Mixing Events at Mooring DN

We found an overall time-averaged value of dissipation at mooring DN of $1.8\times 10^{-9} Wkg^{-1}$ , corresponding to an averaged eddy diffusivity of $2.5\times 10^{-4} ms^{-2}$ . Due to the large spacing between sensors on the upper half of the mooring ( $\Delta Z=24-32 m$ ), these values are likely to be low estimates as overturns $\le 32 m$ cannot be detected. In comparison, an averaged dissipation of $1.2\times 10^{-8} Wkg^{-1}$ and an eddy diffusivity of $2\times 10^{-3} ms^{-2}$ are estimated for mooring DS using the same method. Most of the dissipation events at the south mooring were linked to an energetic semidiurnal tidal beam propagating near the bottom compared to DS. At mooring DN, the semidiurnal tide is much weaker ($0.02$ for $M_2$ alone compared to $0.05 ms^{-1}$ at DS, Figure 3.11) and we postulated in section 3 that a beam is observed at mooring DN, but it is clearly detached from the bottom. Consistent with the notion that the tides are the dominant energy source for deep mixing at the Hawaiian Ridge, the average dissipation at the north mooring DN is one order of magnitude smaller than at the south mooring DS. At mooring DN, energetic dissipation events appear linked to near-inertial and diurnal events as well as the semidiurnal tide. We use the temporal variations of the semidiurnal and the combined near-inertial/diurnal variance (Figure 4.2) to examine the occurrence of dissipation (Figure 6.10). We find that dissipation is higher during periods when both semidiurnal and near-inertial/diurnal variances are high (Figure 6.10).

To examine the occurrence of mixing relative to the tidal phase, we compute a composite phase average, similar to the one obtained for DS, based on the semidiurnal oscillation of the upper most temperature sensor (Figure 6.11). Because the temperature oscillations near the bottom ( $20-50 mab$ ) are weak, the average tidal strain between $20$ and $220 mab$ is driven primarily by the temperature variations at $220 mab$ . Similar to DS, dissipation at DN tends to occur during a particular range of tidal phase. Unlike DS, only one dissipation "event" is identified. At DN, phase-averaged dissipation is maximum when the flow reverses from up to downslope, just the opposite of DS flow reversal mixing events when the flow switches from down to upslope. At this phase of the tide, however, tidal strain creates the weakest stratification (Figure 6.11) over the semidiurnal cycle. At DS, the timing of the weakest stratification over the cycle occurs near maximum downslope flow, hence the timing of downslope flow mixing. We conclude from these comparisons that tidal strain conditions the water column in a way that is favorable for mixing. Flow reversal mixing at DS does not follow this pattern, and we attribute this to the importance of convective mixing for this particular type of mixing event.

Is the presence of near-inertial and diurnal energy important for mixing at DN compared to DS ? In total, the effect cannot be large since mixing at DS is estimated to be an order of magnitude higher than at DN. Nevertheless, we find compelling evidence to suggest that near-inertial events do play a role in triggering mixing at DN. In chapter 3 we showed that the upper $100 m$ of the mooring ($120$ to $220 mab$ ) is dominated by temperature variability in the semidiurnal band (Figure 4.1), attributed to a semidiurnal beam detached from the bottom. We also showed in chapter 4 that the lower part of the mooring ($20$ to $100 m$ above the bottom) is dominated by near-inertial and diurnal variability, in both temperature and velocity (Figures 4.1 and 4.2). These tendencies are also visible in details of the time-series (Figures 4.3 and 6.13). The upper temperature sensors show a general semidiurnal oscillation (Figures 4.3a and 6.13a), while the sensors close to the bottom oscillate at periods between the diurnal and inertial periods (Figures 4.3a and 6.13 b). At some phases, the semidiurnal oscillation at the top, and the near-inertial/diurnal oscillation near the bottom coincide to create times of high strain, i.e. the temperature (inertial to diurnal) in the lowest sensors is increasing, while the (semidiurnal) temperature at the higher sensors is decreasing. At these times, we observe overturns and associated mixing (Figure 4.3).

We now explore the occurrence of overturns and turbulent mixing in the context of combined near-inertial variability at the bottom and semidiurnal variability further up. The entire seven month temperature time series, measured at the upper most sensor (220 mab) is band-passed filtered around the semidiurnal frequency. The temperature record nearest to the bottom (27 mab) is band-pass filtered between the near-inertial and diurnal frequencies ( $0.7-1.1 cpd$ ). All the recorded dissipation events are then plotted as a function of these two band-pass filtered temperatures (Figure 6.12). Similar to what we observe in Figure 4.3, the majority of dissipation occurs in the upper left quadrant, which corresponds to a low semidiurnal temperature near the top, and a high near-inertial temperature at the bottom. This is the configuration that leads to the weakest temperature gradient and the highest strain over the $200 m$ depth range. Thus we observe overturns and associated mixing during periods of high strain, which are dictated by the occurrence of semidiurnal upwelling (lowest tidal temperature) at some depth from the bottom ( $100-200 m$ ), and near-inertial/diurnal downwelling (warmest temperatures) near the bottom. We conclude that the mixing at DN is strain related, and that this strain is a combination of both tidal and near-inertial internal wave fluctuations.

Figure 6.1: a)The estimated Thorpe scale ($L_T$ ), b) dissipation ($\epsilon$ ), and c) the measured semidiurnal tidal amplitude using horizontal currents at $65 mab$ at mooring DS.

Figure 6.2: A composite semidiurnal tidal cycle at DS, obtained using ensemble phase averages over the entire time series, of a) potential temperature recorded at 27, 43, 59, 75, 91, 107, 124, 147, 171, 195, and 220 mab, with blue lines corresponding to sensors closer to the bottom, depth averaged buoyancy frequency ($27$ to $220 mab$ , dashed black line), b) estimated dissipation ($\epsilon$ , equation 5.1.3), and c) horizontal currents, rotated so that cross-slope velocity is vertical. Depth bins with suspect side lobe contamination are shown in gray. Estimates of the barotropic current (TPXO, (Egbert, 1997)) are included. Shaded areas indicate phases of intense mixing associated with downslope flow (dark), and flow reversal (light).

Figure 6.3: A characteristic overturn event depicted in 12 hour time series (day 233) of a) potential temperature recorded at 27, 43, 59, 75, 91, 107, 124, 147, 171, 195, and 220 mab, with blue lines corresponding to sensors closer to the bottom, b) estimated dissipation ($\epsilon$ , equation 5.1.3, thin gray line) and depth-averaged buoyancy frequency ($27$ to $220 mab$ , thick black line), and c) horizontal currents, rotated so that cross-slope velocity is vertical. Depth bins with suspect side lobe contamination are shown in gray.

Figure 6.4: Same as figure 6.3 for day 249, showing an overturn during a different phase of the tide.

Figure 6.5: a) Dissipation ($\epsilon$ ) for the DS mooring, averaged over a semidiurnal cycle, is classified in terms of the dominant mixing types that occur during the cycle. b) The eccentricity of the semidiurnal current ellipse, quantified as the ratio of the minor over the major axis current amplitude. Ellipse amplitudes are obtained from a harmonic analysis of 7 day subrecords.

Figure 6.6: Downslope flow mixing events at mooring DS in 3 day time series of a) potential temperature, b) depth-averaged buoyancy frequency $N$ ($27$ to $220 mab$ , thick black line), and estimated dissipation (thin gray line), c) square of the horizontal current shear (from $41$ to $65 mab$ ), d) inverse Richardson number (from shear and $N$ above), and e) the horizontal velocity (at $65 mab$ and rotated so that across-slope velocity is vertical).

Figure 6.7: Same as figure 6.6 for a period of flow reversal mixing events.

Figure 6.8: Reproduced figure 4 from Gemmrich and van Haren (2001), Showing temperature (a) and velocity (b) measured 7.9 m above the bottom on the continental slope of the Bay of Biscay. The occurrence of thermal front passages are evident in a). The alongslope (thick line) and cross-slope (thin line) current component are shown.

Figure 6.9: Reproduced figure 6 from Gemmrich and van Haren (2001), showing a plan view of the idealized distortion of initially parallel isotherms due to cross-slope temperature gradients being advected by oblique internal waves. Note that for clarity the flow field (arrows) presents conditions at a quarter wave period prior to the instant of the depicted temperature field. Only a narrow beam, containing one wavelength of a periodic wave, is shown. Dashed lines mark locations where a thermal front is being generated. Here $T_0 < T_1$ . The star represents the measurement site: (a) $t = t_0$ , representing unstable stratification at measurement site, (b) $t = t_0 + \tau/2$ , where $\tau$ is the wave period, representing stable stratification at measurement site.

Figure 6.10: 24 hours running average of dissipation (in color) as a function of the current variance in the inertial-diurnal frequency band ( $0.7-1.1 cpd$ , horizontal) and the semidiurnal frequency band ( $1.9-2.1 cpd$ , vertical). a) is the average dissipation per bin (top), b) is the total dissipation per bin (middle), and c) is the number of samples per bin (bottom). Color scale for the top 2 panels are log10 of the dissipation in $Wkg^{-1}$ , log10 of samples in the bottom panel.

Figure 6.11: A composite semidiurnal tidal cycle at mooring DN, obtained using ensemble phase averages over the entire time series based on the temperature at 220 mab, of a) potential temperature recorded at 28, 36, 44, 52, 60, 68, 92, 125, 156, 188, and 220 mab, with blue lines corresponding to sensors closer to the bottom, b) estimated dissipation ($\epsilon$ , equation 5.1.3), and depth averaged buoyancy frequency ($27$ to $220 mab$ , dashed black line),and c) horizontal currents, rotated so that cross-slope velocity is vertical.

Figure 6.12: Dissipation at mooring DN, as a function of the temperature at $27 mab$ band-passed filtered in the inertial-diurnal frequency band ( $0.7-1.1 cpd$ , ordinate) and at $220 mab$ band-passed in the semidiurnal band ( $1.9-2.1 cpd$ , abscissa). Pictured are the average dissipation per bin (top), the total dissipation per bin (middle), and the number of samples per bin (bottom). Color scale for the top 2 panels are log10 of the dissipation in $Wkg^{-1}$ , log10 of samples in the bottom panel.

Figure 6.13: 3 day time series at DN of potential temperature between 68 and 220 mab (a), of potential temperature between 28 and 68 mab (colored lines in b), and dissipation (black line on b), the buoyancy frequency calculated between sensor pairs ( $10^{-3} s^{-1}$ ),(c) overlaid with a measure of the top (crosses) and bottom (circles) of overturns. Velocity, rotated so that the across slope component is in the ordinate direction (d)