Longshore currents generated by obliquely incident sea waves: 2

TLDR

Current profiles peak in the surf zone and vanish at the swash line. The authors derive longshore current profiles from radiation stress and a horizontal eddy viscosity μe = ρNx(gh)½, yielding a family of profiles governed solely by the nondimensional parameter P = (Π/2)(sN/αC). Experimental comparison confirms good agreement when C = 0.010, and indicates that P does not exceed 0.4.

Abstract

The profile of the longshore current, as a function of distance from the swash line, is calculated by using the concept of radiation stress (introduced in an earlier paper) together with a horizontal eddy viscosity μe of the form μe = ρNx(gh)1/2, where ρ is the density, x is the distance offshore, g is gravity, h is the local mean depth, and N is a numerical constant. This assumption gives rise to a family of current profiles whose form depends only on the nondimensional parameter P = (Π/2)(sN/αC), where s denotes the bottom slope, α is a constant characteristic of breaking waves (α ≑ 0.41), and C is the drag coefficient on the bottom. The current profiles are of simple analytic form, having a maximum in the surf zone and tending to zero at the swash line. Comparison with the laboratory experiments of Galvin and Eagleson (1965) shows remarkably good agreement if the drag coefficient C is taken as 0.010. The theoretical profiles are insensitive to the exact value of P, but the experimental results suggest that P never exceeds a critical value of 2/5.