NIVEL DE IMPACTO

The current depth was measured during each experiment at a fixed point alongside the wall of the tank. The point at which the depth measurements are made is taken as close to the source as possible, without interference from the outflow vortex, to allow maximum time between the first depth measurement and the end of the experiment. Full details of the methodology

I^∗ Q[cm³s⁻¹] f [s⁻¹] g^′[cm s⁻²] H₀[cm] D[cm]

0.19 74 1 69.1 2 2.5

0.60 42 2 70.3 2 5

0.75 47.5 1 15.8 2 5

0.95 72 2 15.4 4 5

1.15 42 0.5 2.3 2 5

1.55 45 2 14.7 2 5

1.73 62 2 13.5 2 5

Table 4.5Experimental parameters for the experiments shown in figure 4.17.

Figure 4.17The fixed point current depth scaled with the maximum current depth,h₀, for a subset of the experiments. The legend gives theI^∗values for the data shown.

are given in chapter 2 and the experimental parameters are shown in table 4.5.

Figure 4.17 plots the measured current depth over time for a subset of the experi-ments. The data from seven experiments are shown which are representative of the different behaviour seen across all of the stable experiments. The aspect ratio ratio has a range 0.19≤I^∗≤1.73. The current depth is scaled with the maximum geostrophic current depth valueh₀= (2f Q/g^′)^1/2and time with the rotation rate f. The general pattern across all of the data is the same. The fastest increase in depth is seen initially, with the rate of increase gradually slowing down over time. For around 2/3 of the experiments the current depth reaches an approximately constant value at long times. This can be seen in figure 4.17 for

4.4 Current measurements 85 the experiment withI^∗=0.60 which reaches an approximately constant value at T ∼80 that is maintained until the end of the experiment atT =125. In the remaining cases the depth is still increasing at the end of the experiment. An example of this behaviour is seen in figure 4.17 forI^∗=0.19. The fact that some of the experiments are stopped before a constant current depth has been reached is a constraint of the experimental setup. Each experimental run has to be stopped once the boundary has propagated around the full perimeter of the tank and returned back to the source. If we were to allow the experiment to continue beyond this point the current would interfere with the freshwater being released from the source and alter the initial conditions. This means that the experiments with the largest current velocity, which in general corresponds to lowI^∗, are less likely to reach a steady state and a constant current depth. Some of the experiments also show fluctuations in the measured values for the current depth, for example the runs withI^∗values of 1.55,1.73 and 0.60 in figure 4.17.

These fluctuations are possibly the result of waves along the density interface.

4.4.1.1 Theoretical comparison

In chapter 3 we saw that the theoretically predicted maximum current depth is the same across all models, regardless of the initial PV or the choice of wall velocity. The value of h₀= (2f Q/g^′)^1/2 is the same as that in previous models of TL, Avicola and Huq (2002), Lentz and Helfrich (2002) and Horner-Devine et al. (2006) and is in fact fixed under the assumption of geostrophic balance in the current. The theory predicts that the maximum cur-rent depth will be achieved at the boundary wall and that it is independent of thex-coordinate meaning it will be the same along the length of the current. We saw in figures 4.1 - 4.3 that the depth is approximately constant in thex-direction once the initial current front has passed.

The depth is also seen to increase with time as the flow tends towards a steady state and a final constant depth value. Since the theoretical model of chapter 3 assumes that a steady state has been reached, we will concentrate only on those experiments which demonstrate such be-haviour, i.e. where the value of the current depth remains approximately constant at late times.

Figure 4.18 plots the ratio of the experimentally measured steady state current depthh_ss and the theoretically predicted maximum current depthh₀versus the experimental Rossby numberRo_exp=u_exp/(f w_exp), whereu_exp andw_exp are the experimentally measured current velocity and width respectively. The agreement between the theoretical model and the ex-perimental data is on the whole quite good across a wide range of exex-perimental parameters.

The final values forh/h₀ lie in the approximate range 0.7≤h_ss/h₀≤1.2. In general the

Figure 4.18The ratio of the maximum experimentally measured steady state current depthhss and the theoretically predicted current depthh₀, versus the experimental Rossby numberRoexp. Only the data from the experiments deemed to have reached a steady state before the end of the experiment are included.

experiments with the lowest Rossby number show the best agreement with the theory. For the lowest values of the Rossby number,Ro<0.3, the agreement is good with 0.8≤h_ss/h₀≤1.1.

As the value ofRois increased further, the level of agreement decreases as we see the theory begins to over-estimate the experimentally measured values. The steady state theoretical model relies on the assumption that the flow is in geostrophic balance and the depth scaling h₀ is a direct consequence of this assumption. The assumption of geostrophy is valid for small Rossby number and the data in figure 4.18 suggest that the overestimation of the current depth for some of the experiments may be caused by the large value of the Rossby number.