RESULTS
As you can see in pictures below, the simulations for the GRS are quite interesting. The first set has a Gaussian radius of 0.05, the second set has a Gaussian radius of 0.1, and the third has a Gaussian radius of 0.25. The Gaussian radius is the only difference for each of the simulations, being the initial radius for the GRS. Because of the long amount of loading time, all 36 pictures are not shown. Only three of each are present.
Each of the simulations started out similar, the difference being the depth of the vortex due to different Gaussian hill numbers. Once the time step continued, the similarities ended. Each simulation became elongated, and the time it took to become elongated depended upon the original size of the vortex. The 0.05 took the longest to stretch out and elongate.
Continuing on, the 0.1 and 0.25 radius simulations seemed to be shedding off smaller vortices, which seemed to indicate that there is a preferred size for the GRS. The 0.1 simulation continued this for about 135,000 time steps, which is about 2.45 years. The 0.25 radius simulation continued to shed vortices off for the entire time, trying to reach the preferred size. If we had run the program longer, it is likely that it would have eventually reached the preferred size.
The 0.05 simulation, starting out under the preferred size, was generally stable for the first 60,000 time steps. After this time, the 0.05 simulation had diminished in sized and was surrounded by eddy currents. These eddy currents seemed to overtake the vortex and remain there for the remainder of the trial.
The 0.1 simulation basically stays visible throughout the entire trial, although it sheds off small pieces of itself periodically. By the end of our trial it appeared to have stabilized into one vortex, although had we allowed the simulation to run longer, it may have shed off more pieces.
Data Simulation 1
Gaussian radius of 0.05
Data Simulation 2
Gaussian radius of 0.1
Data Simulation 3
Gaussian radius of 0.25
CONCLUSION
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.