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Bounds on complex eigenvalues in a hydromagnetic stability problem

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Abstract

We consider an eigenvalue problem of hydromagnetic stability and obtain instability regions within which the complex eigenvalues corresponding to unstable modes should lie.

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References

  1. Acheson, D.J., and Hide. 1973. Hydromagnetics of rotating fluids. Reports on Progress in Physics 36 (159): 160–219.

    Google Scholar 

  2. Adam, J.A. 1986. Critical layer singularities and complex eigenvalues in some differential equations of mathematical physics. Physics Reports 142 (5): 263–356.

    Article  MathSciNet  Google Scholar 

  3. Anil Iype, M.S., and M. Subbiah. 2008. Eigen Value Bounds in the Stability Problem of Hydromagnetic Swirling Flows. Indian Journal of Pure and Applied Mathematics 39: 211–225.

    MathSciNet  MATH  Google Scholar 

  4. 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: 1–15.

    Article  Google Scholar 

  5. Chandrasekar, S. 1961. Hydrodynamic and Hydromagnetic Instability. Oxford: Clarendon Press.

    Google Scholar 

  6. Chimonas, G. 1970. The Extension of the Miles–Howard theorem to compressible flows. Journal of Fluid Mechanics 43 (4): 833–836.

    Article  Google Scholar 

  7. Dandapat, B.S., and A.S. Gupta. 1975. On the stability of swirling flow in magnetogasdynamics. Quarterly of Applied Mathematics 33 (2): 182–186.

    Article  Google Scholar 

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

    MATH  Google Scholar 

  9. Ganguly, K., and A.S. Gupta. 1985. On the hydromagnetic stability of helical flows. Journal of Mathematical Analysis and Applications 106: 26–40.

    Article  MathSciNet  Google Scholar 

  10. Howard, L.N. 1961. Note on a paper of John W. Miles. Journal of Fluid Mechanics 10: 509–512.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  12. Jain, R.K., and G.T. Kochar. 1983. Stability of Stratified Shear Flows. Journal of Mathematical Analysis and Applications 96: 269–282.

    Article  MathSciNet  Google Scholar 

  13. Kochar, G.T., and R.K. Jain. 1979. Note on Howard’s semicircle theorem. Journal of Fluid Mechanics 91: 489–491.

    Article  MathSciNet  Google Scholar 

  14. Miles, J.W. 1961. On the stability of heterogeneous shear flows. Journal of Fluid Mechanics 10: 496–508.

    Article  MathSciNet  Google Scholar 

  15. Sasakura, Y. 1984. Semi-Ellipse Theorem for the Heterogeneous Swirling Flow in an Azimuthal Magnetic Field with respect to Axisymmetric Disturbance. Journal of the Physical Society of Japan 53: 2012–2017.

    Article  MathSciNet  Google Scholar 

  16. Velikhov, E.P. 1959. Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field. Soviet Physics JETP 36 (9): 995–997.

    MathSciNet  Google Scholar 

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Funding

The first author’s work was supported by CSIR-Junior Research Fellowship with Award number: 09/559(0134)/2019-EMR-I which is acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Pondicherry University, Kalapet, Puducherry, 605014, India

    S. Prakash & M. Subbiah

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  1. S. Prakash
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  2. M. Subbiah
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Correspondence to S. Prakash.

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The authors declare no conflict of interest in this work.

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Communicated by Samy Ponnusamy.

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Prakash, S., Subbiah, M. Bounds on complex eigenvalues in a hydromagnetic stability problem. J Anal 29, 1137–1150 (2021). https://doi.org/10.1007/s41478-020-00301-6

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  • DOI: https://doi.org/10.1007/s41478-020-00301-6

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