Studies on finite amplitude waves in bounded water bodies

The problem treated here is the dynamics of a bay where water is driven through its opening periodically in time. The basic equations are expressed in the two horizontal coordinates and time and they are obtained by an integration of the Navier-Stokes equations in the vertical coordinate. The equations are nonlinear because of the convective terms in the acceleration. The problem of harbor dynamics provides a natural parameter as the ratio of mass of water entering the bay through the waves to the total mass of water in the bay. This small parameter multiplies the nonlinear terms and thus the problem is ideally suited for a perturbation analysis. The nonlinear terms are responsible for the generation of secondary flows and are particularly important near resonant frequences. The analysis further indicates the existence of a time independent flow analogous to acoustic streaming, known from solutions of the Navier-Stokes equations. The question of vorticity is studied and is seen that: a constant dissipation coefficient precludes the generation of vorticity even for the nonlinear case: and that only a weak (second order) vorticity can exist in the case of a variable dissipation term expressed through the Chezy coefficient. The study suggests also a semi analytic-numerical scheme with savings of 0(10²) for irregular geometries through the separation of the various order harmonics as opposed to the usual integration in time.