Estimation of Incident and Reflected Wave Trains in Highly Nonlinear Two-Dimensional Irregular Waves

Abstract

Most existing methods for separation of two-dimensional (long-crested) waves into incident and reflected components are based on linear wave theory. Recently, a new method for separation of incident and reflected nonlinear regular waves was presented including separation of bound and free superharmonics. The present paper extends this method to irregular waves. Irregular waves are much more complicated to separate because bound components are caused by interaction of many different frequencies, thus, some simplifications are needed. The presented nonlinear separation method is based on narrowband approximation. Second-order wave theory is used to demonstrate that errors for more broad-banded spectra are acceptable. Moreover, for highly nonlinear waves, amplitude dispersion occurs and is included by a simplified amplitude dispersion correction factor. Both assumptions are evaluated based on numerical and physical model data. The overall conclusion is that existing reflection separation methods are reliable only for linear and mildly nonlinear nonbreaking irregular waves, whereas the present method seems reliable for the entire interval from linear to highly nonlinear nonbreaking irregular waves. The present method is shown to be an efficient and practical approximation for an unsolved theoretical problem in the analysis of waves in physical models.