Vortex Flows and Related Numerical Methods II
ESAIM: Proceedings,
Vol. 1, 1996, pp. 255-265
Vortex Problems, Rotating Spiral Structures,
and the Hannay-Berry Phase
Paul K. Newton and Banavara Shashikanth
Department of Aerospace Engineering
University of Southern California
Los Angeles, CA 90089-1191, USA
Abstract
This paper describes the occurence of phase anholonomies in the
context of point vortex problems for two-dimensional incompressible flows.
After giving a brief description of anholonomic effects in other contexts,
we focus attention on the restricted three-vortex problem and a simpler
modified problem where the "Hannay-Berry" phase can be computed using
multi-scale asymptotic methods. Our main emphasis in this paper is to show
how the Hannay-Berry phase arises as the leading term in an asymptotic
expansion as the result of a non-uniform limit process. We show how it
arises when computing the long time growth rate of passive scalar
interfaces as they wrap around vortex cores in the presence of a slowly
varying background field due to other vortices, and discuss the results in
the context of "spiral-vortex" models for 2D turbulence.
Vortex Flows and Related
Numerical Methods II
Contents / Table des matières
Index by Author / Index par auteur