Modeling the Frictional Effect on the Rip Current on a Linear Depth Profile

We develop an analytical theory for the interaction between waves and currents induced by breaking waves on a depth profiles. Here we examine the effect of friction on the rip currents and so are not particularly concerned with frictionally determined rip currents. The near shore is characterized by the presence of breaking waves, and so we develop equations to be used outside the surf zone, based on small-amplitude wave theory, and another set of equations to be used inside the surf zone, based on an empirical representation of breaking waves. Suitable matching conditions are applied at the boundary between the offshore shoaling zone and the near shore surf zone. Both sets of equation are obtained by averaging the basic equations over the wave phase. Thus the qualitative solution constructed is a free vortex defined in both shoaling and surf zone where in the surf zone the free vortex is perturbed by a long shore component.