The vast majority of flows in our daily experience are turbulent and yet we see patterns all around us. Ordered arrays of cloud streets, (turbulent) wind-driven waves with distinct wavelengths, and---for a more exotic example---Jupiter's red spot all testify to the ability of ordered patterns to arise and persist amidst turbulent fluctuations. In this project, we will specifically focus on understanding how patterns with length and time scales much greater than the turbulent flow arise and survive. Specific problems with important applications include flames fluttering in a turbulent flow and roll-like patterns in a convecting fluid.
This project will involve understanding and applying theories of pattern formation, stability analysis, and stochastic models of turbulence. Simulations will also be needed, but of simplified models, as the very nature of these problems precludes the use of direct numerical approaches. To get started, a knowledge of fluid dynamics, mathematics of ODEs and preferably also of PDEs is important. Experience using Matlab or Python is also useful. If you don't have a background in some of these areas, then don't worry---you can learn, but you must have a strong interest in them.
For information on the other problems my group works on, you can visit my personal and group webpages.