Skip to main content
SpringerLink
Log in

The calculation of eigenvalues for the stationary perturbation of couette-poiseuille flow

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The problem considered is that of two-dimensional viscous flow in a straight channel. The decay of a stationary perturbation from the Couette-Poiseuille flow in the downstream is sought. A differential eigenvalue equation resembling the Orr-Sommerfeld equation is solved by using a spectral method and an initial-value method (the compound matrix method) for values of the Reynolds number R between 0 and 2000. The eigenvalues are presented for several of interesting cases with different measures of mass flux. These eigenvalues determine the rate of decay for the purturbation.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. S. Bramely, Note on the calculation of eigenvalues for stationary perturbation of Poiseuille flow.J. Comput. Phys.,53 (1984), 524–529.

    Article  Google Scholar 

  2. J. S. Bramley and S. C. R. Dennis, The calculation of eigenvalues for the stationary perturbation of Poiseuille flow.J. Comput. Phys.,47 (1982), 179–198.

    Article  Google Scholar 

  3. J. S. Bramley and S. C. R. Dennis, The calculation of eigenvalues for the stationary perturbation of Poiseuille flow using initial value methods.J. Math. Anal. Appl.,101 (1984), 30–38.

    Article  MathSciNet  Google Scholar 

  4. S. D. R. Wilson, The development of Poiseuille flow.J. Fluid Mech.,38 (1969), 793–806.

    Article  Google Scholar 

  5. G. A. Ache, Computation of the eigenvalues for perturbations of Poiseuille flow using a two-point boundary value method,SIAM J. Sci. Statist. Comput.,10 (1989), 1097–1112.

    Article  MathSciNet  Google Scholar 

  6. F. Gilbert and G. E. Backus, Propagator matrices in elastic wave and vibration problems.Geophysics,31 (1966), 326–332.

    Article  Google Scholar 

  7. B. S. Ng and W. H. Reid. An initial value method for eigenvalue problems using compound matrices.J. Comput. Phys.,30 (1979), 125–136.

    Article  MathSciNet  Google Scholar 

  8. S. A. Orszag. Accurate solution to the Orr-Sommerfeld stability equation.J. Fluid Mech.,50 (1971), 689–703.

    Article  Google Scholar 

  9. J. H. Wilkinson,The Algebraic Eigenvalue Problem, Clarendon, Oxford (1965).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Inner Mongolia, 010021, Huhehaote, P. R. China

    Song Jinbao & Chen Jianning

Authors
  1. Song Jinbao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chen Jianning
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Li Jiachun

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jinbao, S., Jianning, C. The calculation of eigenvalues for the stationary perturbation of couette-poiseuille flow. Appl Math Mech 16, 985–994 (1995). https://doi.org/10.1007/BF02538840

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02538840

Key words

Search

Navigation