Topographically-induced enstrophy production/dissipation in coastal models
E. Terrile, R. Briganti, M. Brocchini, J. T. Kirby
Physics of Fluids
Vorticity and enstrophy production and dissipation are studied for both wave-averaged and wave-resolving ͑Boussinesq-type͒ models of wave-induced near shore circulation. Quadratic flow properties of fundamental importance for shallow-water turbulence, i.e., energy and enstrophy, whose sources/sinks are clearly identifiable by positive/negative-definite contributions in the appropriate transport equations, are taken as the most suitable indicators for assessing model performance in describing
... ws characterized by large-scale vortices. Two state-of-the-art models, SHORECIRC and FUNWAVE2D, have been evaluated in detail. Suitable transport equations for enstrophy are derived and analyzed to get a clear insight into the mechanisms of generation/ dissipation of this quantity in both models. Analytical results show that steep gradients of the total flow depth act as sinks as well as sources for vorticity and entrophy, similar to the results of Brocchini and Colombini ͓M. Brocchini and M. Colombini, Phys. Fluids 16, 2469 ͑2004͔͒. Predictive estimates have been given for the rate of change of circulation for waves breaking over a bar or breakwater and the vorticity source and sink terms have been numerically analyzed. The comparison between numerical results obtained using the two different circulation models reveals that while wave-resolving computations give well-structured rip currents, the wave-averaged model predicts less organized flows, given the different structure of the circulation forcing terms. The analysis of equivalent enstrophy-forcing terms characterizing the two models shows that they are all proportional to depth gradients in the case of wave-resolving models while their intensity is mainly due to the gradients of the wave-induced velocity for wave-averaged models. Energetic considerations are also given in support of the proposed vorticity/enstrophy generation mechanisms. Wave-averaged computations clearly show that, apart from bottom friction, the most intense dissipation mechanism is due to classic viscous effects ͓− T ٌ͑ ͒ 2 ͔ while depth gradients weakly contribute. Rather surprisingly this also occurs for the wave-resolving model.