A numerical method for the coastal-trapped wave problem

Abstract

A numerical method is presented to solve the coastal-trapped wave (CTW) problem. The method is the explicitly shifted inverse power algorithm for the generalized eigenvalue problem. Problems non-linear in the eigenvalue, such as the dispersive baroclinic CTW problem, are addressed by expressing them as linear problems of expanded dimension. The novelty of the technique is its ability to compute complex eigenvalues directly. -- In this thesis two applications of the method are presented. First, the effect of stratification on CTW's is investigated by determining their dispersion characteristics. These are computed for both real propagating and complex evanescent wavenumber solutions. Second, the influence of a mean alongshore current on CTW's is studied. The results are compared to observations made along the eastern Australian coast.