Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 39
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ghadimi, Masoud Farshchi, Mohammad and Hejranfar, Kazem 2016. On spatial filtering of flow variables in high-order finite volume methods. Computers & Fluids, Vol. 132, p. 19.

    Merrill, Brandon E. Peet, Yulia T. Fischer, Paul F. and Lottes, James W. 2016. A spectrally accurate method for overlapping grid solution of incompressible Navier–Stokes equations. Journal of Computational Physics, Vol. 307, p. 60.

    Kaviani, Ramin and Nikkhah-Bahrami, Mansour 2015. Improved Navier–Stokes Boundary Conditions Based on Generalized Characteristics. Journal of Computational Acoustics, Vol. 23, Issue. 02, p. 1550006.

    Wang, Gaofeng Duchaine, Florent Papadogiannis, Dimitrios Duran, Ignacio Moreau, Stéphane and Gicquel, Laurent Y.M. 2014. An overset grid method for large eddy simulation of turbomachinery stages. Journal of Computational Physics, Vol. 274, p. 333.

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

    Steinitz, Uri Prior, Yehiam and Averbukh, Ilya Sh. 2012. Laser-Induced Gas Vortices. Physical Review Letters, Vol. 109, Issue. 3,

    Albin, Eric D’Angelo, Yves and Vervisch, Luc 2011. Flow streamline based Navier–Stokes Characteristic Boundary Conditions: Modeling for transverse and corner outflows. Computers & Fluids, Vol. 51, Issue. 1, p. 115.


    Guézennec, Nicolas and Poinsot, Thierry 2009. Acoustically Nonreflecting and Reflecting Boundary Conditions for Vortcity Injection in Compressible Solvers. AIAA Journal, Vol. 47, Issue. 7, p. 1709.

    Lodato, Guido Domingo, Pascale and Vervisch, Luc 2008. Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows. Journal of Computational Physics, Vol. 227, Issue. 10, p. 5105.

    Aboelkassem, Yasser and Vatistas, Georgios H. 2007. New Model for Compressible Vortices. Journal of Fluids Engineering, Vol. 129, Issue. 8, p. 1073.

    KAM, E. W. S. LEUNG, R. C. K. SO, R. M. C. and LI, X. M. 2007. A LATTICE BOLTZMANN METHOD FOR COMPUTATION OF AEROACOUSTIC INTERACTION. International Journal of Modern Physics C, Vol. 18, Issue. 04, p. 463.

    Kontis, Konstantinos An, Ran and Edwards, John A. 2006. Compressible Vortex-Ring Interaction Studies with a Number of Generic Body Configurations. AIAA Journal, Vol. 44, Issue. 12, p. 2962.

    Leung, Randolph C. K. So, Ronald M. C. Kam, Elizabeth W. S. and Li, X. M. 2006. 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference).

    Vatistas, Georgios H. and Aboelkassem, Yasser 2006. Extension of the Incompressible n = 2 Vortex into Compressible. AIAA Journal, Vol. 44, Issue. 8, p. 1912.

    Hagstrom, Thomas Goodrich, John Nazarov, Igor and Dodson, Chris 2005. 11th AIAA/CEAS Aeroacoustics Conference.

    Iourokina, Ioulia and Lele, Sanjiva 2005. 43rd AIAA Aerospace Sciences Meeting and Exhibit.

    Prosser, R. 2005. Improved boundary conditions for the direct numerical simulation of turbulent subsonic flows. I. Inviscid flows. Journal of Computational Physics, Vol. 207, Issue. 2, p. 736.

    Jacobs, G. B. Kopriva, D. A. and Mashayek, F. 2004. Compressible Subsonic Particle-Laden Flow over a Square Cylinder. Journal of Propulsion and Power, Vol. 20, Issue. 2, p. 353.

    Men'shov, Igor and Nakamura, Yoshiaki 2003. 33rd AIAA Fluid Dynamics Conference and Exhibit.

  • Journal of Fluid Mechanics, Volume 230
  • September 1991, pp. 45-73

The free compressible viscous vortex

  • Tim Colonius (a1), Sanjiva K. Lele (a1) and Parviz Moin (a1)
  • DOI:
  • Published online: 01 April 2006

The effects of compressibility on free (unsteady) viscous heat-conducting vortices are investigated. Analytical solutions are found in the limit of large, but finite, Reynolds number, and small, but finite, Mach number. The analysis shows that the spreading of the vortex causes a radial flow. This flow is given by the solution of an ordinary differential equation (valid for any Mach number), which gives the dependence of the radial velocity on the tangential velocity, density, and temperature profiles of the vortex; estimates of the radial velocity found by solving this equation are found to be in good agreement with numerical solutions of the full equations. The experiments of Mandella (1987) also report a radial flow in the vortex, but their estimates are much larger than the analytical predictions, and it is found that the flow inferred from the iexperiments violates the Second Law of Thermodynamics for two-dimensional axisymmetric flow. It is speculated that three-dimensionality is the cause of this discrepancy. To obtain detailed analytical solutions, the equations for the viscous evolution are expanded in powers of Mach number, M. Solutions valid to O(M2), are discussed for vortices with finite circulation. Two specific initial conditions – vortices with initially uniform entropy and with initially uniform density – are analysed in detail. It is shown that swirling axisymmetric compressible flows generate negative radial velocities far from the vortex core owing to viscous effects, regardless of the initial distributions of vorticity, density and entropy.

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? *