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3 Background theory: Thermal Wind and Margules relation
Figure 3.1: After the can is removed from the tank, the bottom of the dense fluid moves outwards, forming a cone. The less dense fluid converges towards the center of the tank, spiraling cyclonically in order to preserve angular momentum. The dense fluid spreads outwards, spiraling anti-cyclonically in order to preserve its angular momentum.
4 Lab results
In order to collect data from our experiment, we tracked using video processing software buoyant particles at the surface of the fluid, as well as particles with density in between that of the two fluids which sat just above the frontal boundary. The shape of the front, although relatively stable, did vary slightly throughout the course of the experiment, as can be seen from the following images.
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Figure 4.1: The progression of the front. The time stamp shown is relative to the time at which the can was removed.
Figure 4.2: After the can is removed from the tank, the bottom of the dense fluid moves outwards, forming a cone. The less dense fluid converges towards the center of the tank, spiraling cyclonically in order to preserve angular momentum. The dense fluid spreads outwards, spiraling anti-cyclonically in order to preserve its angular momentum.
Initially, the shape of the front resembles a Gaussian, with a wide sloping surface and flat top. As the experiment progresses, the frontal boundary gradually sinks relative to the free surface. Its sides flatten and the width of the center peak narrows (see Figure 4.2).
Using equation x, we calculate the predicted radius of deformation to be around 20 centimeters, or half of the width of the tank. Since the boundary of the front extends all the way to the outside of the tank, about 3/4 of the distance to the bottom of the tank, the actual radius of deformation for this front is slightly larger than this prediction. Therefore, we see the slope of the front decrease towards the edge of the tank, as it has no more room to spread outwards.
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