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Issue ESAIM: Proc.
Volume 1, 1996
Vortex flows an related numerical methods II
Page(s) 255 - 265
DOI http://dx.doi.org/10.1051/proc:1996022

ESAIM: Proc., 1996, Vol. 1, pp. 255-265
DOI: 10.1051/proc:1996022

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.



© EDP Sciences, ESAIM 1996

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