Mixing at Mooring DS

In the field experiment at mooring DS, we find that the semidiurnal tide dominates the current and temperature variability above the steep south flanks of the Kaena Ridge. In particular, near-inertial wave energy, diurnal tides, and subinertial currents, which might contribute to near boundary mixing due to bottom drag, are all much weaker than the semidiurnal tide. The predominance of the semidiurnal tide and lack of diurnal tide energy are consistent with their respective predicted ray paths from the model simulations of Merrifield and Holloway (2002). Barotropic to baroclinic semidiurnal tidal conversion near the top of Kaena Ridge results in downward propagating tidal beams that are the primary source of mechanical energy available for turbulent mixing deep along the ridge (Figure 3.13).

Overturns and the implied associated mixing and dissipation occur predominantly at two phases of the measured semidiurnal tidal cycle (Figure 6.2) : when flows are near maximum in the down-slope direction, and at the flow reversal prior to upslope flow, at maximum downward isopycnal displacements. The mechanism causing the downslope flow mixing events appears to be a shear instability, triggered primarily by high strain, occurring when stratification is minimum over the tidal cycle. Levine and Boyd (2005) find a similar relationship between mixing events and strain at a shallower depth on the ridge. Flow reversal mixing occurs during high strain conditions that do not coincide with the tidal strain maximum. These events appear unrelated to shear, and the associated dissipation is poorly correlated with the inverse Richardson number, suggesting that shear instability is not the primary generation mechanism. Based on similarities with observations made by Gemmrich and van Haren (2001) in the Bay of Biscay, we suspect that the flow reversal mixing events are convectively driven. In this scenario, mixing develops because of the oblique propagation angle of the downward propagating internal tide relative to the slope. This leads to the advection of cold water above warm water along the slope, the generation of a sharp thermal front, and eventually to statically unstable conditions and overturning. Evidence supporting this hypothesis includes the observed orientation of the internal tide relative to the slope, the abrupt temperature decrease associated with the overturn, and the poor correspondence with tidal shear. The enhanced strain preceding these events may result from the development of a statically unstable patch.

Ultimately, we seek a tidal mixing parametrization that can be incorporated into regional numerical models, so that estimates of deep mixing can be extrapolated to the entire ridge system, as well as to other locations. If tidal mixing were related to shear instabilities created by the tidal flow at the boundary, we might expect that the mixing associated with the tide would have a high predictability. The barotropic tide can be accurately predicted by a harmonic analysis. The phase of the freely propagating internal tide, once generated, is decoupled from the astronomical forcing. At this site, although the internal tide provides most of the mechanical energy, a few tidal constituents explain a significant fraction of the observed variability, indicating a good coherence between the phase of the internal tide and the astronomical forcing, presumably due to the proximity of the mooring to the generation site(s).

Although both mixing events are linked to the tide, neither is as predictable as the tide itself. Downslope flow mixing events exhibit a visual correspondence with inverse Richardson number; however, at best the correlation is only 0.4. This may be due to limitations in our current measurements, which only resolved shear over a small fraction of the overturning depth range. Nonetheless, we believe that a traditional mixing parametrization based on tidal strain and shear may be useful to explain downslope flow mixing.

If flow reversal mixing is caused by convective instabilities in the manner described by Gemmrich and van Haren (2001), a mixing parametrization is more complicated. Predictability would depend on the orientation of the internal tide relative to the topography, which in turn requires detailed knowledge of how changes in the background stratification and currents affect the generation and propagation of the internal tide. Small changes in the propagation azimuth of the internal tide presumably would lead to significant changes in mixing.

In the context of the other HOME observations at Kaena Ridge, we find good agreement between our inferred dissipation rates based on Thorpe scales and direct microstructure measurements. Our estimated time-averaged dissipation is $1.2\times10^{-8} Wkg^{-1}$ , but can reach up to $10^{-6} Wkg^{-1}$ . The corresponding time-averaged eddy diffusivity is $2\times10^{-3}m^2s^{-1}$ . For comparison, Levine and Boyd (2005) found comparable an average dissipation value of $2\times10^{-8}Wkg^{-1}$ at the $1450 m$ isobath, based on a similar analysis and Klymak et al. (2005) found $4\times10^{-9}Wkg^{-1}$ at $3000 m$ based on direct microstructure measurements. The microstructure measurements suggest that mixing rates are enhanced $100$ to $200 m$ from the bottom (Klymak et al., 2005). Given the sporadic and event-like nature of the mixing, the value of continuous sampling over time for estimating mixing is highlighted by our observations. It is remarkable that the two methods of estimating mixing, microstructure profiles versus overturns from continuous temperature time series, give such consistent results.