Figures 4.1 - 4.3 display along current profiles for three experiments at low (I∗=0.36), intermediate (I∗=1.23) and high (I∗=4.08) values ofI∗. The profiles shown are charac-teristic for the different values ofI∗. The current depthh is non-dimensionalised by the maximum depth scalingh0= (2f Q/g′)1/2and plotted against the current lengthl, which is non-dimensionalised by the current deformation radiusRdc=√
g′h0/f. Each plot shows a cross section along the current at ten different times, which have been non-dimensionalised by the rotation rate f. The start time at T =0 is defined to be when the current reaches the first corner of the tank and begins to propagate along the edge of the tank where the measurements are taken. This is to ensure consistency across the different experiments as for each different parameter set the current velocity and thus the time taken to reach the point of measurement will vary. The final time is at the end of the experiment. The data have been fitted with a polynomial curve which results in a slight exaggeration of some features, in particular leading to the apparent positive depth values which are not present in reality. See
4.2 Current features 67
Figure 4.1Along current cross-section from a typical experiment with a low value ofI∗. The profile is taken from an experimental run withI∗=0.36. The values ofT =t f for each profile are shown in the legend.
chapter 2 for more details.
There are several general trends that can be seen across the three cross-sections in figures 4.1 - 4.3. Firstly, as the value ofI∗increases we see a decrease in the dimensionless current depth at late times fromh/h0∼1.2 toh/h0∼1 toh/h0∼0.5. This demonstrates a tendency for the current to overshoot the maximum geostrophic depthh0at lower values ofI∗. We also see that in the cases of low and intermediateI∗the depth profiles become increasingly clustered together as time increases, suggesting the existence of a limiting steady state depth.
This feature is particularly clear in figures 4.1 and 4.2 when considering the latest times.
Secondly, we note that across all values ofI∗the current maintains a constant shape once the initial front has passed. This suggests that the shape of the current (away from the current head) is self-similar and again supports the hypothesis of the existence of a steady state, should the experiment be allowed to run long enough for it to be reached. This is in contrast to the observations of TL where the along current depth profile was found to reach a maximum shortly after leaving the source and then decrease moving towards the current head. Near to the current head, which corresponds to the early times in figures 4.1 - 4.3, the current depth decreases towards zero, but the current front is much sharper than seen in the work of TL and the current maintains a relatively consistent depth along its remaining
Figure 4.2Along current cross-section from a typical experiment with an intermediate value ofI∗. The profile is taken from an experimental run withI∗=1.23. The values ofT =t f for each profile are shown in the legend.
Figure 4.3Along current cross-section from a typical experiment with a high value ofI∗. The profile is taken from an experimental run withI∗=4.08. The values ofT =t f for each profile are shown in the legend.
4.2 Current features 69 length, with no obvious maximum. This change in behaviour may be a result of the change in the source structure, where our experiments use a horizontal outflow that discharges the freshwater with a finite value of PV. This differs greatly from the small vertical source used in the work of TL.
For each value ofI∗we are able to identify the propagation of the current front at early times. In each case the front seems to propagate at an approximately constant dimensionless speed, which can be estimated by the distance between the fronts at successive timesteps. For lowI∗in figure 4.1 we estimate the dimensionless speed as 0.83±0.07, for intermediateI∗ in figure 4.2 we estimate the dimensionless speed as 2±0.1 and finally for highI∗in figure 4.3 we obtain the estimated dimensionless speed 2.7±0.3. We will present more detailed measurements of the current velocity in section 4.3.1. The shape of the current front changes across the different values of I∗ and in general is sharper for lower values. We measure the front length as the distance from the leading edge of the current to the point where the gradient of the current slope decreases to less than 1/4 of the initial front gradient. For example, if we consider the profile atT =4 in figure 4.1, the leading edge of the current is at l/Rdc∼3.1 and the gradient becomes sufficiently flat atl/Rdc∼2.4, giving a dimensionless current front length of 0.7. Similar calculations for the profiles at intermediate and high I∗ in figures 4.2 and 4.3 give the estmated current front length as 1 and 1.6 respectively.
The increase in the length of the current front means that the front is becoming more gently sloping asI∗increases.