Extended mild-slope equation for random waves

Abstract

A time-dependent extended mild-slope equation is derived from the elliptic equation of Chamberlain and Porter (1995) using the Taylor series technique. Numerical tests are made on a horizontally one-dimensional case for regular waves over sloping beds and for both regular and irregular waves over a ripple patch. Numerical results prove that the proposed model gives accurate results for both regular and irregular waves over rapidly varying topography.