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A note on linear surface wave‐current interaction over slowly varying topography

A mild slope wave equation is derived which governs the propagation of linear surface waves in the presence of large ambient currents. The equation is shown to differ from two previously derived models, and arguments for the validity of the new version in comparison to previous versions are presented. A linearized evolution equation and parabolic equation approximation are constructed in order to show the correspondence between the present corrected version and a previously derived version of the time-dependent Schrodinger equation.