Vorticity generation due to cross-sea

Abstract

AbstractSimilarly to shore-parallel waves interacting with submerged obstacles, two wave trains, approaching the shore with different angles, generate breakers of finite cross-flow length and an intense vorticity at their edges. The dynamics of crossing wave trains in shallow waters is studied by means of a simple theoretical approach that is used to inspect the flow characteristics at breaking. The post-breaking dynamics, with specific focus on the vorticity generation and evolution processes, is described on the basis of the analytical results of Brocchini et al. (J. Fluid Mech., vol. 507, 2004, pp. 289–307). Ad hoc numerical simulations, performed by means of a nonlinear shallow-water equations (NSWE) solver, are used to support the analytical findings and detail the post-breaking flow evolution. Comparisons between numerical and analytical findings confirm that: (i) the cross-sea theory successfully predicts the breaking position when a finite-length breaker stems from two crossing wave trains and (ii) the dynamics induced by such a breaking (i.e. vorticity generation, mutual-advection and self-advection mechanisms) is similar to that occurring after the breaking event of a shore-parallel wave over a submerged obstacle: vortices generated at the breaker edges are first subjected to wave forcing and self-advection, these pushing the vortices shoreward; then, oppositely-signed vortices pair and the mutual interaction enables them to invert the motion and move seaward. Useful relationships have been found to describe the main features of such a dynamics (i.e. breaker length, vortex trajectories, etc.).