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relied on a bottom boundary condition specifying the mean flow velocity. Stive and Wind, however, stated that a shear stress at the trough level would be more beneficial in determining the internal mean flow distribution. Using measured data from various laboratory experiments, a comparison with the computed values produced results that better represented the strength and direction of the return flow.
Svendsen and Hansen (1988) discuss the problem of incorporating cross shore circulation into a numerical model that predicts wave height and set-up. Two obstacles associated with this are deterring the proper boundary conditions for the return flow and solving the mean bottom shear stress. For the return flow, Svendsen and Hansen counter Stive and Wind on the use of Eulerian streaming as the bottom boundary condition. They "suggest that the problem can be solved by satisfying the no-slip condition but assume a much smaller eddy viscosity in the bottom boundary layer than outside" (Page 1588). This idea is also applied in finding the bottom shear stress. The shear stress is a combination of the return flow and the mean oscillatory motion in the bottom boundary layer. Solving for this quantity is accomplished by simply applying the definition for the bottom shear stress at the point in the velocity profile where the transition occurs between the return flow and the bottom boundary layer. Employing their methods to the cross shore circulation model, Svendsen and Hansen believed that this method predicted circulation patterns more accurately.
Although these circulation models differ in detail, in each case the overall magnitude of below-trough seaward flow is largely determined by the chosen representation of the shoreward mass flux (mass conservation). Therefore, a viable simple alternative to detailed circulation modeling is to estimate the mass flux in the surf zone and then approximate a return flow from this shoreward mass flux.