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Stability of mean flows over an infinite flat plate

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References

  1. Antar, B. N., & J. A. Benek, Temporal eigenvalue spectrum of the Orr-Sommerfeld equation for the Blasius boundary layer, Phys. Fluids 21 (1978), 183–189.

    Google Scholar 

  2. Corner, D., D. J. R. Houston, & M. A. S. Ross, Higher eigenstates in boundarylayer stability theory, J. Fluid Mech. 77 (1976), 81–103.

    Google Scholar 

  3. DiPrima, R. C., W. Eckhaus, & L. A. Segel, Non-linear wavenumber interaction in near-critical two-dimensional flows, J. Fluid Mech. 49 (1971), 705–744.

    Google Scholar 

  4. DiPrima, R. C., & G. J. Habetler, A completeness theorem for non-selfadjoint eigenvalue problems in hydrodynamic stability, Arch. Rational Mech. Anal. 34 (1969), 218–227.

    Google Scholar 

  5. Grosch, C. E., & H. Salwen, The continuous spectrum of the Orr-Sommerfeld equation. Part 1. The spectrum and the eigenfunctions, J. Fluid Mech. 87 (1978), 33–54.

    Google Scholar 

  6. Gustavsson, L. H., Initial-value problem for boundary layer flows, Phys. Fluids 22 (1979), 1602–1605.

    Google Scholar 

  7. Jordinson, R., Spectrum of eigenvalues of the Orr-Sommerfeld equation for Blasius flow, Phys. Fluids 14 (1971), 2535–2537.

    Google Scholar 

  8. Joseph, D. D., Stability of Fluid Motions I, II, Springer-Verlag, New York, 1976.

    Google Scholar 

  9. Joseph, D. D., & D. H. Sattinger, Bifurcating time periodic solutions and their stability, Arch. Rational Mech. Anal. 45 (1972), 79–109.

    Google Scholar 

  10. Kato, T., Wave operators and similarity for some non-selfadjoint operators, Math. Annalen 162 (1966), 258–279.

    Google Scholar 

  11. Kato, T., Perturbation Theory for Linear Operators, 2nd edition, Springer-Verlag, New York, 1976.

    Google Scholar 

  12. Mack, L. M., A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer, J. Fluid Mech. 73 (1976), 497–520.

    Google Scholar 

  13. Murdock, J. W., & K. Stewartson, Spectra of the Orr-Sommerfeld equation, Phys. Fluids 20 (1977), 1404–1411.

    Google Scholar 

  14. Nayfeh, A. H., Stability of three-dimensional boundary layers, AIAA Journal 18 (1980), 406–416.

    Google Scholar 

  15. Reed, M., & B. Simon, Methods of Modern Mathematical Physics IV, Academic Press, New York, 1978.

    Google Scholar 

  16. Rosencrans, S. I., & D. H. Sattinger, On the spectrum of an operator occurring in the theory of hydrodynamic stability, J. Math. and Phys. 45 (1966), 289–300.

    Google Scholar 

  17. Salwen, H., & C. E. Grosch, The stability of Poiseuille flow in a pipe of circular cross-section, J. Fluid Mech. 54 (1972), 93–112.

    Google Scholar 

  18. Salwen, H., & C. E. Grosch, The continuous spectrum of the Orr-Sommerfeld equation. Part 2. Eigenfunction expansions, J. Fluid Mech. 104 (1981), 445–465.

    Google Scholar 

  19. Saric, W. S., & A. H. Nayfeh, Nonparallel stability of boundary layer flows, Phys. Fluids 18 (1975), 945–950.

    Google Scholar 

  20. Sattinger, D. H., Topics in Stability and Bifurcation Theory, Springer Lecture Notes in Mathematics 309, New York, 1973.

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Communicated by D. D. Joseph

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Miklavčič, M., Williams, M. Stability of mean flows over an infinite flat plate. Arch. Rational Mech. Anal. 80, 57–69 (1982). https://doi.org/10.1007/BF00251524

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