Vortex stability and inertial-range cascades

  • Stephen Childress
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 230)


We consider the inviscid stability and evolution of columnar vortices whose cores consist of a disc of constant vorticity ω1 surrounded by an annular coat of constant vorticity ω2. For core parameters in the range suggested by vortex-tube geometries of the inertial-range eddy structure, we find the breakup of unstable cores is largely two-dimensional, particularly if the vortex is being stretched. Tentative studies of the breakup of the core, using vortex methods, are described.


Vortex Tube Inertial Range Vortex Method Inviscid Limit Daughter Tube 


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  1. 1.
    Burgers, J.M., Adv. in Appl. Mech. Vol. 1, 171–99, 1948.Google Scholar
  2. 2.
    Corrsin, S., Phys. Fluids 5, 1301–2, 1962.Google Scholar
  3. 3.
    Tennekes, H., Phys. Fluids 11, 669–71, 1968.Google Scholar
  4. 4.
    Saffman, P.G., Lecture on Homogeneous Turbulence, in Topics in Nonlinear Physics, N. J. Zabusky, ed., Springer-Verlag, 485–614, 1968.Google Scholar
  5. 5.
    Synge, J.L. and Lin, C.C., Trans. Roy. Soc. Canada Sec. 3, 45–79, 1943.Google Scholar
  6. 6.
    Townsend, A.A., Proc. Roy. Soc. Lond. A, 208, 534–540, 1951.Google Scholar
  7. 7.
    Lundgren, T.S., Phys. Fluids 25, 2193–2203, 1982.Google Scholar
  8. 8.
    Frisch, U., Sulem, P.-L., and Nelkin, M., J. Fluid Mech. 87, 719–736, 1978.Google Scholar
  9. 9.
    Childress, S., Geophys. Astrophys. Fluid Dynamics 29, 29–64, 1984.Google Scholar
  10. 10.
    Kelvin, Lord, Phil. Mag. 5, 155–68, 1880.Google Scholar
  11. 11.
    Howard, L.N. and Gupta, A.S., J. Fluid Mech. 14, 463–476, 1962.Google Scholar
  12. 12.
    Leibovich, S. and Stewartson, K., J. Fluid Mech. 126, 335–356, 1983.Google Scholar
  13. 13.
    Drazin, P.G. and Reid, W.H., Hydrodynamic Stability, Cambridge University Press, 1981.Google Scholar
  14. 14.
    Ben-Jacob, E., Nigel Goldenfeld, J.S. Langer, and Gerd Schön, Phys. Rev. Lett. 51, 1930–32, 1983.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Stephen Childress
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew York

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