Professor of Physics
& Director of MCND
G4 (Schuster Lab)
Please replace "-at-" by "@" in the e-mail address
Bifurcation Phenomena in Viscous Fluid
Flows and Granular Media
My primary research interests are
in bifurcation phenomena in viscous fluid flows. Most of my work has been
concerned with instabilities in the flow between concentric cylinders,
commonly called Taylor-Couette flow. I find this a particularily interesting
problem as it is one of the very few fluid dynamical problems where one
can carry out quantitative comparison between the results of numerical
calculations of the Navier-Stokes equations on physical boundary conditions
and experimental observations.
The principle aim of my research
on Taylor-Couette flows has been to determine if the global dynamics are
organised by local bifurcations in the solution set. In particular, I am
interested in the effects of geometrical symmetries on both stable and
unstable solutions and the interaction between them. In using this approach,
I have uncovered some novel features including 'Silnikov dynamics' and
associated homoclinic chaos. The central idea is to search for universality
between apparently different mechanisms for generating chaos in this problem.
Currently, we are extending this approach to other fluid flows in both
simple and complex fluids.
Related fluid dynamical research
is concerned with bifurcations in flow through a suddenly expanding channel,
electrohydrodynamic instabilities in nematic liquid crystal flows and convection
in molten gallium. In the last two flows, Silnikov dynamics have been found
and in the liquid crystal problem small scale fluctuations provide significant
contributions to the macroscopic dynamics. My interests in low-dimensional
chaos is continuing with projects on non-Newtonian flows and chaos in a
closed flow with restricted symmetry.
Perhaps one of the most intriguing
problems in fluid mechanics is the transition to turbulence in a pipe.
Mathematically, the flow is linearly stable and yet it becomes turbulent
in practice at modest Reynolds numbers. Recent research with a colleague,
Alan Darbyshire, showed that there is a 'finite amplitude transition curve'
below which disturbances decay and above they can be amplified and grow
into turbulence. The size of the perturbation required to produce turbulence
diminishes as the Reynolds number increases but appears to remain finite
even at moderate values. This was somewhat of a surprise since previous
work suggested that the slightest disturbance is needed to promote turbulence
at high flow rates. One criticism of our work is that the pipe was not
long enough to establish fully developed conditions. We are currently planning
the construction of a very long pipe in Manchester. It is intriguing that
we should be studying the problem here since Osborne Reynolds did his work
in Engineering in Manchester approximately 100 years ago. Perhaps his spirits
I have always found playing with
'toy' problems helpful in making progress with difficult nonlinear fluid
dynamics problems. These include systems of pendulums, electronic oscillators
and impacting beams. The insight they can give into much more complicated
systems, most often by analogy, is invaluable. In any case, many of them
are interesting in their own right and only the foolhardy would dismiss
them as 'simple' problems. A good example of this is to be found in a set
of coupled electronic oscillators which have produced both novel steady
solutions and dynamical behaviour neither of which are present in the individual
My most recent research has been
on pattern formation in a box of particles which is oscillated from side-to-side.
These are of interest to me because, unlike a fluid, the macroscopic behaviour
depends on the details of the particle shape. This makes any theory of
such phenomena extremely difficult but it is not the job of experimentalists
to make life easy for theoreticians.