Challenge Team Interim Report
Team Number: 039
School Name: Farmington High School
Area of Science: Physics
Project Title: Numerical Simulation of the Vortex on Jupiter
The purpose of this project is to construct a computer simulation of the Great Red Spot on Jupiter. Everything on Earth has to do with fluid flow; atmospheric air, oceanic water, and even the human body (97% fluid). The atmosphere of Earth holds many different storm systems, cloud clusters, and other such fluid activity. Therefore modeling a vortex such as the Great Red Spot may help in the understanding the atmosphere of our own planet. The equations for fluid flow are difficult to use and are frequently chaotic, requiring a numerical solution.
The GRS appears to be very large, but it is a very shallow feature in the upper layers of Jupiterís atmosphere. Keeping this in mind, it is possible to model the GRS using a two-layer model where there is a very shallow layer (GRS) sitting on a very deep layer. In the very shallow layer, it will be assumed that horizontal velocities and length scales are much larger than those in the vertical. It will also be assumed that the density is constant in each layer, and that the density in the lower layer is much larger so the motions in the upper layer do not significantly affect the lower layer. The lower layer, then, is only acting as a boundary for the upper layer. The plan that is being taken to model these layers contains three equations involving the N/S and E/W velocities of the fluid flow and the thickness. These equations are:
The first equation relates to the E/W velocity, the second to the N/S velocity, and the third to the thickness. Each of these has come from other equations simplified and combined to form one simpler set of equations.
To find the variables for each equation, more computations were done. The u represents the horizontal flow and the v the vertical flow. F0 is the rotation of Jupiter in radians per second, g is the acceleration due to gravity on Jupiter, and H is the thickness of the vortex. Each x and y in the equation represents the change in x or y. Each of these equations are very important to the flow of our simulation and have been carefully reviewed during the programming of them.
Each equation has been simplified and rewritten to be easily implemented into the computer program and then solved. So far, all three equations have been programmed and we are getting numbers out, but we are not exactly sure if they are reasonable or not. We plan on linking this program to the super computer and finding a graphics program that will take the numbers we generate and map them into a model of the GRS. We have designed a web-page that includes our progress, but it still needs to be connected to a server.
The results that we expect to get will be, of course, a graphical simulation of the Great Red Spot. Once the basic simulation is complete, we hope to be able to then change some of the variables to see what would happen to the flow of the Great Red Spot. Hopefully we will be able to recognize a specific difference in flow with respect to each variable.