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. How such large scale patterns emerge and persist is a fundamental open question; from a practical perspective, one would like to know how turbulent fluctuations affect the large-scale patterns. Our approach in this project will be to model turbulence as a stochastic forcing and use methods from reduced order modelling and stochastic dynamical systems to answer the above questions. The specific problems we will tackle have applications in weather/climate, human lungs, catalytic converters, etc.

Webpage: https://sites.google.com/view/jrpicardo

Area: Stochastic dynamical systems, turbulence, pattern formation

To enjoy working on this topic you must seriously want to learn, understand, and apply theories of pattern formation, stability analysis, and stochastic dynamics. By year 2 of your PhD, you should be strong in fluid dynamics, mathematics of ODEs and PDEs, and numerical methods. So a good foundation in at least some of these topics will be very helpful.