Abstract
A method for numerical simulation of the unsteady, three-dimensional, viscous Navier–Stokes equations for turbulent nonlinear free-surface flows is presented and applied to simulations of a laminar standing wave and turbulent open-channel flow with a finite-amplitude surface wave. The solution domain is discretized with a boundary-orthogonal curvilinear grid that moves with the free surface, allowing surface deformations to be smoothly resolved down to the numerical grid scale. The nonlinear kinematic and dynamic boundary conditions for boundary-orthogonal curvilinear coordinates are developed and discussed with a novel approach for advancing the free surface in curvilinear space. Dynamic large-eddy-simulation techniques are used to model subgrid scale turbulence effects. The method is shown to correctly produce the shape of a nonlinear free-surface wave and its decay due to viscosity. Application to finite-amplitude waves moving over a turbulent channel flow allows demonstration of the clear differences between a channel flow with and without waves, particularly the instantaneous turbulence structure. An interesting sidelight is the appearance of short-crested cross-channel surface waves caused by natural resonance.
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