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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. Because of thisTherefore, we see the slope of the front decrease towards the edge of the tank, as the front it has no more room to spread outwards.
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Figure 4.2: Trajectory of particles tracked ≈11 minutes into the experiment, for ≈1 minute each. The axes are labeled in pixels, and the dot at the center indicates the center of the front. Each of the different colors corresponds to an individual tracked particle. The particles have small but noticeable radial displacement towards the center of the front.
Figure 4.3: azimuthal velocity as a function of radius for particles tracked at the surface of the fluid.
From the two above plots, one can see that the fluid does behave cyclonically at the surface, as we expected. At large radii, where the frontal boundary has a very small slope, the azimuthal velocity is small, as would be expected from the Margules relation. Notice that the maximum radius of the tracks is less than 12cm, whereas the edge of the tank is ≈20cm from the center of the front. At larger radii, the azimuthal velocity is nearly zero as the frontal slope is so small. As the radius decreases, the slope increases and so does the azimuthal velocity of the fluid, reaching its peak at around 5 centimeters5cm. At very small radii, the azimuthal velocity decreases again as the frontal boundary flattens.
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