Research
t-SNE on CNN embeddings of turbulent Kolmogorov flow, revealing a single class of high dissipation “bursting” events (top right). The octagonal shape is the encoding the shift-reflect symmetry in the flow.
Machine learning and data-driven methods to advance fundamental fluid mechanics
The primary focus of our group is understanding, prediction and control of turbulence in fluids. We use a combination of ideas from dynamical systems theory with direct numerical simulations, and increasingly incorporate and rely on techniques from deep learning. Current work is focused on new methods to identify simple invariant solutions in strongly turbulent systems (neural networks and automatic differentiation more broadly), on using simple invariant solutions to explain key vortical events and their contribution to the overall statistics of the flow and on generalising the “dynamical systems” view to flows which are not statistically steady.
A snapshot of elasto-inertial turbulence in a channel. Colours are contours of polymer stretch, lines the perturbation streamfunction. Mean flow is from left to right.
Transition and turbulence in Viscoelastic liquids
Viscoelastic liquids often exhibit counter-intuitive macroscopic behaviour due to their complex internal microstructure. Our focus is on the “types” of turbulence that are observed in viscoelastic flows in different regions of parameter space. In high-Reynolds number flows, polymer additives result a dramatic reduction in skin friction. At low Reynolds numbers, viscoelastic flows can be chaotic (“elastic” turbulence) due to a new linear instability mechanism associated with finite curvature in tensioned mean-flow streamlines. Somewhere in between, there is a new (two-dimensional) state - elasto-inertial turbulence. We seek to understand and explore the connections between these different regimes using ideas from dynamical systems and asymptotic analyses. Key contributions include the discovery of the first purely elastic exact coherent structure and the identification of a reverse-Orr amplification mechanism for the vorticity — the exact opposite of a Newtonian behaviour.