mechanics)
86A05 Hydrology, hydrography, oceanography

Keywords: linear water wave diffraction-refraction; bed undulations; variational method; continuity of mass flow; interfacial jump conditions

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