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Using the tracked particles, we now analyze the velocity of the fluid both on the surface and at the frontal boundary starting around 11 minutes after the removal of the can. As can be seen from the above images, the fluid appears sufficiently stable at this point in the experiment to assume hydrostatic balance. At this time, we track particles at the surface, resulting in the following set of tracks:
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Figure 4.23: Trajectory of particles at the surface of the fluid 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 4.34: azimuthal velocity as a function of radius for the tracks shown in the Figure 4.2.
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We also track the particles which sit just above the frontal surface. These are the blue spheres seen in Figure 4.1.
Figure 4.45: azimuthal velocity as a function of radius for particles tracked at the surface of the front.
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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 (see Figure 34.12).
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 4.56: 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.
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