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The role of circulation in the collapse of ideal fluids

Monday, February 22, 2010 - 10:00am - 10:45am
EE/CS 3-180
Robert Kerr (University of Warwick)
Keywords: Euler equations, quantum fluids

Abstract: Circulation is an often neglected conservation law in
developing
the mathematics of ideal fluids, meaning the classical 3D
Euler
equations and the quantum defocussing Gross-Pitaevskii
equations.

Recent Euler calculations demonstrated that the numerics
must conserve
circulation and when this is satisfied, it appears that
circulation
controls the growth of enstrophy in a manner consistent
with a
finite-time singularity of these equations.

In a quantum fluid the circulation, that is defects in
phase,
is inherently conserved. These equations allow
reconnection without
dissipation and without singularities.
Nonetheless, when compared with Navier-Stokes reconnection
there are
strong similarities, at least for a new Navier-Stokes
initial
condition which considers the role of circulation more
carefully.

Following reconnection in GP, waves form on vortex lines,
vortex
rings detach, and an inertial subrange develops, all in a
manner that
could explain experimental observations of the decay of
vortex line
length, a proxy for kinetic energy, despite the absence of
viscosity.
MSC Code: 
35Q31
Keywords: