Statistical mechanics and correlation properties of a rotating two-dimensional flow of like-sign vortices

Journal Article · Fri Oct 01 00:00:00 EDT 1993 · Physics of Fluids A; (United States)

DOI:https://doi.org/10.1063/1.858762· OSTI ID:6217659

Viecelli, J A ^[1]

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1. Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)

The Hamiltonian flow of a set of point vortices of like sign and strength has a low-temperature phase consisting of a rotating triangular lattice of vortices, and a normal temperature turbulent phase consisting of random clusters of vorticity that orbit about a common center along random tracks. The mean-field flow in the normal temperature phase has similarities with turbulent quasi-two-dimensional rotating laboratory and geophysical flows, whereas the low-temperature phase displays effects associated with quantum fluids. In the normal temperature phase the vortices follow power-law clustering distributions, while in the time domain random interval modulation of the vortex orbit radii fluctuations produces singular fractional exponent power-law low-frequency spectra corresponding to time autocorrelation functions with fractional exponent power-law tails. Enhanced diffusion is present in the turbulent state, whereas in the solid-body rotation state vortices thermally diffuse across the lattice. Over the entire temperature range the interaction energy of a single vortex in the field of the rest of the vortices follows positive temperature Fermi--Dirac statistics, with the zero temperature limit corresponding to the rotating crystal phase, and the infinite temperature limit corresponding to a Maxwellian distribution. Analyses of weather records dependent on the large-scale quasi-two-dimensional atmospheric circulation suggest the presence of singular fractional exponent power-law spectra and fractional exponent power-law autocorrelation tails, consistent with the theory.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6217659
• Journal Information: Physics of Fluids A; (United States), Vol. 5:10; ISSN 0899-8213
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
VORTICES
CORRELATION FUNCTIONS
STATISTICAL MECHANICS
ATMOSPHERIC CIRCULATION
DISTRIBUTION FUNCTIONS
FERMI STATISTICS
QUANTUM FLUIDS
TEMPERATURE DEPENDENCE
TURBULENT FLOW
FLUID FLOW
FLUIDS
FUNCTIONS
MECHANICS
661300* - Other Aspects of Physical Science- (1992-)