On simulation of turbulent nonlinear free-surface flows

A method for numerical simulation of the unsteady, three-dimensional, visco us Navier-Stokes equations for turbulent nonlinear free-surface flows is pr esented and applied to simulations of a laminar standing wave and turbulent open-channel flow with a finite-amplitude surface wave. The solution domai n is discretized with a boundary-orthogonal curvilinear grid that moves wit h the free surface, allowing surface deformations to be smoothly resolved d own to the numerical grid scale. The nonlinear kinematic and dynamic bounda ry conditions for boundary-orthogonal curvilinear coordinates are developed and discussed with a novel approach for advancing the free surface in curv ilinear space. Dynamic large-eddy-simulation techniques are used to model s ubgrid scale turbulence effects. The method is shown to correctly produce t he shape of a nonlinear free-surface wave and its decay due to viscosity. A pplication to finite-amplitude waves moving over a turbulent channel flow a llows demonstration of the clear differences between a channel flow with an d without waves, particularly the instantaneous turbulence structure. An in teresting sidelight is the appearance of short-crested cross-channel surfac e waves caused by natural resonance. (C) 1999 Academic Press.