Numerical simulation of nonlinear free-surface waves on a turbulent open-channel flow

A new method of numerical simulation for unsteady free-surface flows is developed and applied to the simulation of three-dimensional finite-amplitude surface waves propagating over a turbulent, sheared current. The numerical method uses a finite-volume approach and is discretized in moving, boundary-fitted, curvilinear coordinates. A second-order accurate, fractional-step algorithm with a multigrid solver for the Poisson pressure equation is used to solve the three-dimensional, viscous, unsteady Navier-Stokes equations subject to the nonlinear kinematic and dynamic boundary conditions. The free-surface is integrated in time using a Runge-Kutta 4th-order method applied to a new curvilinear derivation of the kinematic boundary condition. The dynamic boundary condition is invoked at the free surface as a set of pressure and zero tangential stress conditions on the Poisson solution and the velocity computation. The viscous boundary-layer beneath the free surface is resolved with approximately ten computational cells in the surface-normal direction. The curvilinear grid is updated to match the surface motion at each time step using a Poisson solution procedure from the 3DGRAPE/AL code. Large-eddy simulation (LES) with the dynamic two-parameter model (DTM) is applied to capture subgrid-scale turbulance effects.; Simulation results and analyses are provided for water waves with an initial ak of 0.18 that propagate over a turbulent current that has an {dollar}Resb{lcub}tau{rcub}{dollar} of 171. Results are compared to and have reasonable agreement with laboratory experiments. Wave/current interaction effects on the turbulence and the enstrophy are analyzed through comparison with simulations of an open-channel flow without a surface wave. Analysis shows that the surface wave stirs turbulent motions from the sheared current into the near-surface region. The turbulence becomes trapped in the near-surface region and is expanded and contracted by the passage of successive waves. Analysis of the wave-induced enstrophy shows that vortex stretching beneath the trough and crest significantly alters the distribution of enstrophy through the flow core.