Nonlinear Wave Calculations for Engineering Applications

Abstract

Waves in the ocean are nonlinear, random, and directionally spread, but engineering calculations are almost always made using waves that are either linear and random or nonlinear and regular. Until recently, methods for more accurate computations simply did not exist. Increased computer speeds and continued theoretical developments have now led to tools which can produce much more realistic waves for engineering applications. The purpose of this paper is to review some of these developments. The simplest nonlinearities are the second-order bound waves caused by the pairwise interaction of linear components of the wave spectrum. It is fairly easy to simulate the second-order surface resulting from those interactions, a fact which has recently been exploited to estimate the probability distribution of wave crest heights. Once the evolution of the surface is known, the kinematics of the subsurface flow can be evaluated reasonably easily from Laplace’s equation. Much of the bound wave structure can also be captured by using the Creamer transformation, a definite integral over the spatial domain which modifies the structure of the wave field at one instant in time. In some ways, the accuracy of the Creamer transformation is higher than second order. Finally, many groups have developed numerical wave tanks which can solve the nonlinear wave equations to arbitrary accuracy. The computational cost of these solutions is still rather high, but they can directly calculate potential forces on large structures as well as providing test cases for the less accurate, but more efficient, methods.