Ruben R. Rosales
Department of Mathematics
Massachusetts Institute of Technology
USA

“Internal Breaking Waves in the Ocean”

Abstract

Long internal waves in the ocean are nondispersive, so that nonlinearity can deform and break them, producing internal hydraulic jumps. These jumps, when present, can affect significantly the nature of mixing and dissipation in the ocean, as well as the distribution of energy among the various internal modes. Particularly important are the strong internal jumps likely to occur downslope of dense overflows from continental shelves. For these jumps a closure problem arises when trying to formulate the relevant jump conditions.

Here we will consider internal hydraulic jumps in two--layer flows, with particular emphasis on their role in entrainment and mixing. For strong internal jumps, a new closure is proposed for the jump conditions. The closure is based on two main assumptions: (1) Most of the energy dissipated at the jump goes into turbulence, and (2) The amount of turbulent energy that a stably stratified flow may contain (without immediately mixing further) is bounded by a measure of the stratification. Surprising bounds emerge from this closure, particularly on the amount of entrainment that may take place at the location of the jump. These bounds are probably nearly achieved by strong internal jumps, such as those likely to develop in oceanic dense overflows. Their values are in good agreement with the (relatively sparse) existing observations of the spatial development of oceanic downslope currents --- which play a crucial role in the formation of abyssal and intermediate waters in the global ocean.