Obliquely Propagating Internal Tides and Flow Reversal Mixing

Gemmrich and van Haren (2001) documented the occurrence of thermal fronts near the bottom boundary in $\sim850 m$ depth along the Bay of Biscay continental slope. They describe abrupt temperature changes, linked to the presence of an internal tide beam propagating downward at an oblique angle relative to the slope. Gemmrich and van Haren (2001) hypothesized that the obliquely propagating internal tide results in a variation of tidal phase along isobaths, particularly if the internal tide is in the form of a narrow beam. The variable phase of the tidal currents can advect cold water upslope above warm water once per tidal cycle, creating sharp thermal fronts and convective instability. The oblique propagation angle is crucial; an internal tide propagating directly downslope would not generate such unstable fronts. Gemmrich and van Haren (2001) observed sharp temperature drops associated with the collapse and/or passage of these fronts. In contrast to the studies of the reflection of internal tides normally incident on a sloping boundary (Legg and Adcroft, 2003; Nash et al., 2004), the mechanism identified by Gemmrich and van Haren (2001) relies on downgoing internal tides that propagate obliquely along the slope.

Similarities between the Bay of Biscay and the Kaena Ridge observations suggest that this mechanism may explain the mixing events documented here as flow reversal mixing. First, for both experiment sites, the observations were made over a supercritical slope for the semidiurnal tide, which allows a tidal beam generated at a ridge crest or shelf break to propagate downward without reflection. Such a beam would propagate farther from the slope with increasing depth; however, Gemmrich and van Haren (2001) describe how obliquely propagating waves still can intersect the slope. This is apparently also the case at the Kaena Ridge. The observed tidal currents are oriented at an angle relative to the slope (Figure 6.2), consistent with a tidal beam with an oblique propagation azimuth. Following Gemmrich and van Haren (2001), this could lead to the generation of fronts with an angle $\varphi$ between $54^\circ$ and $80 ^\circ$ relative to the isobaths. Here we use equation 1) from Gemmrich and van Haren (2001) with $N^2 = 10^{-6} s^{-2}$ , a topographic slope $\alpha = 18.6 ^\circ$ , a $M_2$ vertical propagation angle of $7.5^\circ$ , and an angle between the isobath and the bottom projection of the group velocity vector between $40 ^\circ$ and $80 ^\circ$ . During the first spring-neap cycle, when flow reversal mixing events are not detected, the current ellipse is more circularly polarized than during the subsequent cycles (Figure 6.5b). This suggests that a circular current ellipse, as opposed to a more unidirectional flow, is not conducive to this overturning mechanism.

Second, the temperature data from the Bay of Biscay and the Kaena Ridge bear a striking resemblance (Figures 6.4 and 6.8). The temperature drops sharply at the time of flow reversal from down to upslope, which Gemmrich and van Haren (2001) characterized as a passing thermal front. The similarities are particularly striking near the bottom (Gemmrich and van Haren (2001) observations were all below $50 mab$ ). Higher in the water column ( $\geq 100 mab$ ), above the elevations sampled in the Bay of Biscay, we see evidence for strong restratification following the front passage.

Third, tidally driven convection is an attractive mechanism for flow reversal events given that tidal current and current shears are weak during this phase of the tide. Enhanced strain, which is observed preceding mixing events (Figure 6.4), can also be a signature of a developing convective instability rather than a shear instability.

Lastly, the dependence of this mechanism on the location of the internal tide beam relative to the mooring (Figure 6.9) can also explain the intermittent nature of the observed mixing events. At our Kaena Ridge site, low dissipation is associated with low tidal amplitude, but high tidal amplitude is not always associated with strong dissipation (Figure 6.1). Our analysis has focused on the relationship of mixing events to the measured tidal currents. We emphasize that the measured tide is dominated by the baroclinic component at the mooring location (Figure 6.2 c). The observed increase in amplitude of the semidiurnal currents (Figure 6.1c), and the change in eccentricity over the duration of the experiment (Figure 6.5b) presumably are attributed to changes in the internal tide. Low frequency currents and changes in stratification higher in the water column, between the mooring location and the generation site near the ridge top, can cause temporal changes in amplitude, phase, position or direction of the internal tide, which apparently influence the level of convective mixing observed at the fixed moored location (Figure 6.5a).