Session A1: Mini-Symposium: Geophysical Turbulence Induced by Flow over Topography I

Internal Wave Breaking in Stratified Flow over Topography

In both atmosphere and oceans, internal waves generated by stratified flow over topography ``break'' when a critical Froude number is exceeded. In the oceans, the global field of such waves forced by the flow of the barotropic tide over bottom topography constitutes an ``internal tide'', the turbulent dissipation of which contributes significantly to the diapycnal diffusivity of mass in the abyss. In the atmosphere, the vertical flux of horizontal momentum in the wave field plays an important role in mediating the strength of the mid-latitude jet streams in the troposphere through the ``gravity wave drag'' that is applied to the mean zonal flow when the waves break. Early work on the atmospheric problem based upon the application of LES methods demonstrated that, in the restricted case of topographically forces 2-D flows, wave breaking aloft led to the development of an intense low level jet in the lee of the topographic maximum, in which an intense secondary instability of Kelvin-Helmholtz type developed which became intensely turbulent. The same methods were later applied to the oceans, initially to develop an understanding of the tidally induced breaking wave mechanics in the Knight Inlet ``flume''. Similar dynamical interactions, to those observed in the atmosphere in connection with severe downslope windstorm formation, have been observed to occur in the deep ocean in the lee of ocean bottom topographic extrema. Current work is underway to determine the extent to which DNS methods applied to the oceanographic context are able to recover the phenomenology revealed by the atmospheric LES analyses.   

Tidal bores, turbulence and mixing above deep-ocean slopes

A tidally driven, stably-stratified turbulent boundary layer over supercritically sloping topography is simulated numerically using a spectral LES approach (Winters, 2015, 2016). The near boundary flow is characterized by quasi-periodic, bore-like motions, whose temporal signature is compared to the high-resolution ocean mooring data of van Haren (2006). The relatively thick bottom boundary layer remains stably stratified owing to the regular cycling of unmixed ambient fluid into the turbulent boundary layer and episodic expulsion events where fluid is ejected into the stratified interior. The effective diffusivity of the flow near the boundary is estimated by means of a synthetic dye tracer experiment. The average dissipation rate within the dye cloud is computed and combined with the diffusivity estimate to yield an overall mixing efficiency of 0.15. Both the estimated diffusivity and dissipation rates are in reasonable agreement with the microstructure observations of Kunze at al (2012) when scaled to the environmental conditions at the Monterey and Soquel Canyons and to the values estimated by van Haren and Gostiaux (2012) above the sloping bottom of the Great Meteor Seamount in the Canary Basin.   

Tidally driven mixing: breaking lee waves, hydraulic jumps and the influence of subinertial internal tides

We present observations of tidally driven turbulence that were obtained in a small channel that transects the crest of the Mendocino Ridge, a site of mixed (diurnal and semidiurnal) tides. At this latitude the diurnal tide is subinertial and evanescent away from the topography, in contrast to the semidiurnal tide which is superinertial and radiating. During the larger of the daily tides, strong turbulence (10 W/m$^2$) is observed, and using a high resolution, two-dimensional, nonhydrostatic simulation, we interpret observed flow features and concomitant turbulent dissipation to arise from both breaking internal lee waves (above the crest of the topography), and turbulent hydraulic jumps (on the flanks of the topography). To understand the nature of the regional scale flows we employ a three-dimensional tidally forced model, which illustrates the presence of diurnal bottom-trapped internal waves. These energetic waves are of leading order importance in determining the timing of the dissipative processes, alternately enhancing and canceling near bottom flows that are of critical importance to near-topographic turbulence.   

Parameterizing turbulence over abrupt topography

Stratified flow over abrupt topography generates a spectrum of propagating internal waves at large scales, and non-linear overturning breaking waves at small scales. For oscillating flows, the large scale waves propagate away as internal tides, for steady flows the large-scale waves propagate away as standing ``columnar modes''. At small-scales, the breaking waves appear to be similar for either oscillating or steady flows, so long as in the oscillating case the topography is significantly steeper than the internal tide angle of propagation. The size and energy lost to the breaking waves can be predicted relatively well from assuming that internal modes that propagate horizontally more slowly than the barotropic internal tide speed are arrested and their energy goes to turbulence. This leads to a recipe for dissipation of internal tides at abrupt topography that is quite robust for both the local internal tide generation problem (barotropic forcing) and for the scattering problem (internal tides incident on abrupt topography). Limitations arise when linear generation models break down, an example of which is interference between two ridges. A single ``super-critical'' ridge is well-modeled by a single knife-edge topography, regardless of its actual shape, but two supercritical ridges in close proximity demonstrate interference of the high modes that makes knife-edfe approximations invalid. Future direction of this research will be to use more complicated linear models to estimate the local dissipation. Of course, despite the large local dissipation, many ridges radiate most of their energy into the deep ocean, so tracking this low-mode radiated energy is very important, particularly as it means dissipation parameterizations in the open ocean due to these sinks from the surface tide cannot be parameterized locally to where they are lost from the surface tide, but instead lead to non-local parameterizations.