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

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 identifie...

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Bibliographic Details
Published inJournal of statistical physics Vol. 169; no. 6; pp. 1045 - 1065
Main Author Esler, J. G.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2017
Springer
Springer Nature B.V
Subjects
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computational fluid dynamics
Computer simulation
COMPUTERIZED SIMULATION
DENSITY OF STATES
ENERGY SPECTRA
EQUATIONS OF MOTION
Fluid flow
FLUIDS
Independent variables
LIMITING VALUES
Mathematical and Computational Physics
Numerical analysis
PERIODICITY
Physical Chemistry
Physics
Physics and Astronomy
PROBABILITY DENSITY FUNCTIONS
Probability distributions
Quantum Physics
Random variables
Statistical analysis
STATISTICAL MECHANICS
Statistical Physics and Dynamical Systems
Statistical tests
STATISTICS
SYMMETRY
Theoretical
TURBULENCE
Turbulence (Fluid dynamics)
TWO-DIMENSIONAL SYSTEMS
Energy spectrum
Statistical mechanics
Point vortices
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Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-017-1903-y