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Violent relaxation in two-dimensional flows with varying interaction range.

A Venaille1, T Dauxois1, S Ruffo2

  • 1Laboratoire de Physique, École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d'Italie, F-69364 Lyon, cedex 07, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 15, 2015
PubMed
Summary
This summary is machine-generated.

Long-range interactions influence how systems reach equilibrium. Weak interactions promote relaxation to equilibrium, while strong interactions lead to dipolar structures in two-dimensional fluid flows.

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Area of Science:

  • Statistical Mechanics
  • Fluid Dynamics
  • Complex Systems

Background:

  • Understanding system relaxation towards equilibrium is a fundamental challenge in statistical mechanics.
  • The influence of interaction range on dynamic processes remains an active area of research.

Purpose of the Study:

  • To investigate the role of long-range interactions in the relaxation dynamics of two-dimensional fluid flows.
  • To determine how interaction strength affects the transition to equilibrium or other stable states.

Main Methods:

  • Analysis of two-dimensional fluid flows with interactions scaling as ~r^(α-2).
  • Examination of flow patterns resulting from varying the interaction parameter α.
  • Derivation of conditions for convergence to equilibrium versus dipolar states based on energy (E) and enstrophy (Z) injection scales.

Main Results:

  • For small α, a coarsening process forms sharp interfaces and homogenized vorticity.
  • For large α, filamentation leads to a stable dipolar structure.
  • Convergence to equilibrium is favored when (2π/L)(α)E/Z approaches one; convergence to a dipolar state occurs when this parameter approaches zero.

Conclusions:

  • The parameter (2π/L)(α)E/Z dictates whether a system relaxes to equilibrium or a dipolar state.
  • Weakly long-range interacting systems are more likely to reach equilibrium than strongly interacting systems.