A parabolic approximation formulation is presented herein to study the wave‐current interactions on a slowly varying topography. Model equations are first derived from the mild‐slope assumption. A parabolic approximation is then applied to convert a boundary value problem to an initial value problem. Several limiting cases are discussed. Numerical examples are given for the case concerning the interactions between jet‐like currents and normal incident waves on a sloping beach (Arthur, 1950).
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Philip L.‐F. Liu (1983) studied this question.
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