Separated flows near a free surface

The understanding of the phenomenon of flow separation is important in a wide variety of flows in marine-related engineering. Particularly, prediction of forces on bodies and their motions is dependent on one's ability to model flow separation accurately. Current numerical methods, however, are useful only in a relatively low Reynolds number regime.;In this work, vortex methods for the simulation of two-dimensional unsteady flows induced by bodies moving in an incompressible viscous fluid are studied, with an emphasis on the incorporation of effects of body motion in the presence of a free surface. Flows due to moving submerged and floating bodies are considered. The random walk method is used for the solution of the Navier-Stokes equation to allow for the simulation of high Reynolds number flows. An extension of this method for free-surface flow problems is developed. Different methods for the solution of the Poisson equation for the stream function are examined. A formulation based on the complex velocity potential is selected for studying flows in the presence of a free surface. This method has the capability of handling arbitrary body geometry and large free-surface deformations. To facilitate the accurate computation of the pressure on body contours, an integral equation for the acceleration potential is simultaneously solved. An O(N) multipole algorithm for computing the N-vortex interaction problem is implemented for the efficient solution of the convection equations.;This highly effective numerical method is validated against experimental results. Effects of changing numerical parameters are studied. The ability of this method in simulating flows due to various body motions and incident flows is demonstrated. Short and long time simulations of uniform flow past a circular cylinder show features that are in agreement with experimental observations. Oscillating flows past a fixed circular cylinder and transversely oscillating cylinders in a fixed stream are also studied.;It is shown that the forces on deeply submerged bodies are mainly due to inertial and viscous effects, the free-surface effects being small. The effect of the vortical wake on the free-surface elevation is found to be significant. The damping effect associated with vortex shedding from the body is studied. The viscous damping is found to dominate over wave damping for large amplitude motion of submerged bodies. Either component may dominate for surface-piercing bodies, depending on the frequency, mode of motion, and body geometry. Vortex shedding patterns related to heave, sway and roll motion of surface-piercing bodies are examined. Wave breaking due to physical and numerical reasons often limit the length of duration of the solution.