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On Howard’s conjecture in heterogeneous shear flow problem

  • R. G. Shandil
  • Jagjit Singh
Article

Abstract

Howard’s conjecture, which states that in the linear instability problem of inviscid heterogeneous parallel shear flow growth rate of an arbitrary unstable wave must approach zero as the wave length decreases to zero, is established in a mathematically rigorous fashion for plane parallel heterogeneous shear flows with negligible buoyancy forcegΒ ≪ 1 (Miles J W,J. Fluid Mech. 10 (1961) 496–508), where Β is the basic heterogeneity distribution function).

Keywords

Heterogeneous shear flows linear stability 

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References

  1. [1]
    Banerjee M B, Shandil R G and Vinay Kanwar, A proof of Howard’s conjecture in homogeneous parallel shear flows,Proc. Indian Acad. Sci. (Math. Sci) 104 (1994) 593–595MATHMathSciNetCrossRefGoogle Scholar
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    Banerjee M B, Shandil R G, Prakash J, Bandral B S and Lal Prem, On Howard’s conjecture in heterogeneous shear flows instability of modifieds-waves,Indian J. Pure Appl. Math. 28(6) (1997) 825–834MATHMathSciNetGoogle Scholar
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    Garcia R V, Unpublished Lecture Notes (Los Angeles: University of California) (1961)Google Scholar
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    Howard L N, Note on a paper of John W Miles,J. Fluid Mech. 10 (1961) 509–512MATHCrossRefMathSciNetGoogle Scholar
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    Miles J W, On the stability of heterogeneous shear flows,J. Fluid Mech. 10 (1961) 456–508CrossRefMathSciNetGoogle Scholar

Copyright information

© Indian Academy of Sciences 2003

Authors and Affiliations

  • R. G. Shandil
    • 1
  • Jagjit Singh
    • 1
    • 2
  1. 1.Department of MathematicsH.P. UniversityShimlaIndia
  2. 2.Sidharth Govt. Degree CollegeIndia

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