WAVE EQUATION MODEL FOR SHIP WAVES IN BOUNDED SHALLOW WATER

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Ships were modelled as moving pressure disturbances on the free surface of a shallow water basin in the present paper.The moving-pressure generating waves were subjected to the reflection of land boundaries and the radiation of open boundaries.This paper proposed and examined a wave equation model (WEM) to solve the shallow water equations with moving surface pressures simulating ship waves in a bounded shallow water region.The Galerkin finite element method was used to solve a second order wave equation for the free surface elevations and the hydrodynamic pressure of the ship bottom simultaneously.Horizontal velocities were obtained from the momentum equations.Numerical solutions of Series 60 CB=0.6 ships moving with the depth Froude number of Fh=0.6, 1.0, 1.3 in a rectangular shallow water harbor were investigated.Three dimensional surface elevation profiles and the depth-averaged horizontal velocities were analysed.The numerical results characterised very well the ship waves in shallow water.Strong boundary reflection waves were found in the case of high depth Froude number (Fh=1.3).Waves generated by the interactions of two ships moving in the same directions and in the opposite directions were also numerically investigated in the present study.
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