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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    CHENG, MINQUAN and CHANG, HSUEH-CHIA 1992. STABILITY OF AXISYMMETRIC WAVES ON LIQUID FILMS FLOWING DOWN A VERTICAL COLUMN TO AZIMUTHAL AND STREAMWISE DISTURBANCES. Chemical Engineering Communications, Vol. 118, Issue. 1, p. 327.
    Lin, S. P. and Creighton, B. 1990. Energy Budget in Atomization. Aerosol Science and Technology, Vol. 12, Issue. 3, p. 630.
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    Urintsev, A. L. 1979. Branching of solutions in the problem of the wavy flow of a viscous liquid with a free boundary. Journal of Applied Mechanics and Technical Physics, Vol. 19, Issue. 4, p. 526.
    Tougou, Hirohumi 1979. Stability of a Two-Layer Film Flow of Viscous Fluids down an Inclined Plane. Journal of the Physical Society of Japan, Vol. 47, Issue. 2, p. 646.
    Lin, S. P. and Krishna, M. V. G. 1977. Stability of a liquid film with respect to initially finite three-dimensional disturbances. Physics of Fluids, Vol. 20, Issue. 12, p. 2005.
    Krishna, M. V. G. and Lin, S. P. 1977. Nonlinear stability of a viscous film with respect to three-dimensional side-band disturbances. Physics of Fluids, Vol. 20, Issue. 7, p. 1039.
    Lin, S. P. 1974. Finite amplitude side-band stability of a viscous film. Journal of Fluid Mechanics, Vol. 63, Issue. 03, p. 417.
    Boyadjiev, Ch. and Krylov, V.S. 1973. Analysis of stability of laminar liquid film flow. The Chemical Engineering Journal, Vol. 6, Issue. 3, p. 225.
    LIN, S.P. 1972. Proceedings of the International Symposium on Two-Phase Systems. p. 263.
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Roles of surface tension and Reynolds stresses on the finite amplitude stability of a parallel flow with a free surface

  • S. P. Lin (a1)
Abstract

Subcritically stable motion of long gravity waves of finite amplitude in a liquid layer flowing down an inclined plane is shown to be impossible. However, super-critically stable wave régimes for such flows are found and curves of constant wave amplitude in such régimes are obtained. The mechanism of non-linear stability is investigated by considering the energy transfer between the mean flow and the disturbances. The results obtained show that the mechanism of stability in a parallel flow with a free surface is quite different from that in a parallel flow without a free surface.

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© 1970 Cambridge University Press
References
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Journal of Fluid Mechanics
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