We investigate, within the framework of the nonlinear shallow water equations (NSWE), the generation and evolution of large-scale eddies with vertical axis (macrovortices hereinafter) which are responsible for much of the horizontal mixing occurring at the boundaries between the main channel and the flood planes of a compound channel. We show that the mechanism of generation of vorticity is essentially inviscid and is analogous to that occurring at a curved shock. Numerical experiments performed by means of a recently developed shock-capturing model for the solution of the NSWE, and described in Brocchini et al. (2001), clarify some features of macrovortices generation and allow us to quantify the momentum transfer across the channel.
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-two-dimensional 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.
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