Tubes, Sheets and Singularities in Fluid Dynamics Tubes, K. BAJER

Tubes, Sheets and Singularities

in Fluid Dynamics

Edited by

K. BAJER

Vortex tubes and vortex sheets can be thought of as the fundamental building blocks of fluid flow at high Reynolds number, whether laminar or turbulent. It is therefore important to understand their structure, stability and evolution, and the various non-linear interactions that can occur among them. Similar problems in relation to magnetic flux tubes arise in magnetohydrodynamics (MHD) at high magnetic Reynolds numbers; and the analogies between MHD and vortex dynamics can be exploited
in the development of insight in both fields.
The dynamics of vortex tubes, sheets and more complex structures plays a central rôle in the description of turbulent shear flows, whose ‘coherent structures’ can be most naturally interpreted as vortical structures subject to both self-induced evolution and the complex interactions with a random environment and with boundaries.
The interaction of skewed vortex tubes is a problem of acute current interest, because the intense stretching associated with the mutual interaction when such tubes are close to each other leads to rapid growth of vorticity. Whether this growth is or is not bounded within any finite time-interval is one of the famous open problems of fluid dynamics, and is the subject of much current analytical and numerical work.
The papers collected in this volume range over the above topics, and constitute the Proceedings of a NATO ARW and IUTAM Symposium held in Zakopane, Poland, 2-7 September 2001. They are grouped in six parts as follows:
part 1 :Vortex structure, stability and evolution
part 2 :Singular vortex filaments
part 3 :Magnetic structure, topology and reconnection
part 4 :Vortex structures in turbulent flow
part 5 : Finite-time singularity problems
part 6 : Stokes flow and singular behaviour near boundaries

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