Vertical mixing due to the breaking of critical internal waves on sloping boundaries

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Abstract
A laboratory experiment is used to examine the vertical mixing resulting from the breaking of internal waves on a sloping boundary in a continuously stratified fluid. Attention is confined to the case of critical waves when the slope of the group velocity vector of the incident waves is equal to the bottom slope. Along the sloping boundary a turbulent bottom boundary layer forms with a thickness dependent on the incident wave amplitude. The mixing efficiency, defined as the ratio of the increase in potential energy due to mixing to the loss of kinetic energy by the incident waves, is dependent upon the stability of the flow and has an upper bound of approximately 0.20.By examining the increase in potential energy of the fluid as a result of sustained mixing, we are able to compute the transition value of the dissipation εtr below which no mixing occures. For mixing due to the breaking of critical internal waves on sloping boundaries we find that εtr = (8±2)νN2. From comparisons with experiments with grid-generated turbulence, this suggests that while εtr/νN2 = 0(10) in the available data sets, the specific value of εtr may be mechanism dependent.