We are looking for new solutions to nonlinear extensions of Rossby wave theory. My primary focus is using the method of group foliation to simplify the Flierl-Petviashvilli equation (one such extension to linear Rossby wave theory) by removing its symmetries, find solutions, then returning solutions to the full space. In addition, I have also written some code to numerically solve the FP equation and am now starting to use ROMs, a model which uses the primitive fluid equations, to analyze the behavior of the known solution.
I wrote some code in objective-c and c using cocoa to numerically solve the FP equation. I think the code is interesting for two reasons. First, it uses some fun technologies in the Accelerate framework for the FFTs and vector operations, as well as new classes like NSOperation for some easy multithreading. But second, and more importantly, it shows how modern programming can help a reseacher make equation and initial condition changes, then view the results and diagnostics in real time. No need to wait for stupid Matlab.
I am initializing a system with the FP monopole using ROMs, a primitive equation model.