• Chaotic advection in three-dimensional  flows. Recent work includes studies of eccentric Taylor vortex flow and studies of nonaxisymmetric flows in the concentric Taylor-Couette system (flow between rotating cylinders). For a description of some interesting applications see the home pages of Rich Lueptow and Murray Rudman and in particular see Murray's MPEG movie!  Also, we have obtained a new and exciting result on relating the effective diffusion coefficient to properties of the velocity field in the case of  wavy Taylor-vortex flow.  This work has now appeared and can be found in (at) Phys. Fluids 13 (2001) 2522 - 2528.

• Sub-critical transition to turbulence.  The explosive or subcritical onset of turbulence is an important unsolved problem in fluid dynamics.  By subcritical, we mean that a flow passes abruptly from a laminar or spatially ordered state to turbulence when the Reynolds number is increased past a critical value.  Turbulent bursts take the form of isolated spots or patches of turbulence that are randomly created in time and space.  In open flows, such as channel and pipe flows and boundary layer flows over flat plates, the turbulent bursts decay or advect out of the experimental apparatus.  In closed systems, such as Rayleigh-Benard convection or the flow between rotating cylinders (Taylor-Couette flow), the turbulent bursts are characterised by a decay time that becomes longer as a critical Reynolds number is approached, reminiscent of phase transition behaviour.  Furthermore, for certain parameter values the bursting takes the form of a repetitive laminar-turbulent burst cycle.


Turbulent bursts (of energy and mass) also occur in plasma confinement systems, such as the earth's magnetosphere, the solar corona,
accretion disks and, in the laboratory, tokamaks.

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