Abstract
It is shown how the linear three-dimensional equations for surface water waves over a bottom of slowly varying depth may be approximated by a set of two-dimensional equations, the first of which is a simple extension of the equation derived by Berkhoff. Although the equation coefficients and the set structure are not simple, however this kind of approach does provide a new tool for the numerical solution of certain three-dimensional problems, for which, at present, other alternative approaches do not exist.
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