Stability of the Stuart Vortices in a Rotating Frame

  • S. Leblanc
  • C. Cambon
Conference paper
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 36)


Linear stability of the two-dimensional Stuart array of co-rotating vortices is investigated in a rotating frame. The effect of the Coriolis force, that acts only on three-dimensional perturbations, is in partial agreement with the Bradshaw-Richardson criterion, that is to say that cyclonic or strong anticyclonic rotation is stabilizing by cut-off of the spanwise wave number, whereas weak anticyclonic rotation enhances non-rotating growth rate of both fundamental and subharmonic modes. The results are compared to simpler model problems, i.e. parallel flow and elliptic vortex in a rotating frame.


Basic Flow Coriolis Force Temporal Growth Rate Floquet Mode Subharmonic Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bayly, B.J., Orszag, S.A. and Herbert, T. (1988) Instability mechanisms in shear-flow transition, Ann. Rev. Fluid Mech. 20, 359–391.ADSCrossRefGoogle Scholar
  2. 2.
    Cambon, C., Benoît, J.-P., Shao, L. and Jacquin, L. (1994) Stability analysis and large eddy simulation of rotating turbulence with organized eddies, J. Fluid Mech.. 278, 175–200.MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    Craik, A.D.D. (1989) The stability of unbounded two- and three-dimensional flows subject to body forces: some exact solutions, J. Fluid Mech. 198, 275–292MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    Herbert, T. (1988) Secondary instability of boundary layers. Ann. Rev. Fluid Mech. 20, 359–391ADSCrossRefGoogle Scholar
  5. 5.
    Kloosterziel, R.C. and van Heijst, G.J.F. (1991) An experimental study of unstable barotropic vortices in a rotating fluid, J. Fluid Mech. 239, 607–629ADSCrossRefGoogle Scholar
  6. 6.
    Pedley, T.J. (1969) On the stability of viscous flow in a rapidly rotating pipe, J. Fluid Mech. 35, 97–115.ADSzbMATHCrossRefGoogle Scholar
  7. 7.
    Pierrehumbert, R.T. and Widnall, S.E. (1982) The two- and three-dimensional instabilities of a spatially periodic shear layer, J. Fluid Mech. 114, 59–82.ADSzbMATHCrossRefGoogle Scholar
  8. 8.
    Stuart, J.T. (1967) On finite amplitude oscillations in laminar mixing layers, J. Fluid Mech. 29, 417–440.ADSzbMATHCrossRefGoogle Scholar
  9. 9.
    Tritton, S.C. and Davies, P.A. (1981) In Hydrodynamic Instabilities and the Transition to Turbulence, ed.H. L. Swinney & J. P. Gollub, pp. 229–270. Berlin: Springer-VerlagGoogle Scholar
  10. 10.
    Yanase, S., Flores, C., Metáis, O. and Riley, J.J. (1993) Rotating free-shear flows. I. Linear stability analysis. Phys. Fluids A. 5 (11), 2725–2737ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • S. Leblanc
    • 1
  • C. Cambon
    • 1
  1. 1.LMFAEcole Centrale de LyonEcully CedexFrance

Personalised recommendations