PAGO VIATICOS Y SUBSISTENCIAS

A total of four PIV experiments focusing on the boundary current were carried out. The PIV data are measured close to the surface of the flow at a depth of ∼0.5−1.5 cm. The parameter values were chosen to provide as good a representation as possible of the different behaviours seen across the full parameter range at low, intermediate and high values ofI^∗. For the highI^∗regime the parameters were chosen such that the vortex only goes unstable at the very end of the experiment to allow measurements of the current properties to be made for the majority of the experiment before the current is distorted by the shedding of vortices from the outflow vortex. The experimental parameters used are displayed in table 4.3. Full details of the methodology of the PIV measurements are given in chapter 2.

Across current velocity profiles for the three regimes of low, intermediate and high values ofI^∗ are displayed in figures 4.9 - 4.11 for six different timesteps. The profiles are taken across the current at approximately one-fifth of the distance around the perimeter of the tank.

The boundary wall is located aty/R_dc =0.

The data in figure 4.9 show the current velocity increasing away from the boundary wall, reaching a maximum value aty/R_dc∼0.2−0.4, before then decreasing to zero at the far-edge of the current. For early times, T ≤40 there is a general increase in the current velocity as the current is established and tends towards a quasi-steady state. The maximum velocity remains approximately constant forT =40−60 until the experiment ends. The profile retains a reasonably consistent shape throughout the experiment, with a narrow region of peak velocity in the centre of the current and the velocity decreasing towards the edges

Figure 4.9Across current velocity profiles for the lowI^∗=0.42 regime.

of the current. Alongside the wall at y/R_dc =0 the value of the dimensionless velocity remains reasonably consistent at∼0.5. This is equal to approximately 1/3−1/2 of the maximum velocity reached at the centre of the current depending on the time of measurement.

The experimental velocity at the wall must be zero in reality, but due to limitations in the measurement techniques (see chapter 2) we were unable to resolve the full velocity profile in the narrow region at the wall. The closest measurements were made approximately 0.1−0.2 cm from the boundary.

Figure 4.10 displays the across current velocity profiles for an intermediate value of I^∗=0.81. The current velocity increases at early times up to T =10 and then we see a decrease atT =30 before it remains reasonably constant for the remainder of the experiment.

The profiles show a decrease in the current velocity away from the maximum value that is achieved at the centre of the current as seen in figure 4.9 for lowI^∗. The velocity close to the wall is in general quite large ranging from 1/3−1 times the maximum current velocity.

For the velocity profiles for the highI^∗ regime in figure 4.11 we see an increase in the velocity forT ≤30, where it then remains approximately constant until very late times at T =110 when it increases again. This late increase is a result of the outflow vortex going unstable, with vortices shed from the main bulge being carried along by the current. The shape of the profiles in figure 4.11 is different to those seen above for PIV runs 1 and 2, as

4.3 Model parameters 77

Figure 4.10Across current velocity profiles for the intermediateI^∗regime withI^∗=0.81.

Figure 4.11Across current velocity profile from an experiment in the highI^∗regime withI^∗=1.80.

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.