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

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.

Wind-Driven Overturning, Mixing and Upwelling in Shallow Water: A Nonhydrostatic Modeling Study

“…Here, reflection doubles the wave amplitude and triggers mixed-layer deepening to a depth of >6 m. Under the action of breaking internal waves, sub-surface water from depths of up to 10 m becomes entrained into the surface mixed layer ( Figure 12). Wave reflection and breaking on sloping boundaries, similar to the results shown here, have been extensively studied before (e.g., [20][21][22][23][24]). On timescales of 10 h, such reflection patterns can only develop in closed water bodies on horizontal scales of less than a few kilometres.…”

“…To make the bathymetry more realistic as opposed to a channel with vertical sidewalls, total water depth is assumed to gradually deepen away from the shorelines to its maximum value over a distance of 200 m. It should be pointed out that, irrespective of the shape of bathymetry chosen, the wind forcing will always create an undercurrent potentially leading to instability, vertical stirring and the generation of internal waves. Slope effects, as discussed by [22][23][24], are of secondary importance to the findings reported here. While exploring the lee effect with a nonhydrostatic model, the author made the surprising observation that situations of onshore rather than offshore winds trigger a dramatic dynamical response in the water column in the form of large-amplitude internal waves and strong vertical mixing.…”

“…As the proposed mechanism creates large-amplitude internal waves propagating offshore after each onshore wind pulse, it also contributes to the dissipation of energy in the oceans [31]. Indeed, there are ample studies on the generation and modification of waves over variable topography in shelf seas and lakes (e.g., [19][20][21][22][23][24][25]), but as far as the author is aware, the fundamental mechanism of wave generation due to instabilities of the overturning circulation that forms under onshore winds has not been described before.…”

“…For clarity it should be noted that the overall structure of the overturning circulation driven by onshore wind has been simulated with a hydrostatic numerical model before [18], but not the nonhydrostatic instability and mixing processes that follow from this. It should also be noted that there is ample previous work on the creation and modification of internal waves over variable bathymetry (e.g., [19][20][21][22][23]). None of these studies, however, explicitly addressed the situation discussed in the present work.…”

Transition from partly standing to progressive internal tides in Monterey Submarine Canyon

“…If α > 1 (supercritical) waves will be reflected back offshore. If α = 1 (critical) linear theory breaks down, leading to nonlinear effects, wave breaking, and turbulent mixing (Eriksen, 1982;Ivey and Nokes, 1989;Dauxois et al, 2004). For obliquely incident internal waves, the effective topographic slope is less than the maximum topographic slope.…”