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Related Experiment Videos

Stable elliptical vortices in a circular disk.

P Chen1

  • 1Department of Physics and Center for Complex Systems, National Central University, Chungli 320, Taiwan. peilong@toast.phy.ncu.edu.tw

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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See all related articles

Large elliptical vortices in two-dimensional (2D) ideal fluids are stable. This finding, confirmed by simulations, extends to plasma physics and clarifies previous stability analyses.

Area of Science:

  • Fluid dynamics
  • Plasma physics
  • Vortex dynamics

Background:

  • Elliptical vortices in 2D ideal fluids and quasi-2D non-neutral plasmas are common.
  • Previous studies suggested potential instabilities in these systems.

Purpose of the Study:

  • To determine the stability of large elliptical vortices in a finite disk.
  • To provide a clear condition for vortex stability without complex eigenanalysis.
  • To reconcile differing results from previous theoretical and numerical investigations.

Main Methods:

  • Energy comparison between elliptical and symmetrical vortex states.
  • Analytical expansion for small ellipticity and exact numerical calculations for uniform vortices.
  • Approximating calculations for general smooth vortices.

Related Experiment Videos

  • Numerical simulations of the 2D Euler equation.

    • Main Results:

    • A sufficient condition for the stability of large elliptical vortices was established.
    • Analytical and numerical results confirm the stability for uniform vortices across various ellipticities.
    • Numerical simulations validated the stability condition and indicated stability persists to smaller vortex sizes.
    • The study explains discrepancies with prior eigenanalysis results regarding decaying modes.

    Conclusions:

    • Large elliptical vortices in 2D ideal fluids and related plasma systems are stable.
    • The energy comparison method provides a reliable criterion for assessing vortex stability.
    • This work clarifies the conditions under which elliptical vortices remain stable, resolving previous ambiguities.