The Two Types of Mixing Events

At mooring DS, the estimated Thorpe scales tend to be large/small during spring/neap tides (Figure 6.1a). Thorpe scales range from $20$ to $100 m$ for overturns of $24$ to $190 m$ . Dissipation values range from $10^{-7}$ to $10^{-6} Wkg^{-1}$ during spring tides, and from $10^{-8}$ to $10^{-7}Wkg^{-1}$ during neap tides (Figure 6.1b). The minimum attainable dissipation with this method is $1.2\times 10^{-10}Wkg^{-1}$ .

Because the observations are dominated by oscillations at the $M_2$ frequency, we divide the time series into 163 $M_2$ cycles to investigate the mixing events in relation to tidal phase. A complex demodulation of the horizontal velocity is used to assign each time step to an $M_2$ phase. With 8 minute sampling, 93 phases are specified in a $12.4 hour$ $M_2$ cycle. Temperature, current, stratification and dissipation occurring at the same phase are then averaged and displayed as a function of $M_2$ phase, which forms a composite tidal cycle (Figure 6.2). With this convention, upslope flow occurs for phases between $-90^\circ$ and $90^\circ$ , downslope flow occurs during the rest of the cycle.

Enhanced dissipation occurs during two distinct phases of the tidal cycle (shaded areas on figure 6.2). The first is centered around $140^\circ$ and is associated with maximum downslope flows, increasing water temperatures, and low stratification. We refer to this mixing phase as "downslope flow mixing". Figure 6.3 is an example of a downslope flow mixing event. The current starts flowing downslope and the temperature increases near the bottom first, compared to at a distance from it, thus lowering the stratification. The temperature becomes nearly homogeneous over the $200m$ depth range during the event, followed by temperature inversions that affect the entire range.

The second dissipation peak, centered around $-90^\circ$ , is associated with the flow reversal from downslope to upslope, maximum water temperatures, and increasing stratification with a pronounced local minimum. We refer to this phase as "flow reversal mixing". Figure 6.4 is an example of a flow reversal mixing event. At the end of the downslope flow, the temperature has reached a maximum, isotherms start to converge before overturning, and the event is followed by a sharp temperature drop and a subsequent restratification.

Although observed mixing events are linked to tidal phase, they do not occur as regularly as the tide itself. To illustrate the variability of tidal mixing, we visually inspect each $M_2$ cycle and assign the cycle to one of five categories: "downslope flow mixing only" when dissipation occurs near the maximum downslope current, "flow reversal only" when dissipation occurs at the reversal from down to upslope flow, "both downslope flow mixing and flow reversal" when both events occur during the same cycle, "no mixing" when dissipation failed to reach a threshold value of $0.5\times10^{-7}Wkg^{-1}$ , and "random mixing event" when dissipation events occur at other phases of the tide. We find that 63% of the tidal cycles contain flow reversal and/or downslope flow mixing, 21% have no significant mixing, and 16% show only odd mixing events. Tidal cycles containing flow reversal mixing events account for 40% of the total estimated dissipation, downslope flow events account for 20%, combined events 21%, and random events 16%. Although downslope flow mixing events appear throughout the experiment, flow reversal mixing events are nearly absent during the first spring-neap cycle, and their occurrence and amplitude appear to increase over time (Figure 6.5a). We attribute this increase in part to the increase in semidiurnal current amplitude (Figure 6.1). In addition, the first spring-neap cycle is characterized by more circularly polarized tidal currents than the other cycles (Figure 6.5b). We will return to this point when considering the cause of flow reversal mixing events in section 6.1.2.

We next consider whether tidal shear and strain act to trigger mixing events, in the manner of a shear instability. We calculate the shear over the depth range $41$ to $65 mab$ . Again, the ADCP only samples a small fraction of the $200 m$ length of the thermistor chain. $N$ is averaged over the same range as the ADCP, and also over the full range of the thermistors ($27$ to $220 mab$ ).

Representative downslope flow mixing events (Figure 6.6) occur during each semidiurnal cycle near the time of maximum downslope flow. Flow reversal mixing events are absent during the time period shown. Downslope flow mixing occurs when the stratification is at a minimum, or equivalently the strain is a maximum, over the tidal cycle. Tidal current shear tends to peak twice during the cycle during both up and downslope flow (Figure 6.6 b and c); however, the combination of high shear and strain during the downslope phase results in an inverse Richardson number highly correlated with the dissipation events (Figure 6.6 b and d). The results are similar using different depth ranges for computing $N$ (i.e. $20 m$ , versus $200 m$ ). Figure 6.6c shows the results using $N$ averaged over $200 m$ because it is less noisy than that based on a $20 m$ average. We conclude that downslope flow mixing events are the result of shear instability.

During other time periods, flow reversal mixing events are dominant and noticeable downslope flow events are absent (Figure 6.7). Strong flow reversal mixing events occur every other semidiurnal cycle. There are also other periods (not shown) when moderate flow reversal events occur at every semidiurnal cycle. In sharp contrast to downslope flow mixing, flow reversal mixing events do not coincide with elevated shear between $45$ and $65 mab$ or elevated inverse Richardson number (Figure 6.7 c and d). Similar results are obtained using $N$ averaged over the common $20 m$ depth range as shear, and also using shear and strain computed over $10 m$ spacings. Stratification minima occur during the events at a phase of the tidal cycle when the stratification would otherwise be increasing (Figure 6.7 b) . The stratification begins to decrease approximately one hour before the main overturning event. This increased strain occurs because of a phase lag of the temperature signal with depth. Inspection of the temperature record for a typical event (Figure 6.7 a) shows that the isotherms begin to converge prior to mixing because temperatures decrease in the upper water column ($150$ to $220 mab$ ) one hour before the lower water column ($27$ to $75 mab$ ). In the lower water column, the measured currents and temperatures are consistent in that temperatures increase during downslope flows. In the upper water column, we do not have reliable current measurements to confirm that the early temperature decrease is due to a change to upslope currents.

The poor relationship between flow reversal mixing events and shear or Richardson number may be due to the lack of reliable current observations above $65 mab$ . For example, a shear instability, similar to the downslope flow mixing event and occurring above $65 mab$ , may create an overturn that is advected into the sample range. We believe this is unlikely, however, because the background currents below $65 mab$ are near zero or directed upslope (i.e., at flow reversal or shortly thereafter), while the temperature record below $65 mab$ shows a decrease much larger than the temperature changes observed during downslope flow mixing.

The character of the temperature signal strongly suggests that cold water downslope of the mooring has been lifted above the mooring, resulting in a convective instability. Levine and Boyd (2005) also observed mixing associated with the semidiurnal tide to occur at two distinct phases on the north side of Kaena Ridge at $1500 m$ depth (Big Boy mooring, Figure 1.3). In their case, overturns near $100 mab$ occur $180^\circ$ out of phase with overturns near $300 mab$ , which is attributed to a $180^\circ$ phase shift in maximum tidal strain between these depth ranges.

For both mixing types, strain appears to be an important precursor to overturning. For downslope flow mixing, overturns occur during the maximum strain over the semidiurnal tidal cycle (Figure 6.2 and 6.6). For flow reversal mixing, overturns occur during a secondary strain maximum that is out of phase with the semidiurnal cycle. Over the entire dataset, the correlation between the strain and dissipation is insignificant (0.19); however, when calculated for a subrecord when downslope flow mixing is dominant (the 3 days shown on Figure 6.6), the correlation improves (0.45). For subrecords of similar length, at times when flow reversal mixing is dominant, the correlation between the strain and dissipation does not exceed 0.2 . Tidal current shear, at least over the measured depth range, is not significantly correlated with dissipation, even over short periods when only one mixing type is observed (Figures 6.6 and 6.7). Combining the effects of shear and strain, in the form of an inverse Richardson number, does not improve the correlations obtained using strain alone, which again highlights the primary importance of strain for downslope flow events, and further discounts shear instability as a mechanism for flow reversal events.