Pattern formation amid turbulence: how large-scale order survives small-scale chaos


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. A well-known, yet still unexplained, example from the laboratory is the ghost vortices in turbulent Taylor-Couette flow. 

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. We will do this in the specific context of waves driven by a tangential flow of turbulent air over the surface of a liquid layer. As we gain insight into this problem, we will be able to address other situations as well, and thereby attempt to uncover some general principles underlying pattern formation in turbulent flows. 

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.  

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