Parnovski: Existence of eigenvalues of a linear operator pencil in a curved waveguide localized shelf waves on a curved coast

Abstract. The question of the existence of nonpropagating, trapped continental shelf waves (CSWs) along curved coasts reduces mathematically to a spectral problem for a self-adjoint operator pencil in a curved strip. Using methods developed for the waveguide trapped mode problem, we show that such CSWs exist for a wide class of coast curvature and depth profiles