Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On stability of the flow of a stratified gas over a liquid

Authors: John F. Sontowski, Barry S. Seidel and William F. Ames
Journal: Quart. Appl. Math. 27 (1969), 335-348
DOI: https://doi.org/10.1090/qam/99820
MathSciNet review: QAM99820
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Abstract: Instabilities of the superposed flow of a gas over a liquid are considered under the assumption of inviscid, incompressible flow. The effects of density stratification in the gas are examined, and in so doing, two separate and different types of instabilities are revealed. As the velocity of the gas relative to the liquid increases from zero, there first appears an instability of a selective and relatively weak nature referred to as the initial instability. This is followed, at higher velocities, by a stronger type of instability called the gross instability. The initial instability takes the form of two distinct waves of different lengths, one superimposed upon the other. This superposition of two waves at low velocity is in accord with experimental observations, as are the calculated critical velocity and wavelength at which they first occur. The gross instability, on the other hand, is composed of a continuous spectrum of unstable waves, and is simply a slight refinement of the classical result of Kelvin. Such an occurence of two separate instabilities is in agreement with Munk's experimentally based contention that Kelvin's solution is not incorrect, as originally believed, but rather represents an actual instability which, however, is preceded by an additional and different type of instability.

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DOI: https://doi.org/10.1090/qam/99820
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society