# Theory and application of scattering from an object in an ocean waveguide

## Description

The treatment of scattering from submerged objects in an unbounded environment is of considerable interest to both the academic and technological communities. Several approaches have yielded results for different classes of problems and have proven manageable for the free environment case. The problem of scattering in a confined environment has proven more difficult to formulate in a form useful for calculation due to the coupling of effects from the scattered object with that of the boundaries. The purpose of this work is to propose a numerical scheme that will adequately describe scattering from realistic objects in a confined environment. Some of the realistic objects that are of interest are elongated objects such as spheroids and cylinders with rounded end-caps. Boundary conditions of interest range from those associated with rigid objects to those associated with elastic shells. We will start by developing the incident field in terms of Normal Mode theory. We next develop the near field scattered field. This will be obtained using a transition matrix that relates the incident field to the scattered field. The transition matrix which is obtained from the Extended Boundary Condition (EBC) method of Waterman does not account for boundaries other than that of the object. We then couple the solution with a waveguide solution to satisfy all boundary conditions. By appropriately coupling the two solutions we can satisfy all boundary conditions and preserve continuity of the solution throughout all space. The method that couples the solutions is an application of Huygens' principle. This application of Huygens' principle leads to a manageable direct solution of the problem. This method also satisfies all appropriate boundary conditions and yields a continuous solution throughout space. Details of this method will be presented along with examples