The flow and sediment transport in the boundary layer at the sea bottom due to the passage of surface waves are determined by considering small values of the wave steepness and of the ratio between the thickness of the boundary layer and the local water depth. Both the velocity field and the sediment transport rate are determined up to the second order of approximation thus evaluating both the steady streaming and the net (wave-averaged) flux of sediment induced by nonlinear effects. The flow regime is assumed to be turbulent and a two-equation turbulence model is used to close the problem. The bed load is evaluated by means of an empirical relationship as function of the bed shear stress. The suspended load is determined by computing the sediment flux, once the sediment concentration is determined by solving an appropriate advection–diffusion equation. The decay of the wave amplitude, which is due to the energy dissipation taking place in the boundary layer, is taken into account. The steady streaming and the sediment transport rate at the bottom of sea waves turn out to be different from those which are observed in a wave tunnel (U-tube), because of the dependence on the streamwise coordinate of the former flow. In particular, in the range of the parameters presently investigated, the sediment transport rate at the bottom of sea waves is found to be always onshore directed while, in a water tunnel (U-tube), the sediment transport rate can be onshore or offshore directed
SUMMARYAn application of multidomain decomposition to the computation of the steady free surface flow past a ship hull is presented. Viscous effects are taken into account in the neighbourhood of solid walls and in the wake by the Reynolds averaged Navier-Stokes equations, whereas the assumption of irrotationality in the external flow allows a description by a potential model. Free surface boundary conditions have been implemented in a linearized form at the undisturbed waterplane. Suitable matching conditions are enforced at the interface between the viscous and the potential regions. The numerical results obtained for two merchant ship forms (the HSVA tanker and the Series 60 hull) are compared with experimental data available in the literature.
This study deals with the instabilities that arise in the flow generated in a rotating tank by the evolution of a two-layer density stratified fluid. Numerical investigations have been performed by direct simulation of the Navier-Stokes equations for axisymmetric and fully three-dimensional flows. In the former case results have shown the attainment, in a very short time, of an equilibrium position and the formation of an anticyclonic structure in the upper light layer and a cyclonic one in the lower layer, consistently with the observation of Griffiths and Linden. In the long term, however, the Ekman layer at the bottom damps out the cyclone and a steady state with only an anticyclone in the upper layer is reached. In three-dimensions the flow is unstable to azimuthal disturbances and the steady state is no longer achieved. In particular a ring of cyclonic vorticity, surrounding the anticyclone, by the combined effects of baroclinic and barotropic processes, breaks, entrains vorticity from the anticyclone and eventually forms vortex pairs. As observed by Griffiths and Linden the azimuthal wave number (n*) of the instability depends on the Richardson number (Ri) and the ratio between the depth of the light fluid and the total depth (δ). However, since several modes, in addition to the most unstable, are amplified an initial perturbation whose energy is not equidistributed among the modes can lead to an instability with wave number different from the expected n*. Finally, the analysis of the equation for the energy of the instability has shown that the instability is initially driven by baroclinic effects, even for low values of δ. The barotropic source, in contrast, sets in only in the large-amplitude phase of the instability and its effect is larger when δ is small.
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