A dissipative point-vortex model for nearshore circulation

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Abstract
The hydrodynamic circulation of a nearshore region with complex bathymetry is inves- tigated by means of a point-vortex approach similar, but more complete and suited to practical applications, to that of Kennedy (J. Fluid Mech. vol. 497, 2003, p. 225). The generation and dissipation of each single-point vortex are analysed in detail to obtain a complete description of the vortex dynamics. In particular, we clarify how the mechanism for the generation of breaking-wave-induced macrovortices (large-scale two-dimensional horizontal vortices) can be practically implemented and we discuss in detail the mechanism leading to the dissipation of the circulation assigned to each vortex. Available approximate relations for the rate of generation of bar vortices are placed in context and discussed in detail, and novel approximate relations for the shore vortex generation and for the vortex viscous dissipation are proposed, the latter largely improving the description of the point vortex dynamics. Results have been obtained using three ‘typical’ rip-current bathymetries for which we also test qualitatively and quantitatively the model comparing the vorticity dynamics with the results obtained by means of both wave-resolved and wave-averaged circulation models. A comparison of dynamically equivalent flow configurations shows that the dissipative point-vortex model solutions, neglecting any influence of the wave field, provide rip current velocities in good agreement with both types of numerical solution. A more complete description of the rip current system, not limited to the rip-neck region as given by Kennedy (2003) by mean of an inviscid model, has been achieved by including dissipative effects.

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