Numerical Simulation of a Fully-Nonlinear Free-Surface Flow and its Application on the Studies of Microscale Dynamics in the Upper Oceans

• Main Author: 洪立萍
• Other Authors: 蔡武廷
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/76260273995611416353

博士 === 國立交通大學 === 土木工程系所 === 95 === A numerical model for simulating a three-dimensional flow bounded by a fully-nonlinear, free-surface boundary is developed. The free-surface boundary conditions are satisfied on the free-moving surface exactly without any approximation or linearization. The governing equations and the boundary conditions on the time-dependent, physical domain are transformed onto a regular domain for numerical computations. The major implementations of the developed model include: Pseudo-spectral and finite-difference schemes are employed to approximate the spatial-differential operators in the horizontal and vertical directions, respectively. A second-order Runge-Kutta method is adopted to integrate in time for the velocity field and the free-surface elevation. The solenoidal condition of the velocity field is satisfied by solving the transformed pressure Poisson equation. A modified secant method is used to accelerate the iterative solution of the non-separable Poisson equation. We first apply the numerical model to study the development and evolution of parasitic capillary ripples on a two-dimensional gravity-capillary wave. The simulation results reveal that strong vortices are shed from the troughs of the capillary ripples, convected backward, and form a strong boundary layer. As a result, energy dissipation is enhanced with the generation of parasitic capillaries. The model capabilities for resolving nonlinear interactions among the surface waves are then demonstrated by simulating the three-dimensional evolutions of the short-crested waves and the crescent waves. Finally, the developed model is applied to simulate a wind-driven turbulent boundary layer bounded by a dynamic water surface. The simulation results reveal fine surface structures, including parasitic capillary waves developed from the front face near the crest of the dominant gravity wave and streamwise velocity streaks on the back gravity-wave surface. These surface structures have been widely observed in the laboratory and field experiments. The three simulation examples also indicate the capabilities of the present model in resolving flow processes of various length scales, including gravity and capillary waves, viscous sublayer and coherent eddies of a turbulent boundary layer.