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Bounds on the phase velocity in the linear instability of viscous shear flow problem in the β-plane

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Abstract

Results obtained by Joseph(J. Fluid Mech. 33 (1968) 617) for the viscous parallel shear flow problem are extended to the problem of viscous parallel, shear flow problem in the beta plane and a sufficient condition for stability has also been derived.

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References

  1. Banerjee M B, Shandil R G, Gourala M G and Chauhan S S, Eigenvalue bounds for the Orr-Sommerfeld’s equation and their relevance to the existence of backward wave motion,Stud. Appl. Math. 103 (1999) 43–50

    Article  MATH  MathSciNet  Google Scholar 

  2. Banerjee M B, Shandil R G, Chauhan S S and Sharma D, Eigenvalue bounds for the Orr-Sommerfeld’s equation and their relevance to the existence of backward wave motion-II,Stud. Appl. Math. 105 (2000) 31–34

    Article  MATH  MathSciNet  Google Scholar 

  3. Drazin P G and Howard L N, Hydrodynamic stability of parallel flow of inviscid fluid, in: Advances in Applied Mechanics (1966) (New York: Acdemic Press) vol. 9

    Google Scholar 

  4. Fjortoft R, Application of integral theorems in deriving criteria of stability of laminar flow and for the baroclinic circular vortex,Geofys. Publ. 17 (1950) 1–52

    MathSciNet  Google Scholar 

  5. Friedlander S and Howard L, Instability in parallel flows revisited,Stud. Appl. Math. 101 (1998) 1–21

    Article  MATH  MathSciNet  Google Scholar 

  6. Hickernel F J, An upper bound on the growth rate of a linear instability in a homogeneous shear flow,Stud, Appl. Math. 72 (1985) 87–93

    MathSciNet  Google Scholar 

  7. Joseph D D, Eigenvalue bounds for the Orr-Sommerfeld equation,J. Fluid Mech. 33 (1968) 617–621

    Article  MATH  MathSciNet  Google Scholar 

  8. Kuo H L, Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere,J. Meteorol. 6 (1949) 105

    Google Scholar 

  9. Rayleigh J W S, On the instability of certain fluid motions,Proc. London Math. Soc. 9 (1880) 57–70

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, H.P. University, 171 005, Shimla, India

    R. G. Shandil & Jagjit Singh

  2. Sidharth Govt. Degree College, Nadaun, 177 033, Distt Hamirpur, India

    Jagjit Singh

Authors
  1. R. G. Shandil
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  2. Jagjit Singh
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Shandil, R.G., Singh, J. Bounds on the phase velocity in the linear instability of viscous shear flow problem in the β-plane. Proc. Indian Acad. Sci. (Math. Sci.) 113, 207–212 (2003). https://doi.org/10.1007/BF02829771

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  • DOI: https://doi.org/10.1007/BF02829771

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