Abstract
A new form of the Boussinesq equations applicable to irregular wave propagation on a slowly varying bathymetry from deep to shallow water is introduced. The equations incorporate excellent linear dispersion characteristics, and are formulated and solved in two horizontal dimensions. In an earlier paper we concentrated on wave propagation and diffraction on a horizontal bottom in deep water. In this paper these principles are generalized and the Boussinesq equations are extended to include terms proportional to the bottom slope, which are essential for the shoaling properties of the equations. The paper contains a linear shoaling analysis of the new equations and a verification of the numerical model with respect to shoaling and refraction-diffraction in deep and shallow water.
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