Mooring DN

Spectra of temperature at the north mooring (DN) are calculated for the 8 month long time series. The temperature spectrum at the highest sensor ($220 mab$ ) shows a sharp peak at the semidiurnal $M_2$ tidal frequency, as well at the $M_3$ and $M_4$ harmonics (Figure 3.7). In contrast to DS, at the sensor closest to the bottom ($20 mab$ ) the semidiurnal spectral peak is one order of magnitude smaller than at $220 mab$ , and the near-inertial/diurnal ( $0.7-1.1 cpd$ ) band is much more energetic (Figure 3.7). There is also more energy in the high frequency band ($3$ to $16 cpd$ ) as the distance from the bottom increases. The spectra at the other nine sensors show a smooth transition in energy with depth.

The kinetic energy spectrum shows the same features as the temperature spectra (Figure 3.7) at similar depths (Figure 3.8), i.e., a peak in semidiurnal energy and a wide peak in the near-inertial band. Due to the limited vertical coverage of current measurements, variations with depth of the energy in these bands were not observed. The kinetic energy at DN in the near inertial/diurnal band is one order of magnitude higher than at DS (Figure 3.9). The temperature variations in the near inertial/diurnal band are also more energetic at DN than at DS at all the depths sampled (Figure 3.9). We will examine this frequency band in more detail in chapter 4.

At DN, the critical frequency of $\sim 1.8 cpd$ is close to the semidiurnal frequency, yet the temperature spectra show a clear increase in energy with increasing distance from the bottom in this band. This is contrary to both the observations at DS (critical frequency of $3.34 cpd$ ) where energy levels increase with decreasing distance from the bottom, and the linear theory of internal wave critical reflection (Eriksen, 1982), that predicts increased levels of energy around the critical frequency near the bottom. We conclude that the vertical structure of the semidiurnal band energy at mooring DN is inconsistent with wave reflection processes.

The DS and DN moorings were deployed in the path of expected tidal beams that originate near the edges of the ridge, and propagate down and away from the ridge flanks. In situ observations near the ridge edge confirm the presence of downward propagating beams (Nash et al., 2005; Martin et al., 2005; Rainville and Pinkel, 2005). We now consider whether the observed temporal and spatial variations of the semidiurnal band energy are consistent with these predictions. To isolate the astronomically coherent part of the variability, a harmonic tidal analysis (Foreman, 1978) is performed on the temperature and current speed records (Figure 3.10 and 3.11). All resolvable tidal constituents are used at each mooring (35 at DS, 59 at DN). On the north side of the ridge (DN), the percentage of total temperature variance explained by the harmonic tidal analysis increases from $20 \%$ near the bottom, to $50\%$ at $200 mab$ . In contrast, $50$ to $70 \%$ of the total variance is explained by the harmonic tidal analysis over the entire depth range at DS. We find similar differences between the moorings for the current data harmonic analysis (Figure 3.10). These differences are attributed to the weaker semidiurnal variability at DN compared to DS, especially near the bottom, and the higher near-inertial to diurnal variablity at DN. At both moorings, a weakened acoustic return signal higher than $60 mab$ leads to an increasing number of missing data, which in turn artificially decreases the performance of the tidal analysis for the current data (Figure 3.10). The phase information from the harmonic analysis supports the notion of downward semidiurnal energy propagation (Figure 3.11). There is a steady increase in temperature phase with increasing depth at DN, and also at DS, indicating downward energy propagation. We assume that we are in the presence of internal tidal beams, and that we only sample the lower part of the beams. Given the short mooring lengths, we cannot infer the vertical wavelength of the internal tide from our measurements. The large confidence intervals for the phase near the bottom are a result of small temperature amplitudes at mooring DN. At all depths, the temperature amplitudes are a factor of 2-3 smaller at DN than at DS. The temperature amplitude increases tenfold between $30$ and $220 mab$ at DN (from 3 to 30 millidegree), while the amplitude increase over the same depth range at mooring DS is only $30\%$ (60 to 80 millidegree).

The measured $M_2$ current ellipses at DN are quite weak ( $0.02 ms^{-1}$ ) and are directed along the local topography (Figure 3.12), instead of across the topography as is found in other frequency bands (Figure 3.8). The observed ellipses are weaker in amplitude than either the barotropic ellipse predicted by the TPXO model, or the combined baroclinic and barotropic ellipse from the Merrifield and Holloway (2002) numerical model (Figure 3.12). In contrast, at DS Aucan et al. (2005) measured $M_2$ current ellipses directed across the slope that are much larger than the predicted TPXO barotropic ellipse, and equivalent in amplitude to Merrifield and Holloway (2002) numerical estimates. Nash et al. (2005) measured barotropic semidiurnal velocities of $0.04 ms^{-1}$ near the 3000 m isobath on the south side of the ridge, with baroclinic velocities exceeding the barotropic velocity. We note that their measurement does not differentiate between $M_2$ and other semidiurnal constituents ($S_2$ , $N_2$ ), that we are able to separate in our analysis.

Aucan et al. (2005) concluded that a semidiurnal beam propagates near the bottom at DS, with little variability in amplitude over the first $200 mab$ . From these considerations, we conclude that a semidiurnal beam propagates downward over DN, at a distance further from the bottom compared to DS. Assuming that the beams originate near the $1000 m$ isobath, we suggest that the beam center is further from the bottom at DN than DS, and hence less tidal energy is present at the bottom at DS than DN.

We cannot resolve the barotropic tidal current directly from the data. Except near the boundary, the barotropic tidal velocities are constant with depth, and we do not believe that the weak tidal amplitudes at DN near the boundary are due to shears in a frictional bottom boundary layer since a similar effect was not observed at DS. In addition, the observed vertical displacement amplitude decreases near the bottom at DN (Figure 3.11), while the vertical displacement amplitudes of a barotropic flow up a slope increase near the boundary. We conclude that the barotropic tide alone cannot explain the observed vertical structure of the semidiurnal band variability at DN. Furthermore, the TPXO and POM models both predict similar barotropic amplitudes on either side of the ridge. This view is consistent with geometrical considerations of the local Kaena Ridge topography.

At DS, the local slope is super-critical with regard to $M_2$ , allowing the propagation of a beam from an upper generation site, down and away from the ridge that grazes the mooring site (Figure 3.13). The mooring DN is located on a relatively flatter area on the ridge flank, and the slope is locally sub-critical for $M_2$ . The geometry of the ridge may not allow for the propagation near the bottom of a downward propagating beam originating near the ridge top (Figure 3.14). Instead, the beam at mooring DN is likely to detach from the bottom, as suggested in Figure 7 in Nash et al. (2005). The displacement phase information $200 m$ above the bottom indicates that the $M_2$ beam at mooring DN is still propagating downward, however not necessarily right at the bottom as it does at DS.

Figure 3.1: Representative 14 day time series of temperature ($75 mab$ ), and across-slope and along-slope currents ($65 mab$ ) at mooring DS.

Figure 3.2: Representative 14 day time series of temperature ($52 mab$ ), and across-slope and along-slope currents ($55 mab$ ) at mooring DN.

Figure 3.3: Vertical profiles at DS (red) and DN (blue) of mean current speed (upper left), current speed standard deviation (upper right), across (thick) and along (thin) slope velocity standard deviation (middle left), ratio of along to across slope velocity standard deviation (middle right), temperature standard deviation (lower left), and corresponding vertical displacement standard deviation (lower right).

Figure 3.4: Power spectra at DS of a) horizontal current ($65 mab$ ), b) temperature ($220 mab$ and $27 mab$ ), c) vertical shear of the horizontal current (between $40$ and $65 mab$ ), d) depth-averaged buoyancy frequency ($27$ to $220 mab$ ). Top abscissa is in cycles per day (cpd). The Coriolis, $M_2$ and critical frequencies are indicated.

Figure 3.5: Temperature spectra for all available sensors at DS. Corresponding sensor elevations in mab are indicated in the legend. Top abscissa is in cycles per day (cpd).

Figure 3.6: The $M_2$ (left) and $S_2$ (right) measured horizontal current ellipses at DS, with suspect depth bins in gray (i.e., side lobe contamination problems). Barotropic current ellipses predicted by the TPXO model (Egbert, 1997) are depicted at the top. The direction of the topographic gradient is indicated with the red arrow on the left.

Figure 3.7: Temperature spectra for all available sensors at DN. Corresponding sensor elevations in mab are indicated in the legend. Top abscissa is in cycles per day (cpd).

Figure 3.8: Rotary Velocity spectrum (top) and across and along slope current spectrum (bottom) at DN ($48 mab$ ).

Figure 3.9: Velocity spectra at DN (blue) and DS (red) moorings, 48 mab (top), temperature spectra at 220 mab (middle) and temperature spectra at 28 mab (bottom).

Figure 3.10: Percentage of variance explained by a harmonic tidal analysis for a) temperature, and b) current velocity, at mooring DS (red) and DN (blue)

Figure 3.11: $M_2$ phase (left) and amplitude (right) of the temperature (top) and the current velocity (bottom) at the DN mooring (blue), and at DS mooring (red). Results from the TPXO models are indicated as 'x'

Figure 3.12: Bathymetry around mooring DN (top) and DS (bottom), with the measured (thin red) $M_2$ velocity ellipses, the predicted barotropic $M_2$ ellipses from TPXO (thick red), and the combined barotropic and baroclinic $M_2$ ellipses from POM (black, Merrifield and Holloway (2002)). Scale for bathymetry is in meters.

Figure 3.13: Ridge cross-section and theoretical $M_2$ ray paths at DS. Ray paths were constructed step by step by calculating the angle of propagation at each step by using the dispersion relation for a free $M_2$ frequency internal wave and the climatological stratification profiles from station ALOHA

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Figure 3.14: Same as figure 3.13 but for the north side of the ridge

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