Geodesic
Vortex problems, rotating spiral structures, and the Hannay-Berry phase
Paul K. Newton1 ; Banavara Shashikanth1
1 Department of Aerospace Engineering University of Southern California Los Angeles, CA 90089-1191, USA
ESAIM. Proceedings, Tome 1 (1996), pp. 255-265.

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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.
DOI : 10.1051/proc:1996022

Paul K. Newton 1 ; Banavara Shashikanth 1

1 Department of Aerospace Engineering University of Southern California Los Angeles, CA 90089-1191, USA 
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Paul K. Newton; Banavara Shashikanth. Vortex problems, rotating spiral structures, and the Hannay-Berry phase. ESAIM. Proceedings, Tome 1 (1996), pp. 255-265. doi : 10.1051/proc:1996022. http://geodesic.mathdoc.fr/articles/10.1051/proc:1996022/

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