Applied Mathematics Seminar

Internal wave radiation from a localized source into a space- and time-varying medium can be analyzed by combining an integral representation in the near-field with a numerical ray-tracing in the far-field. One complication with this approach is that the ray solution breaks down at caustics where the slowly-varying assumptions of ray theory become invalid. We try a different approach, known as Maslov's method. The ray equations are initialized and solved in Fourier space (which is simple for depth-dependent mean wind and buoyancy frequency). The result is then Fourier transformed to provide a spatial description that matches the linear integral solution. Caustics of all types are automatically accounted for without specifying the functional form near the caustic (as has to be done in the more familiar method of matching ray solutions locally to a prescribed caustic solution) and without a normal-mode analysis (as required in the more familiar integral technique). This is a first attempt to devise a systematic way to deal with internal-wave caustics in a numerical ray-tracing scheme. We examine applications in which the method is most straightforward to apply, including internal waves generated by shear flow over topography and around obstacles.
(Joint work with Dr D. Broutman, Computational Physics, Inc., Springfield, VA)