Flow mixing solutions of a Boussinesq-tye model: towards a dispersive HLES

Horizontal mixing of shallow coastal flows is studied with specific focus on the role played by large-scale horizontal eddies (macrovortices). Description of macrovortex-induced mixing is given on the basis of numerical solutions of a specific Boussinesq-type model, FUNWAVE2D, commonly used for analyses of nearshore circulation. Validation of the model results is first made against a set of experimental data, concerning single breakwater and rip current bathymetries, forming the `Bari dataset', here taken to represent the ground truth. The model's tunable parameters are, then, calibrated to satisfy an overall best agreement between the numerical solutions and the measurements. The main results of the work are concerned with a sensitivity analysis of the numerical solutions on both the type/intensity of subgrid scale (SGS) turbulence modelling and the intensity of the breaking induced dissipation. Statistics of mixing, rather than inspection of the velocity spectra, are used to assess the value of the best-fitting parametrization. Such analysis reveals that the model's results depend very weakly on the type and intensity of the subgrid turbulence representation (no dependence at all is found for the longer waves), while they are very sensitive to the intensity of wave breaking. For both types of bathymetries at hand (neighbouring or isolated submerged breakwaters) an increasing intensity of wave breaking leads increasing values of dispersion and diffusivity. A discussion is, finally, provided on the role of the mentioned parametrizations towards suitable Horizontal Large Eddy Simulations (HLES) of coastal flows performed by means of depth averaged, frequency-dispersive models. It seems well evident that, provided small enough grid sizes are used (smaller than the representative water depth), also for dispersive models much more important is to focus on the correct parametrization of breaking than on that of the subgrid turbulence.