A set of fully nonlinear mild slope equations

Abstract

A set of time-dependent fully nonlinear mild slope equations is established in terms of velocity vector at still water level and free surface elevation, which is derived from the Euler equations without approximation in nonlinearity and only with the potential flow assumption adopted for bottom slope terms. Apart from the fully nonlinear property, the model is also different from previous nonlinear mild slope equations by adopting the velocity expression accurate to the first-order in bottom slope, which allows the new expressions of higher-order bottom slope terms to be established and the fully nonlinear terms related to bottom slope to be included in the equations. The model can be reduced to the classical mild slope equation for linear waves and the fully nonlinear Boussinesq equations for nonlinear waves. The advantages of the present model are validated against the related laboratory experimental results and demonstrated by comparison with the numerical results of other relevant models.