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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.
Using the Margules relation and the data collected for the velocity of particles at the boundary of the front to solve for the frontal slope, we "backed out" what the boundary of the front would look like according to the theory.
Figure 4.5: Predicted frontal boundary using the Margules relation at the velocity of particles tracked at the boundary. The particle with smallest radius was assumed to be near enough to the highest point of the frontal boundary. The largest radius of the tracked particles is about halfway between the center of the front and the edge of the tank.
Accurately comparing the images taken (Figure 4.1) to the plot above would be difficult due to issues of distortion. However, just looking at the 3rd image in Figure 4.1, the closest in time to when the particles were tracked, one can see that the overall shape of the front aligns well with the prediction. Therefore, we conclude that the Margules relation provides a good estimate for the shape of a front, given that geostrophic assumptions hold.
5 Challenge: Inverting the Dome!
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