Skip to main content
Log in

On sufficient conditions for stability in the circular Rayleigh problem of hydrodynamic stability

  • Original Research Paper
  • Published:
The Journal of Analysis Aims and scope Submit manuscript

Abstract

Two sufficient conditions for stability are presented for the circular Rayleigh problem of hydrodynamic stability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Walton, A.G. 2004. Stability of circular Poiseuille–Couette flow to axisymmetric disturbances. Journal of Fluid Mechanics 500: 169–210.

    Article  MathSciNet  Google Scholar 

  2. Chandrasekhar, S. 1961. Hydrodynamic and hydro magnetic instability. Oxford: Clarendon Press.

    Google Scholar 

  3. Batchelor, G.K., and A.E. Gill. 1962. Analysis of the stability of axisymmetric jets. Journal of Fluid Mechanics 14: 529–551.

    Article  MathSciNet  Google Scholar 

  4. Howard, L.N., and A.S. Gupta. 1962. On the hydrodynamic and hydro magnetic stability of swirling flows. Journal of Fluid Mechanics 14: 463–476.

    Article  MathSciNet  Google Scholar 

  5. Pavithra, P., and M. Subbiah. Note on instability regions in the circular Rayleigh problem of hydrodynamic stability. Proc. Natl. Acad. Sci. India (Submitted).

  6. Anil Iype, M.S., and M. Subbiah. 2010. On the hydrodynamic and hydromagnetic stability of inviscid flows between coaxial cylinders. International Journal of Fluid Mechanics Research 37 (2): 1–15.

    Google Scholar 

  7. Banerjee, M.B., R.G. Shandil, and V. Kanwar. 1993. A proof of Howard’s conjecture in homogeneous parallel shear flows. Proc. Indian Acad. Sci. Math. Sci. 104: 593–596.

    Article  MathSciNet  Google Scholar 

  8. Banerjee, M.B., R.G. Shandil, and V. Kanwar. 1995. A proof of Howard’s conjecture in homogeneous parallel shear flows-II: limitations of Fjortoft’s necessary instability criterion. Proc. Indian Acad. Sci. Math. Sci. 105 (2): 251–257.

    Article  MathSciNet  Google Scholar 

  9. Banerjee, M.B., R.G. Shandil, K.S. Shirkot, and D. Sharma. 2000. Importance of Tollmien’s counter example. Studies in Applied Mathematics. 105: 191–202.

    Article  MathSciNet  Google Scholar 

  10. Dattu, H., and M. Subbiah. 2012. On the two-dimensional stability of incompressible swirling flows. J. Analysis. 20: 25–45.

    MathSciNet  MATH  Google Scholar 

  11. Drazin, P.G., and W.H. Reid. 1981. Hydrodynamic stability. UK: Cambridge University Press.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Pavithra.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pavithra, P., Subbiah, M. On sufficient conditions for stability in the circular Rayleigh problem of hydrodynamic stability. J Anal 27, 781–795 (2019). https://doi.org/10.1007/s41478-018-0128-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41478-018-0128-z

Keywords

Mathematics Subject Classification

Navigation