Nonlinear Wave Deformation on a Beach with Arbitrary Profile

Summary

A new wave equation has been derived for fully nonlinear dispersive waves propagating over an arbitrarily shaped sea bed. The method of the derivation of the equation uses a conformal mapping technique by which the original domain can be transformed onto a uniform depth region to make the basic equation easily integrable vertically. By taking an inverse Fourier transform, the velocity potential obtained by the integration can be expressed in the form which can construct the exact wave equation from the water surface boundary conditions. An example of the numerical solution is presented to demonstrate the availability of the proposed wave equation. Further, for practical use, a WKB approximate solution is also presented.