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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 5cm. This radius approximately corresponds to the location of the edge of the can before it was removed. We would expect the pressure gradient at this radius to be largest, which implies fluid at this radius should also have the largest velocity (see equation y). At very small radii, the azimuthal velocity decreases again as the frontal boundary flattens and the pressure gradient decreases.
We also track the particles which sit just above the frontal surface. These are the blue spheres seen in Figure 4.1.
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These particles are more difficult to track, hence the tracks are shorter, and the concentration of dye and particles at the center of the front makes it impossible to track the particles for very small radii accurately. Still, it is clear from this plot that the azimuthal velocity of the fluid at the frontal surface has the same overall radial dependence as that of the fluid at the free surface for large radii. However, we see only a small peak at 5cm, unlike the very defined peak at that radius for the velocity of the fluid at the surface.
As expected, for the same radius, these particles have smaller azimuthal velocity than those at the surface. Upon removal of the can, the fluid at the surface is displaced towards the center more than the fluid at lower depths, therefore in order to preserve angular momentum the fluid at the surface must acquire greater azimuthal velocity.
5 Challenge: Inverting the Dome!
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