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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.
Figure 4.1: The progression of the front. The time stamp shown is relative to the time at which the can was removed, allowing the two fluids to meet.
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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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The 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 correspond corresponds to an individual tracked particle. The particles have small but noticeable radial displacement towards the center of the front.
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. As the radius decreases, the slope increases and so does the azimuthal velocity of the fluid, reaching its peak at around 5 centimeters. At very small radii, the azimuthal velocity decreases again as the frontal boundary flattens.
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These particles are more different to track, hence the tracks are shorter, and the concentration of dye and particles at the center of the front made makes it impossible to track the particles for very small radii. Still, it is clear from this plot that the fluid at the frontal surface has the same dependence on radius, although
5 Challenge: Inverting the Dome!
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