Horizontal refraction of 3-D curvilinear wedge modes

Abstract

For shallow-water acoustic propagation, the wavelength is commensurate with the water depth but short compared to the horizontal extent of the problem. Under these conditions a sloping bottom causes the development of normal modes having wavefronts that are curved in the vertical direction. For simple slopes, such wedge modes have been shown to propagate with cylindrical wavefronts along characteristics in the horizontal plane. This work extends adiabatic wedge mode theory to regions of arbitrary bathymetry by constructing a three-dimensional curvilinear coordinate system that follows the contours of the ocean bottom. The requirement for separation of the depth coordinate from the coupled horizontal coordinates produces a nonlinear differential equation for a potential field. The gradient of this field then gives the depth scale factors and curved shape of the wedge modes. A standard normal mode problem is then solved to obtain the curvilinear wedge modes and a ray-trace method is used to study the horizontal motion of those modes. An overview of the model formulation and some examples will be presented.