Conservation Properties of the Mild Slope and Boussinesq Equationsby Rodney J. Sobey, Univ of California, Berkeley, United States,
Abstract: Common water wave evolution equations, such as the mild slope equation, parabolic approximations and Boussinesq equations, are approximate statements of conservation laws. A feasible measure of their adequecy is their ability to predict steady progressive wave propagation over a horizontal bottom, where near-exact kinematics are predicted by steady wave theory. None of the common evolution equations satisfy the conservation laws. The relative errors are surprisingly large and no existing evolution is acceptable. A Boussinesq-style equation, with almost acceptable error levels, is suggested. An accurate, robust and viable water wave evolution equation for an uneven bottom is not presently available.
Subject Headings: Water waves | Wave equations | Water conservation | Progressive waves | Slopes | Boussinesq equations | Laws
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