Abstract
The asymptotic equations of surf are derived for shallow beaches with a geometry causing long-shore variations in the water motion. Such surf is generally governed by three-dimensional nonlinear shallow-water equations. When the seabed profile parallel to shore is of gentler slope than the profile normal to shore, however, the asymptotic equations are shown to differ only in minor respects from those of two-dimensional surf. Such ‘weakly three-dimensional’ surf can be analyzed directly in terms of the results of the two-dimensional theory, and the run-up bounds of that theory are extended accordingly.
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