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  Warwick Turbulence Symposium

Workshop: Singularities, coherent structures and their role in intermittent turbulence    September 9-17, 2005.
maths building


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.


Timetable

List of participants

Copies of presentations contributed by participants. Due to potential copyright issues, these materials submitted on a completely voluntary basis.