FREE-SURFACE WAVES GENERATION BY A FULLY SUBMERGED WAKE

The nonlinear evolution of two-dimensional instability waves in a full y submerged wake is studied numerically through direct numerical simul ation of the incompressible Euler equations subject to the dynamic and kinematic boundary conditions on the ocean surface. For a parallel, f ully submerged wake flow, the sinuous mode of linear instability is mo re unstable than the varicose mode. Therefore, the nonlinear evolution of the instability results in a staggered-vortex pattern in the bulk of the fluid, while the free-surface signature depends on the submerge nce depth of the mean velocity profile and the Froude number of the fl ow. Specifically, for large submergence depth and low Froude number th e flow reaches a quasi-equilibrium state, where the free surface takes the form of a propagating gravity wave with a very small height. Howe ver, for the same submergence depth, increasing the Froude number beyo nd a certain value causes breaking of the free-surface wave. For high a Froude number, wave breaking is caused by the presence of a sharp ve rtical velocity shear along the free surface for deep and shallow wake s alike. For small submergence depth. on the other hand, the free-surf ace wave breaks even for low Froude number, because of the sharp horiz ontal velocity shear that is induced along the free surface by the vor tices of the flow.