4 Turbulence, Density and Flow Distribution along the Channel
4.2 Average Velocity and Density Field
4.2.2 Vertical along-Channel Flow and Density Distribution
In order to identify the physical process controlling the mixing downstream of the sill, the vertical along-channel distribution of flow throughout the channel is dis-cussed below. For determining the average flow field individual LADCP-derived velocity profiles were averaged with respect to their location according to the grouped stations U3 to D4 (Table 2.1 and Figure 2.1). To interpolate between average profiles of the group-stations a quasi terrain following interpolating tech-nique was used (Kanzow and Zenk, 2014). Froude numbers to characterize the flow regime were computed from the same averaged profiles following Equation 1.5 and are given at the top of the figures respectively.
The station-wise averaged along-channel velocity component showed highest flow speeds at the downstream station D1 exceeding 18 cm/s (Fig. 4.6). Froude Num-bers were found to be elevated at the station D1 and dropped in both, upstream and downstream direction (top Fig. 4.6). According to Thorpe (2010), a Froude Number of 1.4 is close to the critical value where an undular or a weak hydraulic jump may occur (Section 1.4).
The flow was directed along the channel not only at the station D1 but at all group stations below 1600 m. Thus the average unidirectional flow along the chan-nel observed by St. Laurent and Thurnherr (2007) was confirmed. Furthermore, the Froude Numbers indicate the existence of an hydraulic jump downstream of the sill, at least a transient, undular or weak hydraulic jump (Section 1.4).
The average density distribution which was computed analogously to the velocity distribution also showed indications for an hydraulic jump. Downstream of the sill, isopycnals were displaced downward following the topography below 2000 m depth,
Mooring Along channel Cross channel Flow speed DOF velocity [cms ] velocity [cms ] velocity [cms ]
mean std sem mean std mean std sem
UM 3.7 2.8 0.4 0.0 1.7 4.4 2.2 0.3 59
DM1 5.8 3.4 0.6 0.0 2.0 6.2 3.2 0.6 33
DM2 8.6 3.0 0.6 0.0 3.0 8.8 2.9 0.6 25
Table 4.2:Along- and across-channel velocity components as well as the flow speed with standard deviations (std) and the standard error of the mean (sem) from moored ADCPs. The corresponding degrees of freedom (DOF) used for the esti-mation of the sem were computed using the time-lag of zero autocorrelation. Data were low-pass filtered with a cutoff frequency of 1/6 1/min.
4 Turbulence, Density and Flow Distribution along the Channel
but exhibited an upward displacement above 2000 m depth starting at about 1 km downstream of the sill. Deviations from horizontal density contours were observed up to 1500 m water depth. Far upstream of the sill isopycnals were oriented nearly horizontally above the sill depth, while closer to the bottom, they slightly bended upwards in downstream direction and then intersected the topography, still up-stream of the sill.
The distribution of the density and Froude Numbers together were very much con-sistent with a hydraulic jump. At this point it is unclear, whether the hydraulic jump is a transient feature. Further analysis regarding this question is reported in Section 5.3. Upward radiating internal waves induced by a hydraulic jump as de-scribed by e.g. Legg and Huijts (2006) might induce the deviation from horizontal isopycnals observed here up to a depth of 1500 m.
Figure 4.6: Station averaged along-channel LADCP derived velocity. The stations are given at the top of each panel together with Froude Numbers. Vertical lines mark the latitude of each station. At the Stations D2 and D3 only the central stations have been used (Table 2.1 and Fig. 2.1). The color refer to along-channel velocity but Froude Numbers were computed from absolute flow speeds. Contour lines denote potential density (spacing ∆σ2= 0.002 kg/m3) with colored contours indicating the isopycnals used for Froude Number computation (Section 1.4). Topography as in Fig. 4.1.
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4.2 Average Velocity and Density Field
The average across-channel velocity component (zonal velocity) was generally be-low 2 cm/s throughout the channel (Fig. 4.7). The deviation from the along-channel direction with weak westward flow at station D3 could be attributed to the bottom elevation around 37.305◦N, which reaches up to 2000 m (Fig. 4.5), or to the north-westward orientation of the western channel boundary (the Lucky Strike volcano). The flow above ∼1800 m showed higher westward velocities with a maximum of 7 cm/s at Station D1 which might already be situated above the ridge flank topography confining the flow below into along-channel direction.
The weak across-channel velocity component again confirmed that the flow is di-rected along the channel. Therefore, the across-channel component will not be discussed any further throughout this thesis.
Figure 4.7:Station averaged across-channel LADCP derived velocity. The stations are given at the top of each panel together with Froude Numbers. Vertical lines mark the latitude of each station. At the Stations D2 and D3 only the central stations have been used (Table 2.1 and Fig. 2.1). The color refer to across-channel velocity but Froude Numbers were computed from absolute flow speeds. Contour lines denote potential density (spacing ∆σ2 = 0.002 kg/m3) with colored contours indicating the isopycnals used for Froude Number computation (Section 1.4). Topography as in Fig. 4.1.
4 Turbulence, Density and Flow Distribution along the Channel
Vertical Shear of along-Channel Velocity
The distribution of the flow velocity along the channel with its strong maximum just downstream of the sill revealed strong shear close to the sill (Fig. 4.6) which might potentially lead to shear instabilities. Shear instabilities are likely to occur if the ratio of buoyancy frequencyN and vertical shear of horizontal velocityδU/δz, expressed as the Richardson number Ri=N2/(δU/δz)2, falls below 1/4 (Thorpe, 2005). Richardson numbers were computed over 50 m layers from all individual profiles along the channel (Fig. 4.8). The layer thickness of 50 m was chosen to compute the Richardson Number over stable stratified layers. The vertical length scale of stable stratification was estimated based on the Ozmidov scale of about
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
Figure 4.8: Richardson numbers along the channel from station averaged velocity and stratification. The stations are given at the top of each panel together with Froude Numbers. At the Stations D2 and D3 only the central stations have been used (Table 2.1 and Fig. 2.1). Vertical lines mark the latitude of each station. Con-tour lines denote potential density (spacing ∆σ2 = 0.002 kg/m3) with colored con-tours indicating the isopycnals used for Froude Number computation (Section 1.4).
Topography as in Fig. 4.1.
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4.2 Average Velocity and Density Field 30 m indicating the maximum overturn size (Ozmidov (1965). For details regard-ing the overturn size see Section 4.4.3. Critical numbers of less than 1/4 were found twice in the area just downstream of the sill close to the sea floor. Values below unity were found rather frequently in the range of 1 to 4 km downstream of the sill close the bottom, but also at shallower depth. Upstream of the sill low Ri were found below 1800 m at station U3 and U2 as well as between 1400 m and 1500 m depth at station D2.
While low Richardson numbers downstream of the sill are probably caused by strong shear induced by the overflow it is unclear what caused the low Richardson numbers at shallower depths. Upward propagating internal waves possibly gener-ated by overflow relgener-ated processes at the sill could be a possible explanation (Legg and Huijts, 2006).
As the Ri was below the critical value of 1/4 only twice in all the observations available here, shear instabilities can probably not explain the strong mixing down-stream of the sill. This further supports the evidence of the mixing being caused by a hydraulic jump.