1 Waves Generated by Moving Pressure Disturbances in Rectangular and Trapezoidal Channels Philip L.-F. Liu and Tso-Ren Wu School of Civil and Environmental Engineering Cornell University, Ithaca, NY 14853 1. Introduction It is well known that in modeling the generation and propagation of ship waves the moving vessel can be modeled as a moving free surface pressure field. Since the ship waves might consist of both long wave and short wave components, the depth integrated long wave equations, such as the Green-Naghdi (GN) equations and the forced KdV (fKdV) equation might not be suitable for computing short wave components. Furthermore, the fKdV equation can only be applied to uni-directional wave propagation problems. For small Froude number flows, the fKdV equation approach is not valid. Although the Boundary Integral Equation Method (BIEM) approach, based on the Laplace equation and exact free surface boundary conditions, has been proposed (e.g., Cao et al., 1993), test cases are usually limited to the two-dimensional (vertical plane) cases. Because of the heavy computational demand, actual three- dimensional BIEM realizations are still not practical. In this paper, we shall focus our investigation on waves generated by a moving pressure disturbance in a straight channel. Although the model presented here allows an arbitrary channel cross- section, only the results for rectangular and trapezoidal cross-section are discussed. The model equations are capable of modeling a wide range of wave components, 0 kh π ≤ ≤ , where k is the wave number and h the water depth. It is well known that for the rectangular channel, a runaway solitary wave can be generated by a moving ship if the Froude number, / Fr U gh = , with U being the speed of the moving pressure field and g the gravitational acceleration, is near unity. In this paper, we shall investigate the effects of the slope of sidewalls on the characteristics of the runaway solitary waves, if any. 2. Model equations and numerical scheme The depth-integrated model equations for describing fully nonlinear and weakly dispersive waves have been presented by many researchers. In these models the atmospheric pressure is always assumed to be a constant. Therefore, these models cannot be used to investigate the wave generation and propagation induced by moving pressure disturbances. To include the atmospheric pressure variation in the existing models is straightforward: The only term needs to be added is the free surface pressure gradient in the momentum equation. Thus, the resulting model equations take the following form: ( ) [ ] ( ) ( ) [ ] ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 4 2 6 2 1 1 1 2 2 3 z h h h h z h h t z h z O α α α α α α α α α ζ εζ μ εμ ζ εζ εζ μ ∂ +∇⋅ + + ∇⋅ - ∇ ∇⋅ + + ∇ ∇⋅ ∂ + ∇⋅ - ∇ ∇⋅ + - ∇ ∇⋅ = ì ü æ ö æ ö í ý ç ÷ ç ÷ è ø è ø î þ ì ü é ù æ ö æ ö í ý ç ÷ ç ÷ ê ú è ø è ø ë û î þ u u u u u (1)