Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 16
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Hiejima, Toshihiko 2014. Criterion for vortex breakdown on shock wave and streamwise vortex interactions. Physical Review E, Vol. 89, Issue. 5,

    Kozubskaya, Tatiana Kopiev, Victor and Menshov, Igor 2014. Tearing instability of isolated compressible vortices. International Journal of Aeroacoustics, Vol. 13, Issue. 1-2, p. 113.

    Hiejima, Toshihiko 2013. Linear stability analysis on supersonic streamwise vortices. Physics of Fluids, Vol. 25, Issue. 11, p. 114103.

    Tang, HongZhe 2011. Particle size polydispersity of the rheological properties in magnetorheological fluids. Science China Physics, Mechanics and Astronomy, Vol. 54, Issue. 7, p. 1258.

    Mitchell, T. B. and Rossi, L. F. 2008. The evolution of Kirchhoff elliptic vortices. Physics of Fluids, Vol. 20, Issue. 5, p. 054103.

    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.

    Schecter, David A. and Montgomery, Michael T. 2006. Conditions That Inhibit the Spontaneous Radiation of Spiral Inertia–Gravity Waves from an Intense Mesoscale Cyclone. Journal of the Atmospheric Sciences, Vol. 63, Issue. 2, p. 435.

    Men’shov, Igor and Nakamura, Yoshiaki 2005. Instability of isolated compressible entropy-stratified vortices. Physics of Fluids, Vol. 17, Issue. 3, p. 034102.

    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.

    Men'shov, Igor and Nakamura, Yoshiaki 2002. 3rd Theoretical Fluid Mechanics Meeting.

    MEN'SHOV, Igor and NAKAMURA, Yoshiaki 2002. Advanced Fluid Information. On Instability of Acoustic Waves Propagating in Stratified Vortical Flows.. JSME International Journal Series B, Vol. 45, Issue. 1, p. 79.

    Leblanc, Stéphane 2001. Acoustic excitation of vortex instabilities. Physics of Fluids, Vol. 13, Issue. 11, p. 3496.

    Lou, Yu‐Qing Yuan, Chi and Fan, Zuhui 2001. Spiral Magnetohydrodynamic Density Waves with a Tangential Shear Force. The Astrophysical Journal, Vol. 552, Issue. 1, p. 189.

    Ford, Rupert 1994. The response of a rotating ellipse of uniform potential vorticity to gravity wave radiation. Physics of Fluids, Vol. 6, Issue. 11, p. 3694.

    Polvani, L. M. McWilliams, J. C. Spall, M. A. and Ford, R. 1994. The coherent structures of shallow-water turbulence: Deformation-radius effects, cyclone/anticyclone asymmetry and gravity-wave generation. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 4, Issue. 2, p. 177.

  • Journal of Fluid Mechanics, Volume 253
  • August 1993, pp. 173-209

Instabilities of two-dimensional inviscid compressible vortices

  • W. M. Chan (a1) (a2), K. Shariff (a3) and T. H. Pulliam (a3)
  • DOI:
  • Published online: 01 April 2006

The linear stability and subsequent nonlinear evolution and acoustic radiation of a planar inviscid compressible vortex is examined. Linear-stability analysis shows that vortices with smoother vorticity profiles than the Rankine vortex considered by Broadbent & Moore (1979) are also unstable. However, only neutrally stable waves are found for a Gaussian vorticity profile. The effects of entropy gradient are investigated and for the particular entropy profile chosen, positive average entropy gradient in the vortex core is destabilizing while the opposite is true for negative average entropy gradient.

The linear initial-value problem is studied by finite-difference methods. It is found that these methods are capable of accurately computing the frequencies and weak growth rates of the normal modes. When the initial condition consists of random perturbations, the long-time behaviour is found to correspond to the most unstable normal mode in all cases. In particular, the Gaussian vortex has no algebraically growing modes. This procedure also reveals the existence of weakly decaying and neutrally stable waves rotating in the direction opposite to the vortex core, which were not observed previously.

The nonlinear development of an elliptic-mode perturbation is studied by numerical solution of the Euler equations. The vortex elongates and forms shocklets; eventually, the core splits into two corotating vortices. The individual vortices then gradually move away from each other while their rate of rotation about their mid-point slowly decreases. The acoustic flux reaches a maximum at the time of fission and decreases as the vortices move apart.

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? *