By: Bea Beatrice Nash and Bethany Cates
1 Introduction
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Figure 4.2: 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.
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Figure 4.3: azimuthal velocity as a function of radius for particles tracked at the surface of the fluidthe tracks shown in the Figure 4.2.
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. At very small radii, the azimuthal velocity decreases again as the frontal boundary flattens.
We also track the particles which sit just above the frontal surface. These are the blue spheres seen in Figure 4.1.
Figure 4.4: azimuthal velocity as a function of radius for particles tracked at the surface of the front.
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 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 general overall radial dependence. As expected, at the same radii, these particles have smaller azimuthal velocity than those at the surface. The fluid at the surface is displaced towards the center more than the fluid at lower depths is, therefore in order to preserve angular momentum the surface fluid must acquire greater azimuthal velocity.
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