Wave‐current interactions on a slowly varying topography

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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