Manchester Centre for Nonlinear Dynamics

The Manchester Centre for Nonlinear Dynamics is comprised of researchers from the School of Mathematics and the School of Physics and Astronomy at the University of Manchester. Research within the group is based upon the application of a combined approach of theoretical modelling, computation and detailed quantitative experimental investigations of nonlinear phenomena.

Granular jets and hydraulic jumps on an inclined planeMulti-component particle-size segregation in shallow granular avalanchesGravity-driven granular free-surface flow around a circular cylinderRaleigh-Taylor instability in a finite cylinderParticle-size segregation in dense granular avalanchesUnderlying asymmetry within particle size segregationSegregation induced finger formation in granular free-surface flows

Latest News: Work at the MCND on the curling of ribbons has been featured in a BBC News article. For more details see Anne Juel's site or our paper in PNAS.

Features

A semi-infinite air finger propagates into an elastic-walled channel initially filled by a viscous fluid. The influence of gravity causes asymmetries in the channel wall shapes and in the thicknesses of the fluid films above and below the finger, leading to a monotonic relationship between the air pressure and finger speed.
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Numerical bifurcation tracking.

Contours of axial velocity for the flow past a cylindrical obstacle in a channel (top). A Hopf bifurcation occurs at Re ≈ 92, and the contours of the axial velocity for the critical eigenfunction (bottom) illustrate the complex downstream structure that must be resolved to accurately determine the location of the bifurcation.

Granular shocks in shallow free-surface flows

Granular avalanches exhibit discontinuous shocks and bores with complex interaction dynamics.

Pipe turbulence.

A turbulent puff in pipe at Re = 2200.

Viscous fingering under an elastic membrane.

Above a critical flow rate of air injection into a oil-filled elastic cell, the interface becomes unstable and an unusual fingering pattern develops.