Abstract
Abstract The scattering of internal gravity waves at finite topography in two dimensions is studied theoretically and numerically for a finite depth ocean. A formal solution is derived using a mapping function based on ray tracing. The solution satisfies radiation conditions. Energy is conserved. The incoming energy flux is redistributed in physical and modenumber space. Numerical solutions are calculated for a single plane wave propagating from the ocean side onto slope–shelf configurations where a flat shallow shelf is connected to a flat deep ocean by linear slopes, staircases, convex or concave parabolic profiles, and half-cosine slopes. The fraction of the incoming energy flux transmitted onto the shelf and reflected back to the deep ocean and the distribution of these fluxes in modenumber space are calculated. The results depend on the parameters of the incident wave and of the topography. Especially important is the distinction between supercritical topography, where the slope of the topography exc...
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