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Percolation transition in the kinematics of nonlinear resonance broadening in Charney–Hasegawa–Mima model of Rossby wave turbulence
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Harris, Jamie, Connaughton, Colm and Bustamante, Miguel D. (2013) Percolation transition in the kinematics of nonlinear resonance broadening in Charney–Hasegawa–Mima model of Rossby wave turbulence. New Journal of Physics, Volume 15 (Number 8). Article number 083011. doi:10.1088/1367-2630/15/8/083011 ISSN 1367-2630.
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Official URL: http://dx.doi.org/10.1088/1367-2630/15/8/083011
Abstract
We study the kinematics of nonlinear resonance broadening of interacting Rossby waves as modelled by the Charney-Hasegawa-Mima equation on a biperiodic domain. We focus on the set of wave modes which can interact quasi-resonantly at a particular level of resonance broadening and aim to characterize how the structure of this set changes as the level of resonance broadening is varied. The commonly held view that resonance broadening can be thought of as a thickening of the resonant manifold is misleading. We show that in fact the set of modes corresponding to a single quasi-resonant triad has a non-trivial structure and that its area in fact diverges for a finite degree of broadening. We also study the connectivity of the network of modes which is generated when quasi-resonant triads share common modes. This network has been argued to form the backbone for energy transfer in Rossby wave turbulence. We show that this network undergoes a percolation transition when the level of resonance broadening exceeds a critical value. Below this critical value, the largest connected component of the quasi-resonant network contains a negligible fraction of the total number of modes in the system whereas above this critical value a finite fraction of the total number of modes in the system are contained in the largest connected component. We argue that this percolation transition should correspond to the transition to turbulence in the system.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QC Physics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Rossby waves, Percolation (Statistical physics) | ||||||
Journal or Publication Title: | New Journal of Physics | ||||||
Publisher: | IOP Publishing | ||||||
ISSN: | 1367-2630 | ||||||
Official Date: | 6 August 2013 | ||||||
Dates: |
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Volume: | Volume 15 | ||||||
Number: | Number 8 | ||||||
Article Number: | Article number 083011 | ||||||
DOI: | 10.1088/1367-2630/15/8/083011 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 26 December 2015 | ||||||
Date of first compliant Open Access: | 26 December 2015 | ||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), University of Toronto. Fields Institute, University College, Dublin (UCD) | ||||||
Grant number: | EP/H051295/1 (EPSRC), SF564 (UCD), SF652 (UCD) |
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