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In order to predict the frontal slope, one can we first find the change in pressure along two different paths: one through the dense fluid and the other through the light fluid, but both with the same start and end point.  Since they have the same start and end point, we require that the change in pressure calculated along these paths must be equal (see Figure 3.1).

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Figure 3.1: 

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body \rho_{1}

 is the denser fluid, 

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body \rho_{2}

 the less dense fluid.  γ is the angle between the denser fluid and the bottom of the tank.  We calculate the changes in pressure along paths 1 and 2 , and require that they be equal.

We Next, we assume that the flow is in geostrophic balance:

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where γ is the angle the dense fluid makes with the horizontal, 

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body u_{2}

, 

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body \rho_{2}

 are the azimuthal velocity and density of the less dense fluid, respectively, 

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body u_{1}

, 

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body \rho_{1}

 are the azimuthal velocity and density of the denser fluid, and 

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body \Omega

 is the rate at which the system is rotating, in radians/second.

Assuming that angular momentum of the fluid is conserved (only a valid assumption when friction can be discountedis negligible), we get the following relation for the (approximate) deformation radius:

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In order to collect data from our experiment, we tracked using video processing software track the motion of 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.

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Figure 4.1: The progression of the front.  The time stamp shown is relative to the time at which the can was removed.  The green dye is placed just outside the frontal boundary and the blue spheres just above it.

Figure 4.2: After the can is removed from the tank, the bottom of the dense fluid moves outwards, forming a cone.  The less dense fluid converges towards the center of the tank, spiraling cyclonically in order to preserve angular momentum.  The dense fluid spreads outwards, spiraling anti-cyclonically in order to preserve its angular momentum.

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