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The Kelvin-Helmholtz instability for a viscous Interface

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This paper discusses the Kelvin-Helmholtz instability for the interface between a visous and an inviscid fluid. The incipient boundary layer is modelled as a two dimensional viscous interface.

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References

  1. Dussan, E. B.: Hydrodynamic stability and instability of fluid systems with interfaces. Arch. Rational Mech. Anal.57, 363–379 (1975).

    Google Scholar 

  2. Joseph, D. D.: Stability of fluid motions II. (Springer Tracts in Natural Philosophy, Vol. 28). Berlin-Heidelberg-New York: Springer 1976.

    Google Scholar 

  3. Barratt, P. J., Jenkins, J. T.: Interfacial effects in the magneto-hydrostatic theory of nematic liquid crystals. J. Phys.A 6, 756–769 (1973).

    Google Scholar 

  4. Jenkins, J. T.: The equations of mechanical equilibrium of a model membrane. SIAM J. Appl. Math.32, 755–764 (1977).

    Google Scholar 

  5. Jenkins, J. T., Barratt, P. J.: Interfacial effects in the static theory of nematic liquid crystals. Q. J. Mech. Appl. Math.27, 111–127 (1974).

    Google Scholar 

  6. Scriven, L. E.: Dynamics of a fluid interface. Equation of motion for Newtonian surface fluids. Chem. Eng. Sci.12, 98–108 (1960).

    Google Scholar 

  7. Gurtin, M. E., Murdoch, A. I.: A continuum theory of elastic material surfaces. Arch. Rational Mech. Anal.57, 291–323 (1975).

    Google Scholar 

  8. Moeckel, G. P.: Thermodynamics of an interface. Arch. Rational Mech. Anal.57, 255–280 (1974).

    Google Scholar 

  9. Lindsay, K. A., Straughan, B.: A thermodynamic viscous interface theory and associated stability problems. Arch. Rational Mech. Anal.71, 307–326 (1979).

    Google Scholar 

  10. Green, A. E., Laws, N., Naghdi, P. M.: On the theory of water waves. Proc. R. Soc. Lond.A 338, 43–55 (1974).

    Google Scholar 

  11. Green, A. E., Naghdi, P. M.: Directed fluid sheets. Proc. R. Soc. Lond.A 347, 447–473 (1976).

    Google Scholar 

  12. Naghdi, P. M.: The theory of shells and plates. In: Handbuch der Physik (Flugge, S., ed.), Vol. via/2, p. 425. Berlin-Heidelberg-New York: Springer 1972.

    Google Scholar 

  13. Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability. The international series of monographs on Physics. Oxford University Press 1961.

  14. Miles, J. W.: On the generation of surface waves by shear flows, Pt 3. J. Fluid. Mech.1959, 583–598.

  15. Lord Kelvin: Mathematical and physical papers. iv, hydrodynamics and general dynamics, p. 69. Cambridge, England 1910.

  16. Francis, J. R. D.: Wave motions and the aerodynamic drag on a free oil surface. Phil. Mag. Ser.7, 45, 695–702 (1954).

    Google Scholar 

  17. Green, A. E., Naghdi, P. M., Wainwright, W. L.: A general theory of a Cosserat surface. Arch. Rat. Mech. and Anal.20, 287–308 (1965).

    Google Scholar 

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Visiting Simon Fraser University, Burnaby, B.C., Canada, for year 1982/83/

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Lindsay, K.A. The Kelvin-Helmholtz instability for a viscous Interface. Acta Mechanica 52, 51–61 (1984). https://doi.org/10.1007/BF01175964

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  • DOI: https://doi.org/10.1007/BF01175964

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