A Theory of Nonlinear Wave Loading on Offshore Structures

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, D F + FD for estimating wave forces on offshore structures is suggested in this paper. The modified equation is found in the form D F% + Fn% + D where Fn -= Fd + F + F is the nonlinear contriw q bution 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. 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 bdy’s responses to the oncoming wave’s fluctuating velocity and its fluctuating extension. It is found 590 L. DEBNATH and M. RAHMAN 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.