Internal hydraulic jumps in two-layer flows are studied, with particular emphasis
on their role in entrainment and mixing. For highly entraining internal jumps, a
new closure is proposed for the jump conditions. The closure is based on two main
assumptions: (i) most of the energy dissipated at the jump goes into turbulence,
and (ii) the amount of turbulent energy that a stably stratified flow may contain
without immediately mixing further is bounded by a measure of the stratification. As
a consequence of this closure, surprising bounds emerge, for example on the amount
of entrainment that may take place at the location of the jump. These bounds are
probably almost achieved by highly entraining internal jumps, such as those likely to
develop in dense oceanic over flows. The values obtained here are in good agreement
with the 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.
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