Selection of internal wave beam directions by a geometric constraint provided by topography

Direct numerical simulations are performed to investigate the generation of internal waves in a linearly stratified fluid by oscillating barotropic flows over a model continental shelf-slope topography. The presence of a third wave-beam emitted from an abrupt shelf break and transverse to the topography, which has not been adequately interpreted, is now explained in terms of a geometric constraint provided by the topography. This explanation applies to wave beam selection at any abrupt topographic junction point, no matter whether it is convex or concave, or its nearby slope is subcritical or supercritical. One exception is that, at an abrupt concave point with a nearby supercritical slope, the blocking effect leads to the presence of "dead water" (i.e., no flow) and thus no wave beam is emitted. On a critical slope, two beams with opposite directions are emitted from an amphidromic point that has a distinct distance from the shelf break. In addition to the internal wave dispersion relation that restricts possible wave beam directions to form an X-pattern, the geometric constraint proposed in the present work serves as a second selection mechanism that further restricts wave beam directions. The reflective direction of a wave beam incident onto a slope can also be explained by this geometric constraint. The present work provides an updated explanation of internal wave beams emitted at abrupt topographic junction points and unifies the explanation of the wave beam direction for both wave generation and reflection processes.