Study of Gravitational Water Wave with Vortex Effect

• Main Authors: Meng-Yu Lin, 林孟郁
• Other Authors: 黃良雄
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/50922953224789802844

博士 === 國立臺灣大學 === 土木工程學研究所 === 96 === The present work develops a 2-D numerical scheme which combines vortex method and boundary integral method to investigate the interaction of water waves with submerged obstacles. The major advantages of this method are the efficiency on solving the free surface motion and the irrotational flow field by using the boundary integral formulations, and the essentially grid-free nature of the vortex particle method for solving the vorticity field. Using this method we may concentrate the computational resources on the simulation of surface waves and on the evaluation of vorticity which is predominantly confined in compact regions. The numerical method is accomplished by using a Helmholtz decomposition which decomposes velocity field into its irrotational and rotational components. The distribution of dipole (vortex) along the free surface determines the irrotational component of flow field, and the distribution of vortex along the solid surface determines the vorticity flux into the fluid. Viscous effects and generation of vorticity on the free surface are neglected. For evaluating the strengths of singularities a boundary integral method is used in which the resulting Fredholm integral equations of the second kind are solved efficiently in both storage and work by iteration. Vorticity generated from the submerged obstacle is convected and diffused in the fluid via a Lagrangian vortex (blob) method, using the particle strength exchange (PSE) method for diffusion, with particle redistribution. A sub-grid eddy viscosity model is used to simulate the turbulent effects. The inviscid part of the numerical method and the performance in the computation of nonlinear waves are tested using a calculation of solitary wave propagation in a uniform channel. A further test for the simulation of the free surface deformation induced by a moving line vortex in the fluid is performed. In these tests good agreements between numerical and theoretical results are obtained. The full model is verified by simulating periodic and solitary waves travelling over a submerged rectangular obstacle, and the results are compared with laboratory measurements. All comparisons exhibit reasonably well agreement. Applications to periodic and solitary water waves over a submerged rectangular obstacle are given. For periodic waves, the effects of the incident wave length, still water depth and the length of the obstacle on the vortex generation and evolution are presented. The results lead us to the conclusion that for periodic water waves the Keulegan-Carpenter number is the key parameter in determining the formation and development of the vortices generated from submerged obstacles. For solitary waves, the effects of the incident wave height are discussed. In contrast with periodic waves, the vortices generated from the submerged obstacle in a solitary wave are preserved in a long period because there is no reversed flow. The strength of vortices and their effects are positively correlated with the incident wave height.