Mooring DS

Spectra of horizontal velocity, shear, and buoyancy frequency all show peak energy at the semidiurnal frequency band (Figure 3.4). Spectral peaks at the diurnal and inertial frequency bands are noticeably smaller than the semidiurnal peak. The semidiurnal band accounts for $60\%$ of the total current variance at each depth, with the $M_2$ constituent alone accounting for $50\%$ of the variance. Similar ratios are found for vertical shear and temperature. The temperature spectra are similar at all the measured depths (Figure 3.5), with slightly less energy in the semidiurnal bands as the distance from the bottom decreases ($36\%$ decrease between $220 mab$ and $27 mab$ ). Around the estimated critical frequency of $\sim 3.3 cpd$ , the temperature oscillations are slightly more pronounced near the bottom, but not dramatically so as has been found in other observations of internal wave reflection (e.g. Eriksen (1982)).

A standard tidal analysis (Foreman, 1978) confirms that the semidiurnal constituents are approximately an order of magnitude larger than the diurnal (Table 3.1). In general, the $M_2$ and weaker $S_2$ constituents create a fortnightly spring-neap cycle with up to a factor of 4 difference in current amplitude. The current ellipses for the dominant $M_2$ tidal constituent are directed almost across the local isobaths (across-ridge). The angle between the topographic gradient and the semimajor axis of the $M_2$ current ellipses varies between $15^{\circ}$ and $30^{\circ}$ over the depth range examined (Figure 3.6). The semimajor axis of the $M_2$ current is $\sim 0.07 ms^{-1}$ with similar ellipse structure between 45 and 65 mab (Figure 3.6). Although the current amplitudes of the other depth bins are suspect (see section 2.1), we include them in Figure 3.6 to show that the orientation and eccentricity of the current ellipses are similar over the depth range. The ellipses also tilt in the across-ridge/depth plane such that the across-ridge flow is parallel to the slope (not shown). Greenwich phases for the current ellipses range from $40^{\circ}$ to $50^{\circ}$ .

The $M_2$ barotropic current, predicted either by the POM simulations (Merrifield and Holloway, 2002) or the TPXO model (Egbert, 1997), is not in phase with the measured semidiurnal current (Figure 3.6). When the semidiurnal surface elevation is high over the ridge, barotropic currents are directed southwestward (Merrifield and Holloway, 2002). At this phase of the tide, baroclinic currents along the south flank nearly oppose the barotropic current in model simulations (Merrifield and Holloway, 2002) in agreement with the observed current (Figure 3.6). The phase comparison suggests that the baroclinic tidal current dominates over the barotropic tidal current at these depths, leading us to conclude that the dominant energy source for tidal motions at the mooring location is the baroclinic component of the tide.

The observed temperature variations (Figure 3.1) are due primarily to the vertical advection of the background stratification by the semidiurnal tide, with maximum temperatures associated with maximum downward displacements. Vertical displacements $\xi$ are computed as $\xi(t)=T(t)/\frac{\partial T}{\partial z}$ where $T(z)$ is the temperature variation and $\frac{\partial T}{\partial z}$ is the temperature gradient. To examine the sensitivity of estimating vertical displacements to the choice of $\frac{\partial T}{\partial z}$ , the vertical displacement time series was first calculated for the sensor located $100 mab$ by using either the mean temperature gradient, or the temperature gradient low-pass filtered with a cut-off period of 48 hours. The standard deviation of vertical displacements is similar ($101 m$ and $98 m$ ) when using the mean and the low-passed $\frac{\partial T}{\partial z}$ respectively, and the RMS difference between the two estimates is $23 m$ . For simplicity, we therefore use the overall mean $\frac{\partial T}{\partial z}$ to calculate vertical displacements from temperature at all the sensors.

The resulting displacement amplitudes exceed $100m$ at all depths, corresponding to $200 m$ peak to peak changes in isotherm depths over a $12.42h$ cycle. Because of the proximity of the bottom boundary, these displacements include a lateral component up and down the slope. Vertical displacement phases show a small increase with distance from the bottom, indicating that displacements near the bottom lead displacements near the top of the mooring by approximately $14^{\circ}$ (30 minutes). Vertical displacements lag currents by $110^{\circ}$ , close to the $90^{\circ}$ difference expected for a freely propagating internal tide, and also consistent with the advection of stratified water up and down the slope.

Table 3.1: The main diurnal and semidiurnal tidal constituents at mooring DS for horizontal velocities at 65 mab (top) and temperature at 60 mab (bottom)

Tidal constituent	$O_1$	$K_1$	$N_2$	$M_2$	$L_2$	$S_2$
m/s	0.0055	0.003	0.025	0.074	0.01	0.029
Greenwich Phase	341	286	83	52	324	89
$\times 10^{-3o}C$	7.1	2.2	27	63.5	4.6	14.2
Greenwich Phase	262	133	337	294	234	338