Numerical Studying Of Ship Waves In Shallow Water Based On Green-Naghdi Equations

With increasing of ship size, speed and power, shipbuilding industry has achieved a great advance in recent years. A great number of ships moved in shallow water, such as rivers, lakes and estuaries. Nonlinearity, frequency dispersion, free surface disturbance, energy dissipation and boundary reflection may play important roles to ship waves in shallow water. Topography complexity, such as irregular boundaries, varying water depth, makes ship waves more difficult. The shallow water ship waves are of great importance to water environments, engineering applications as well as the ships themselves. It is of great importance to investigate the dynamic behavior of the ship waves in shallow water.This work is focused on numerical study of waves generated by ships moving in shallow water based on Green-Naghdi equation. A moving ship is regarded as a moving pressure disturbance on free surface in this study. The moving pressure is incorporated into the Green-Naghdi equations to formulate forcing of ship waves in shallow water. Three-dimensional ship wave profiles, wave resistance and transverse forces are given. Generally speaking, ship waves in shallow water have small values, the ratio of water depth to wave length, and may be thought of as long waves. In fact, the ship wave is a combination of multi-frequency water waves. The wave constituents with finite values may have effects on ship waves. The frequency dispersion cannot be completely ignored. The frequency dispersion term of the Green-Naghdi equations accounts for the effects of finite water depth on ship waves. Kirby reviewed a variety of Boussinesq-type equations, which consider the frequency dispersion with different orders. The Green-Naghdi equation is a typical Boussinesq-type equation, which involves the nonlinearity and frequency dispersion. It does not require irrotational conditions and the limitation of the ratio of wave length to water depth. The Green-Naghdi equations have an analogous form to the two-dimensional non-viscous Navier-Stokes equations with an additional frequency dispersion term. The continuity equation is the first-order hyperbolic differential equation. It is known that the numerical solution of the first-order hyperbolic differential equation had been a difficult problem in computational fluid dynamics field. The numerical solutions of Green-Naghdi equations are easily spoiled by numerical oscillations. Wave equation model can eliminate numerical oscillation effectively and have better stability property. It had been successful used to solve shallow water questions in many practical applications. In this dissertation, a wave equation model and the finite element method (WE/FEM) are adopted to solve the Green-Naghdi equations. As the examples of Series 60 (CB = 60) ship, the numerical solutions of three-dimensional ship wave profiles, wave resistance and transverse forces are presented.The contents of this dissertation are summarized as follows. Chapter 1 introduces the effects of finite water depth on ship waves, and briefly discusses the theory of shallow water equations. Chapter 2 introduces some kinds of Boussinesq-type equations, and briefly discusses the Boussinesq equations. We have also analyzed how the frequency dispersion term in the Boussinesq equations modify the hydrostatical pressure in wate depth. Chapter 3 is devoted to the relation between the Green-Naghdi equations and Boussinesq-type equations. We also discuss frequency dispersion of the linear Green-Naghdi equations. In chapter 4, we present numerical solutions of the Green-Naghdi equations. A wave equation model and finite element method (WE/FEM) are adopted to solve shallow water questions, and the Green-Naghdi equations. Furthermore, the implementation of boundary conditions is also discussed in this chapter. Three-dimensional ship wave profiles and wave resistance when a Series 60 () ship moves at different speed in shallow water are presented in chapter 5. A comparison between the numerical results predicted by the Green-Naghdi equations and the s...