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Warwick Turbulence
Symposium Workshop: Singularities, coherent structures and their role in intermittent turbulence September 9-17, 2005. |
The
challenge to prove the existence (or non-existence) of global solutions
of the
Navier Stokes equations has recently experienced a renewed surge of
attention.
It is one of the Clay
Institute Millennium problems. It is believed that,
should solutions develop finite-time singularities, these solutions may
be
responsible for turbulence intermittency and that they play an
important role
in turbulent energy dissipation mechanisms. There are also other types
of
coherent structures that contribute to these processes in which
vorticity is
amplified via stretching without resulting in a finite-time blow-up.
Examples
are "vortex worms" that have Burgers vortices
as simple prototypes,
"horseshoes", "streaks" and "injections" in
turbulent boundary layers, etc. In magnetic fluids, turbulent
dissipation may
be dominated by electric current filaments and sheets. In Bose-Einstein
condensates
in gases with attractive potentials (e.g. lithium), the active players
are
finite-time collapses which have analytical
prototypes among the solutions of
the Nonlinear Schrödinger equation. This workshop will review the
current state
of the study of the Euler and Navier-Stokes singularities, other
coherent
events and structures, and their role in turbulence intermittency and
energy
dissipation. We will include a review of coherent structures and
patterns that
appear in convection problems, in the turbulent pattern formation and
in
magnetic and quantum turbulence. We will aim at finding the unifying
concepts
and common methods of study for all these applications and we will
encourage a
mutually beneficial interaction of the mathematicians involved in
obtaining
rigorous results and scientists studying the effects of these solutions
using
simplifying models, experiments and numerical analysis.