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Statistics of Point Vortex Turbulence in Non-neutral Flows and in Flows with Translational and Rotational Symmetries

Esler, JG; (2017) Statistics of Point Vortex Turbulence in Non-neutral Flows and in Flows with Translational and Rotational Symmetries. Journal of Statistical Physics , 169 (6) pp. 1045-1065. 10.1007/s10955-017-1903-y. Green open access

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Abstract

A theory (Esler and Ashbee in J Fluid Mech 779:275–308, 2015) describing the statistics of N freely-evolving point vortices in a bounded two-dimensional domain is extended. First, the case of a non-neutral vortex gas is addressed, and it is shown that the density of states function can be identified with the probability density function of an infinite sum of independent non-central chi-squared random variables, the details of which depend only on the shape of the domain. Equations for the equilibrium energy spectrum and other statistical quantities follow, the validity of which are verified against direct numerical simulations of the equations of motion. Second, domains with additional conserved quantities associated with a symmetry (e.g., circle, periodic channel) are investigated, and it is shown that the treatment of the non-neutral case can be modified to account for the additional constraint.

Type: Article
Title: Statistics of Point Vortex Turbulence in Non-neutral Flows and in Flows with Translational and Rotational Symmetries
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10955-017-1903-y
Publisher version: https://doi.org/10.1007/s10955-017-1903-y
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Point vortices, Energy spectrum, Statistical mechanics
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10025921
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