In his doctoral thesis, Michael Roop develops numerical methods that allow finding physically reliable approximate solutions to nonlinear differential equations used to model turbulence.

Many processes in nature can be described by differential equations, but only a few of them can be solved explicitly with solutions in formulas. This is the motivation for developing numerical equations to find approximate solutions. The numerical equations developed in Roop’s thesis have a particular focus on geometric properties. Though the thesis is mathematical, the problems it addresses originate in physics and mainly have to do with magnetohydrodynamic (MHD) turbulence.

“It is difficult to define turbulence rigorously. Intuitively, you can think of the turbulent behavior when a fluid moves, but it is very hard to predict how it will behave in the future. It looks chaotic though there is no randomness in the models of motion.”