New Hamiltonian equations of high accuracy for ocean waves with applications in determining wave forces on offshore structures

Abstract

Purpose The purpose of this paper is to propose a new approach to further obtain reduced Hamiltonian equations for certain nonlinear cases of finite amplitude. Design/methodology/approach Chebyshev polynomials are introduced to best approximate the primitive exact wave equations. Findings New results are derived for certain nonlinear cases of finite amplitude. Furthermore, ranges of applicability are determined in conjunction with the error analyses for various cases. In particular, the new structure can give a new highly accurate formula for determining the wave forces of the offshore structures. Originality/value New reduced Hamiltonian equations for nonlinear surface gravity waves have been derived for certain cases of finite amplitude for the first time. And the new structure can give a new highly accurate formula for determining the wave forces of offshore structures. These results extend the usual results for weakly nonlinear surface waves to nonlinear surface waves over certain finite ranges.