Matter in motion: fluid dynamics from micrometres to megametres

18th February 2011,

with thanks to all those who have put fascinating videos and images on the web...

Research interests: fluid flow, mixing, stability and instability, magnetic fields

Introduction: what do the following have in common?

My research .... as a theoretician ...

a typical figure... (with Walter Pauls (Bielefeld))

Applied Mathematics Paradigm:

Strip problem down to essential aspects.

Study highly simplified models: analytical methods and simulations

Don't simulate the `full' problem

But aim to feed your understanding back in.

Starting point: what is the simplest interesting mathematical model to be understood?

Jack of all trades...?

or Mathematics as the Queen of Sciences...?

Swimming on small scales: how to move through viscous fluid

• swimming nematodes
• swimming in corn syrup I
• swimming in corn syrup II
• swimming in corn syrup III
• swimmer (3mm, on air-glycerine interface, Re = 10^-5)
• pinned swimmer

  Collaboration on theory and applications with Feodor Ogrin, Peter Petrov, Peter Winlove (Physics).

Motion on every day scales, vortex shedding

• bat flying in smoke
• von Karman vortex street
• two synchronised von Karman vortex streets

Von Karman vortex street visible in clouds.

Wing-tip vortices and instability

• wing-tip vortex
• Crow instability
• Delta wing vortex

Vortex reconnection: a million dollar problem

• simulations of vortex reconnection
• Clay Foundation Millenium Prizes

Collaboration with Walter Pauls (Bielefeld, Germany).

Geophysical vortices

• Gulf stream rings
• Hurricane Ike from space
• Hurricane Luis eye from space
• Polar vortex
• Polar vortex splitting
• In the laboratory

Matthew Turner

Stability properties of vortices, mixing, robustness: collaboration with Andrew Basssom (Perth), John Thuburn, Matthew Turner (Surrey).

Astrophysical vortices

Jupiter
• Flows on Jupiter
• Jupiter's great red spot
• Saturn's hexagonal vortex
• Laboratory version from Oxford

Collaboration on banded structures in fluid flows with Andrew Bassom (Perth), Matthew Turner (Surrey).

Banded structures emerging in simulations by Turner, Bassom and Gilbert.

• Generating smoke rings

Andrew D. Gilbert,
Mathematics Research Institute,
University of Exeter,
Harrison Building,
North Park Road,
Exeter,
EX4 4QF, U.K.

e-mail : A.D. Gilbert at ex . ac . uk
Tel. : +44-1392-269222
Fax. : +44-1392-264067