SPECTRAL METHODS FOR FORWARD-PROPAGATING WATER-WAVES IN CONFORMALLY-MAPPED CHANNELS

The prediction of wave fields in domains with complicated geometries m ay be aided by the use of conformal-mapping, which simplifies the shap e of the domain. In this conformal domain, parabolic models have been used previously to treat wave problems. In Cartesian coordinates, the angular spectrum model, based on a Fourier transform in the direction perpendicular to the principal propagation direction, has been shown t o handle, in principle, a wider range of wave directions than the para bolic model. Here, the extension of the angular spectrum model to conf ormally-mapped domains with impermeable lateral boundaries is shown. N ext, the Fourier-Galerkin method is developed for conformal domains; t his is identical to the angular spectrum model in Cartesian coordinate s, but differs in the conformal domain. Finally, a Chebyshev-tau model for conformal domains is developed, based on using Chebyshev polynomi als rather than trigonometric functions as a basis. For all models, fo rward-propagation equations are derived, by splitting the governing el liptic equations into first-order equations. Examples of all methods a re shown for a simple conformal mapping that permits the study of wave s in a diverging channel and in a circular channel. The forward-propag ation models are shown to be optimal for methods that use eigenfunctio ns for the lateral transform and less accurate for others.