EXECUTIVE SUMMARY
The purpose of our study was to model the Great Red Spot (GRS) on Jupiter using the principles of fluid dynamics and a super-computer. Once the initial model was completed, we then changed the initial size of the vortex. This problem involves fluid dynamics, the study of motion and equilibrium of fluids. Fluid dynamics is part of everyday life, especially the weather on earth. The GRS is a storm system similar to a hurricane or tornado on earth, therefore making our simulation very useful.
Our project involves many different principles of fluid dynamics including, conservation of mass, momentum, the lagrangian form, coriolis force, vorticity, and geostrophic balances. In order to effectively model the vortex, we put each of these principles into a system of equations. We then took the partial differential equations and simplified them into numerical equations from which we wrote our code.
We wrote a C++ program with a 100 by 225 grid that integrated for 200,000 time steps, which is about 3.6 years, real time. In the code, we have three different two-dimensional arrays representing the time levels (old, current, and new). There are three different functions to change the u and v velocities and the thickness of the vortex. In order to keep the program stepping, each array was moved down one time level (new becomes current, current becomes old). After a certain number of time steps, we printed out data files. We then made graphs from these data files.
We ran our program three times, with a different Gaussian radius each time. The Gaussian radius is the initial size of the vortex. Each simulation was successful, and it was visible that there was a preferred size for the vortex.
In this challenge, we were able to model the GRS successfully. We also had successful runs of the variations to the initial conditions that we made. We found that there is a preferred size that gives the vortex the greatest stability. It is also evident that the simulation with the 0.1 Gaussian radius is the closest to this preferred size.