MAYO DEL
MARCO JURIDICO
here the velocity decreases to a much lower value at the wall. It generally remains non-zero, however, it is much smaller than the maximum velocity seen in the current at∼1/4 of the peak value. The velocity also demonstrates a consistent decrease near to the boundary, which is in contrast to the profiles in figures 4.9 and 4.10 where the velocity remains approximately constant or increases as it approaches the wall.
In summary, the across current velocity profiles show that the peak current velocity remains reasonably constant for the duration of an experiment following an initial increase.
The largest velocity is achieved across the central part of the current and it decreases towards zero as we move away from the peak value. Close to the boundary wall there is a decrease to a lower speed, which in general remains non-zero. The closest measurements are made
∼0.1 cm from the wall and therefore the velocity does not necessarily have to zero, but the magnitude of the values seen suggests that the flow behaviour may not be adequately captured by a zero wall velocity model for certain parameter regimes. The wall velocity ranges from approximately 0−1/2 times the peak current velocity across the different values ofI∗. This large range of values means that we cannot really draw a firm conclu-sion and as such both a zero value and a finite value for the wall velocity are used in the theory.
4.3 Model parameters 79 Experiment Q[cm3s−1] f [s−1] g′[cm s−2] H0[cm] D[cm] I∗
PIV 5 48 1 12.9 2 5 0.85
PIV 6 48 0.5 12.9 2 5 0.42
PIV 7 48 0.5 3.2 2 5 0.97
PIV 8 48 1 3.6 2 5 1.83
Table 4.4Experimental parameters for the four experiments where PIV measurements of the source conditions were made.
Figure 4.12PIV measurements of the source vorticity ratioαi=−ζi/f for a low value ofI∗=0.42.
Figure 4.12 plots the value of the source vorticity ratioαi=−ζi/f across the source widthDfor the lowI∗regime at early times. When viewed looking out of the source, the left-hand or upstream edge of the source is atx/D=0, with the right-hand edge atx/D=1.
The measurements give a vorticity ratio that remains small and positive in general, though we see fluctuations across the source width and over time. The variability in the data is an unfortunate consequence of the limitations of the experimental setup, with actual measure-ments inside the source required for improved accuracy. The measuremeasure-ments of the vorticity were taken as close to the source as possible, but were still susceptible to interference from the ambient and the flow within the vortex. We expect this interference to cause a decrease in the vorticity and thus we estimate the value ofαiat the source to be the maximum value measured across the source width.
Figure 4.13PIV measurements of the source vorticity ratioαi=−ζi/f for an intermediate value of I∗=0.97.
Figure 4.13 shows the value of the source vorticity ratioαi=−ζi/f across the source width for an intermediate value ofI∗=0.97. Again we see fluctuations across the source width and over time. The value ofαiis much larger however, with the maximum atT =5 reaching the zero PV limit ofαi=1.
The source vorticity ratio measurements for the highI∗regime are displayed in figure 4.14 at early times. The value again fluctuates across the source width and over time, but the profile shape remains relatively consistent, with the maximum value being reached at the right-hand edge of the source.
Figure 4.15 plots the estimated value ofαifrom the four PIV experiments as a function of time. We estimate the value at the source by the maximum value seen in the profiles in figures 4.12 - 4.14. The mean values for each experiment at early timesT <20 are shown as solid lines and the estimated values from the theory are shown as dotted lines. For the data in figure 4.15 we see quite good agreement between the time-averaged mean value and the estimates from the theory, suggesting that the experimental values provide a reasonable estimate of the actual source conditions. Ultimately, measurements are needed inside the source opening just before the freshwater enters into the ambient to accurately quantify the source conditions, however, the measurements obtained here provide some insight into the initial PV at the source. There does not appear to be any trend between the source vorticity
4.3 Model parameters 81
Figure 4.14PIV measurements of the source vorticity ratioαi=−ζi/f for a high value ofI∗=1.83.
ratio and the value of I∗. For example, for the two experiments at intermediate values of I∗=0.85 andI∗=0.97 we see both the smallest and largest estimated values ofαi. The theoretical estimates for αi are calculated by taking the maximum of the experimentally measured Rossby number and the theoretical Rossby number. The theoretical estimates for αiwill be discussed in more detail in section 4.4.4. Another important feature of the data in figure 4.15 is that for three out of the four experiments at low, intermediate and high values ofI∗, the estimated value ofαiis smaller than 1. This means that the source has a non-zero value of potential vorticity for these experiments. We will investigate whether or not the finite PV of the source has an effect on the steady state current properties in the next section.
Whilst the data presented in this section provides some insight into the source conditions, ultimately more accurate measurements are required, in particular for the source vorticity.
The measurements were made as close to the source as possible at∼0.1−0.2 cm in front of the source opening. As a result the values are distorted by the presence of the outflow vortex and by the shear generated at the boundary between the moving freshwater current and the stationary ambient. In future work, measurements are needed inside the source structure to provide a more accurate representation of the vorticity field at the source which can then be used in the theoretical models. We will outline one possible modification to the experimental setup that could be used to achieve the required measurements in future studies.
Figure 4.15The estimated value of the source vorticity ratioαiversus dimensionless timeT.
Currently, the source opening is aligned with the boundary wall which prevents an aerial view of the flow within the source. By offsetting the source opening to be behind the bound-ary wall and creating a gap in the wall at the source, the flow can be viewed from above.
Using similar PIV techniques to those used in the experiments described in this thesis, a light sheet may be used to illuminate the flow at the source which can be seeded with particles and recorded, thus enabling PIV measurements to be made using Digiflow. A diagram of the possible setup is shown in figure 4.16.