Topographically-controlled, breaking wave-induced macrovortices. Part 3. The mixing features.

The series of papers on the flow dynamics due to wave-induced macrovortices is completed with a statistical analysis of the mixing of the shallow flows occurring around submerged structures used for coastal protection. This is investigated with specific focus on the role played by large-scale horizontal eddies shed in coastal areas by waves breaking corresponding to topographic features like submerged breakwaters. As in Part 2, conditions due to isolated or arrays of breakwaters are studied. Analysis of particle statistics is used to determine both the features of the induced quasi-twodimensional flow and to derive general properties. In particular three distinct regimes are found to characterize the flow evolution. Asymptotic regimes for small and large times share in any of the features of typical ‘ballistic’ and ‘Brownian’ regimes. Focus is mainly placed on properties of the ‘intermediate time’ regime which are seen to depend on the chosen topographic configuration. In agreement with the deterministic results of Part 2, we find that, because of an intense longshore current, an isolated breakwater induces a larger dispersion than that due to an array of breakwaters, characterized by a rip current. Moreover, for the same topography, the diffusivity grows with the local wavelength. Comparison with field data suggests that results of scaled-down laboratory experiments reproduce well natural mixing conditions. A simple formulation of absolute diffusivity, to be used in practical applications related to environmental quality management, is, finally, proposed.