...
For our Dig Deeper Project, we wanted to build on our work from Project 3, where we examined the general flow dynamics created by the interaction of fluids of different air masses. In Project 3, we modeled the Hadley circulation as a two-layer system, but we didn't did not really think about how the boundary affected the fluid flow. Of course, fronts are really important for weather systems - most everyday weather phenomena occur at frontal boundaries. In this experiment, we investigated the frontal boundary more closely.
...
In order to predict the frontal slope, one can first integrate find the change in pressure along two different paths: one through the dense fluid and the other through the light fluid, but 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).
...
Figure 3.1:
| Mathinline | ||
|---|---|---|
|
| Mathinline | ||
|---|---|---|
|
We assume that the flow is in geostrophic balance:
...
Assuming that angular momentum of the fluid is conserved (only a valid assumption when friction can be discounted), we get the following relation for the (approximate) deformation radius:
, where H is the height of the free surface with respect to the bottom of the tank.
...