Large-eddy simulations (LES's)? for free-surface turbulent flows are conducted by solving the three-dimensional (3D) spatialfiltered Navier-Stokes (NS) equations with the Galerkin-weighted residual minimization. The turbulent closure is based on the Renormalization Group (RNG) theory. The solution procedure employs a projection method that uncouples the pressure from the velocity through enforcement of mass conservation. Fully nonlinear free-surface boundary conditions (BC's) are adopted. The complex processes of boundary layer separations, vortex shedding and turbulence transition beneath the free surface, particularly the wake-wave interactions are investigated. Calibration is made by a uniform flow past a vertical circular cylinder. The computed results correlate fairly well with the available experimental data in the time-averaged sense and indicate that the presence of a free-surface reduces the von Karman instability locally near the free surface. Presumably, this is because the flow instability associated with large-scale flow structures and induced by small-scale ones decreases under such a free-moving boundary, and the kinetic energy is partially transferred to the potential energy in order to follow the wave motion. This inference is further sustained by the variations of the computed hydrodynamic forces on rigid body surfaces.
In marine engineering, the presence of a free surface, which is usually pierced by bluff bodies, makes the wake structure very complicated. With the surface tension and viscous traction at the free surface, the transformation between potential and kinetic energies severely influences the turbulence transition, causes interaction between the wake and wave, and consequently, modifies the drag and lift forces acting on the bodies. In modeling the viscous free-surface flow, one encounters the difficulty arising from the coexistence of viscous and gravity forces, which causes the problem difficult to be totally scale independent. The resultant full-scale requirement dramatically increases the expense for physical experiments or even makes them impractical.
