Vertical Velocities and their High-Frequency VariabilityVariability

Vertical velocities observed during the yoyo-cast downstream of the sill have been interpreted as a dense gravity current flowing down the lee slope by Thurnherr (2011). Froude Numbers computed in this thesis indicated the flow to be partly supercritical indicating a hydraulic jump downstream of the yoyo-cast location (Fig. 5.8). At the end of yoyo-cast, where Froude Numbers indicated sub-critical

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6.2 Vertical Velocities and their High-Frequency Variability Mooring Vertical Maximum Upward Maximum Downward

velocity [^cm_s ] velocity [^cm_s ] velocity [^cm_s ] mean std

UM 0.17 0.58 2.42 -2.02

DM1 -0.16 0.76 2.47 -3.58

DM2 -0.38 0.79 1.96 -2.63

Table 6.1: Vertical velocity average, standard deviation (std) and maximum up-ward and downup-ward velocity of 6 min low-pass filtered time-series observed by the moored ADCPs. The error of the time-average was estimated by 0.12 cm/s for the downstream and 0.08 cm/s for the upstream mooring respectively (error estimates see Section 2.2).

flow vertical velocities were directed upwards (Fig. A.3, Thurnherr (2011)). This might indicate a hydraulic jump propagating towards the sill (Section 6.1). In com-parison to the gravity current flowing down the lee slope a (propagating) hydraulic jump is expected to be associated with vertical velocity anomalies (Section 1.4).

Investigating mooring-based vertical velocities thus might offer a possibility to find indications for upstream propagating hydraulic jumps. Furthermore, vertical ve-locity variability is expected to be elevated in a turbulent region downstream of a hydraulic jump (Section 1.4). Investigating the relation of along-channel and vertical velocities as well as their variabilities might thus provide further indica-tions for the existence and location of a hydraulic jump. It is assessed whether any relation of high-frequency variability or propagating signals as e.g. propagating hydraulic jumps might be found to the magnitude of the along-channel velocity.

Vertical movements of the moored instruments which would induce false vertical velocities have been neglected as pitch and roll angles were below 3.5^◦degrees and variations in pressure were below 1 dbar.

Upstream of the sill average upward velocities of 0.17 cm/s with a maximum of 2.42 cm/s were observed, while downstream of the sill average downward velocities of 0.38 cm/s were found with a maximum of 2.63 cm/s (Table 6.1). The upward velocities upstream of the sill indicated that water from below the sill depth might cross the sill i.e. that blocking of the upstream waters does not necessarily occur at the sill depth (Section 5.5). The downward velocities downstream of the sill were in good agreement with the findings by Thurnherr (2011) and were consis-tent with a gravity current flowing down the lee slope of the sill.

The mooring-based velocity time-series showed strong variability of vertical veloc-ities but without a clear periodicity or relation to the along-channel flow or the TPXO barotropic tides (Fig. 6.3). A lagged correlation between the 3 h low-pass filtered vertical and along-channel velocities was performed using a maximum lag of 6 h. Only weak correlations were found (not shown) which are therefore not further discussed. The strong variability without a clear periodicity especially at the downstream moorings might be associated with turbulence which was found to

6 Signal Propagation

W 6min low−pass TPXO M2, S2, N2, K2 W 3h low−pass

16 00 08 16 00 08 16 00 08 16 00 08 16 00 08 16 00 08 16 00 08 16 00 08 16 00 08

Figure 6.3: Vertical velocity 6 min and 3 h low-pass filtered observed at mooring UM (upper panel), DM1 (middle panel) and DM2 (lower panel). The black line mark theM₂-, S₂-,N₂-, and K₂-tide from TPXO model.

be elevated downstream of the sill (Section 4.1). As vertical velocities are generally small in the ocean they may easily be superimposed by turbulent fluctuations. In-dication for elevated turbulence during phases of stronger along-channel flow were found from high-frequency temperature analyses (Section 5.1.2) and from direct dissipation rate observations (Section 5.4). In the following the high-frequency variability of the vertical velocities is analyzed aiming at identifying a possible re-lation between the high-frequency variability and the strength of the along-channel flow.

For the analyses of the high-frequency variability, the vertical velocities were bandpass filtered in the range of 6 to 30 min. This frequency range was cho-sen to exclude noise and internal waves. The buoyancy period was determined to be about 90 min. To quantify the variability with respect to the tidal cycle the standard deviation (std) was computed over segments of 3 h with 50 % over-lap. The time-series of the 3 h blocks of std showed elevated variability during phases of strong along-channel flow, especially at the DM1 mooring (Fig. 6.5).

A lagged correlation of the time-series of the 3 h blocks of std and the 3 h low-pass filtered along-channel velocities was performed using a maximum lag of 6 h.

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6.2 Vertical Velocities and their High-Frequency Variability Correlation of std of high-pass filtered Correlation coef. with 3 h low-pass vertical velocity at mooring filtered along-channel velocity

UM 0.49 (0.24)

DM1 0.73 (0.53)

DM2 -0.27 (0.07)

Table 6.2: Correlation coefficients R (and fraction of explained variance R² in parentheses) of blocks of 3 h std with 50 % overlap of 30 min high-pass filtered vertical velocity at each mooring location (Fig. 6.5) with the 3 h low-pass filtered observed along-channel velocity. Bold values are significant at a 95 % confidence level.

The correlation was largest at a lag of zero at the UM and at the DM1 moor-ing (Table 6.2 and Fig. 6.4) indicatmoor-ing strong variability in vertical velocities on time scales faster than internal waves during phases of large along-channel flow.

−6 −4.5 −3 −1.5 0 1.5 3 4.5 6

Figure 6.4: Lag correlation of blocks of 3 h std (with 50 % overlap) of 30 min high-pass filtered vertical velocities at each mooring (Fig. 6.5) with the corresponding 3 h low-pass filtered observed along-channel velocity.

Black dots indicate the maxima which are significant at a 95 % confidence level. Cor-responding confidence levels are indicated as dashed lines.

The strong correlation at DM1 (Ta-ble 6.2) might be attributed to tur-bulence or to high frequency waves forced by a hydraulic jump. An un-dular or weak hydraulic jump (Sec-tion 1.4) which was found likely to be located upstream of DM1 (Sec-tions 5.1.2 and 5.5) might induce such high-frequency variability and turbu-lence.

The origin of the correlation at the UM mooring is unclear. It might pos-sibly be related to turbulence induced by near critical reflection of the semi-diurnal tide at the bottom which was found to be likely to occur at least upstream of the UM mooring (Sec-tion 4.1).

At the DM2 mooring the correlation was largest at a lag of 1.5 h but the correlation was negative (Table 6.2 and Fig. 6.4). This indicated that

lit-tle high-frequency variability was observed after phases of strong along-channel flow. Little variability in vertical velocities would be expected in a supercritical flow regime where propagation of internal waves would be largely suppressed (Sec-tion 1.4 and (Thorpe, 2010)).

The absence of a positive correlation at the DM2 mooring indicated no simple, linear relationship of high-frequency variability of the vertical velocity and strong along-channel flow. Nevertheless variability on short time scales was observed (Fig. 6.3). A correlation would be expected only if propagating signals would be

6 Signal Propagation

Figure 6.5: Time-series of blocks of 3 h std from 30 min high-pass filtered vertical velocities and 3 h low-pass filtered along-channel velocities from moorings UM (upper panel), DM1 (middle panel), and DM2 (lower panel). Along-channel velocities were scaled such that the y-axes applies only for vertical velocity std. The black line mark theM₂-, S₂-,N₂-, and K₂-tide from TPXO model.

confined to a clear phase in the tidal cycle. If an undular hydraulic jump is es-tablished downstream of DM2, which was found to be a likely scenario based on Froude Number analyses (Section 5.3.1), upstream propagation of internal waves would be possible during all phases of the tide and might only be weaker dur-ing high along-channel flow (Section 1.4). Furthermore, if propagatdur-ing signals would be induced by a decaying hydraulic jump of any amplitude, the time lag of large along-channel flow and the observation of such a signal would depend on the position of the former jump in relation to the mooring where the signal will be observed. It is likely that the hydraulic jump does not always occur at the same location. In this case the correlation may be rather low. To find a correlation of along-channel flow and elevated variability in vertical velocities which might be

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