International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 589-613

A theory of nonlinear wave loading on offshore structures

Lokenath Debnath1 and Matiur Rahman2

1Mathematical Institute, University of Oxford, Oxford, UK
2Hydraulics Laboratory, Division of Mechanical Engineering, National Research Council of Canada, Ottawa, Canada

Received 1 May 1980; Revised 25 June 1980

Copyright © 1981 Lokenath Debnath and Matiur Rahman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A theoretical study is made of the nonlinear wave loading on offshore structures using the diffraction theory of hydrodynamics. A nonlinear modification of the classical Morison equation, DF+FD for estimating wave forces on offshore structures is suggested in this paper. The modified equation is found in the form DF+Fn+FD where FnFd+Fw+Fq is the nonlinear contribution made up of the dynamic, waterline, and the quadratic forces associated with the irrotational-flow part of the wave loading on structures. The study has then been applied to calculate the linear and the nonlinear wave loadings on a large vertical cylinder partially immersed in an ocean of arbitrary uniform depth. All the linear and nonlinear forces exerting on the cylinder are determined explicitly. A comparison is made between these two kinds of forces. Special attention is given to the nonlinear wave loadings on the cylinder. It is shown that all nonlinear effects come from the interaction between the body's responses to the oncoming wave's fluctuating velocity and its fluctuating extension. It is found that the nonlinear effects are dominated by the sum of the dynamic and waterline forces. The nonlinear correction to Morison's equation increases with increasing kb where b is the characteristic dimension of the body and k is the wave number. This prediction is shown to be contrary to that of the linear diffraction theory which predicted that the Morison coefficient decreases with increasing kb. Several interesting results and limiting cases are discussed in some detail.