A central challenge in modern fluid mechanics is to understand and predict dynamical phenomena that occur across a wide range of scales, especially when the behaviour at various scales is strongly coupled. This multi-scale character can arise from the internal structure of the fluid, as in the case of polymer solutions, or be generated spontaneously through nonlinear mechanisms which when taken to the extreme produce turbulence. Alternatively, a wide range of scales can be imposed by the geometry of the domain or the presence of external structures that drive the flow; an example of current interest is the cilia-driven flow of thin mucus films in human lungs. Our group works on problems that come from all three classes, including their intersection. We use a range of theoretical tools in our work, including reduced-order modelling and asymptotic analysis, direct numerical simulation, and more recently (and tentatively) machine learning.
Turbulent flows are ubiquitous and play an essential role in a wide range of scientific problems: From the transport of oil in pipelines to the production of chemicals in stirred tank reactors; from the transport of plankton in the ocean to the formation of rain in clouds.
Most flows and transport processes encountered in nature and industry are nonlinear and give rise to spatio-temporal patterned states, e.g., wave-trains on the surface of flowing water, droplets arrayed along a thin rod, sediment patterns on the sea floor, and Faraday hexagons on a vibrated liquid pool.
These patterns raise several…