Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 29
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bedrossian, Jacob Masmoudi, Nader and Vicol, Vlad 2016. Enhanced Dissipation and Inviscid Damping in the Inviscid Limit of the Navier–Stokes Equations Near the Two Dimensional Couette Flow. Archive for Rational Mechanics and Analysis, Vol. 219, Issue. 3, p. 1087.

    Bedrossian, Jacob and Masmoudi, Nader 2015. Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations. Publications mathématiques de l'IHÉS, Vol. 122, Issue. 1, p. 195.

    Caillol, P. 2014. A steady nonlinear and singular vortex Rossby wave within a rapidly rotating vortex. Part I: Theory. Geophysical & Astrophysical Fluid Dynamics, Vol. 108, Issue. 4, p. 387.

    Roy, Anubhab and Subramanian, Ganesh 2014. Linearized oscillations of a vortex column: the singular eigenfunctions. Journal of Fluid Mechanics, Vol. 741, p. 404.

    Turner, M. R. 2014. Temporal evolution of vorticity staircases in randomly strained two-dimensional vortices. Physics of Fluids, Vol. 26, Issue. 11, p. 116603.

    Bedrossian, J. and Masmoudi, N. 2013. Asymptotic Stability for the Couette Flow in the 2D Euler Equations. Applied Mathematics Research eXpress,

    Bouchet, Freddy and Morita, Hidetoshi 2010. Large time behavior and asymptotic stability of the 2D Euler and linearized Euler equations. Physica D: Nonlinear Phenomena, Vol. 239, Issue. 12, p. 948.

    Kivotides, Demosthenes and Wilkin, S. Louise 2009. Elementary Vortex Processes in Thermal Superfluid Turbulence. Journal of Low Temperature Physics, Vol. 156, Issue. 3-6, p. 163.

    TURNER, MATTHEW R. BASSOM, ANDREW P. and GILBERT, ANDREW D. 2009. Diffusion and the formation of vorticity staircases in randomly strained two-dimensional vortices. Journal of Fluid Mechanics, Vol. 638, p. 49.

    TURNER, M. R. and GILBERT, A. D. 2009. Spreading of two-dimensional axisymmetric vortices exposed to a rotating strain field. Journal of Fluid Mechanics, Vol. 630, p. 155.

    Schecter, David A. 2008. The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number. Journal of the Atmospheric Sciences, Vol. 65, Issue. 8, p. 2498.

    Schecter, David A. Nicholls, Melville E. Persing, John Bedard, Alfred J. and Pielke, Roger A. 2008. Infrasound Emitted by Tornado-Like Vortices: Basic Theory and a Numerical Comparison to the Acoustic Radiation of a Single-Cell Thunderstorm. Journal of the Atmospheric Sciences, Vol. 65, Issue. 3, p. 685.

    Turner, M. R. Gilbert, Andrew D. and Bassom, Andrew P. 2008. Neutral modes of a two-dimensional vortex and their link to persistent cat’s eyes. Physics of Fluids, Vol. 20, Issue. 2, p. 027101.

    Volponi, Francesco and Okolicsanyi, Marco 2008. Landau pole induced vorticity growth in a class of non-monotonic shear flows. Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue. 14, p. 145501.

    Barba, L. A. and Leonard, A. 2007. Emergence and evolution of tripole vortices from net-circulation initial conditions. Physics of Fluids, Vol. 19, Issue. 1, p. 017101.

    Martinand, D. and Vassilicos, J. C. 2007. Fast chemical reaction and multiple-scale concentration fields in singular vortices. Physical Review E, Vol. 75, Issue. 3,

    Schecter, David A. and Montgomery, Michael T. 2007. Waves in a Cloudy Vortex. Journal of the Atmospheric Sciences, Vol. 64, Issue. 2, p. 314.

    Reasor, Paul D. Montgomery, Michael T. and Grasso, Lewis D. 2004. A New Look at the Problem of Tropical Cyclones in Vertical Shear Flow: Vortex Resiliency. Journal of the Atmospheric Sciences, Vol. 61, Issue. 1, p. 3.

    Schecter, David A. and Montgomery, Michael T. 2004. Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia–buoyancy wave emission. Physics of Fluids, Vol. 16, Issue. 5, p. 1334.

    Hall, Ian M. Bassom, Andrew P. and Gilbert, Andrew D. 2003. The effect of fine structure on the stability of planar vortices. European Journal of Mechanics - B/Fluids, Vol. 22, Issue. 2, p. 179.

  • Journal of Fluid Mechanics, Volume 371
  • September 1998, pp. 109-140

The spiral wind-up of vorticity in an inviscid planar vortex

  • DOI:
  • Published online: 01 September 1998

The relaxation of a smooth two-dimensional vortex to axisymmetry, also known as ‘axisymmetrization’, is studied asymptotically and numerically. The vortex is perturbed at t=0 and differential rotation leads to the wind-up of vorticity fluctuations to form a spiral. It is shown that for infinite Reynolds number and in the linear approximation, the vorticity distribution tends to axisymmetry in a weak or coarse-grained sense: when the vorticity field is integrated against a smooth test function the result decays asymptotically as t−λ with λ=1+(n2+8)1/2, where n is the azimuthal wavenumber of the perturbation and n[ges ]1. The far-field stream function of the perturbation decays with the same exponent. To obtain these results the paper develops a complete asymptotic picture of the linear evolution of vorticity fluctuations for large times t, which is based on that of Lundgren (1982).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *