Boussinesq equations with improved dispersion characteristics are used to simulate the generation and propagation of waves due to moving pressure fields. With surface pressure terms in the momentum equations the numerical scheme is first run for a moving 3-D hemispherical pressure field for a range of Froude numbers. The wedge angles obtained from simulations are compared with the values calculated from the analytical formulas of Havelock. Furthermore, two ship-like slender pressure fields, representing a moving catamaran, are employed to visualize the interaction of the waves generated.
INTRODUCTION He first depth-integrated nonlinear wave model that included the weakly dispersive effects as a non-hydrostatic pressure was derived by Boussinesq (1871) for constant water depth. Much later, Mei and LeMeháute (1966), and afterwards Peregrine (1967) derived Boussinesq equations for variable depth. While Mei and LeMeháute used the velocity at the bottom as the dependent variable, Peregrine used the depth-averaged velocity. Due to wide popularity of the equations derived by Peregrine, these equations are often referred to as the standard Boussinesq equations for variable depth in the coastal engineering community. To obtain a set of equations with better dispersion characteristics Madsen et. al (1991) and Madsen and Sørensen (1992) added higher-order terms with adjustable coefficients into the standard Boussinesq equations for constant and variable water depth, respectively. Beji and Nadaoka (1996) gave an alternative derivation of Madsen et. al's (1991) improved Boussinesq equations. Liu & Wu (2004) presented a model with specific applications to ship waves generated by a moving pressure distribution in a rectangular and trapezoidal channel by using boundary integral method. Torsvik (2009) made a numerical investigation on waves generated by a pressure disturbance moving at constant speed in a channel with a variable cross-channel depth profile by using Lynett et. al (2002) and Liu & Wu (2004)'s COULWAVE long wave model.