Numerical Modeling of Waves Generated by High-Speed Vessels in Shallow Water with a Coupled Boussinesq-Panel Method

A numerical model is developed to simulate waves generated by high-speed vessels traveling at subcritical, transcritical and supercritical speeds in shallow water over water of varying depth. The waves in the far field are assumed to be weakly dispersive with wavelengths much longer than the water depth. The vertical profile of the flow field is obtained from a second-order Taylor series expansion of the velocity potential about an arbitrary elevation in the water column. The velocity potential in the region near the ship is decomposed into a far-field potential, that is valid throughout the computational domain, and a local near-field body potential that decays rapidly away from the body. The boundary integral method is used to solve for the near-field body potential. The formulation leads to a fully nonlinear set of Boussinesq-type water wave evolution equations with forcing terms from the boundary integral of a source distribution over the body surface in the near field. An eddy viscosity-based formulation is used to simulate energy dissipation due to wave breaking. The resulting system of evolution equations are integrated in time using a finite difference method. Numerical model predictions are compared with data from laboratory experiments on ship-generated waves over a wide range of depth-based Froude numbers (0.7 < Fh < 2) in both wide and narrow channels.