Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Effects of surface tension and viscosity on Taylor instability

Authors: Richard Bellman and Ralph H. Pennington
Journal: Quart. Appl. Math. 12 (1954), 151-162
MSC: Primary 76.1X
DOI: https://doi.org/10.1090/qam/63198
MathSciNet review: 63198
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Abstract: The model used is that of two fluids of infinite depth, with the interface initially in the form of a sine wave with amplitude small compared to wave length. The fluids are considered incompressible, and only the linear terms in the equations of hydrodynamics are used. The first four sections discuss the effects of surface tension and viscosity. The fifth gives a few numerical results to illustrate the main points of the preceding sections.

References [Enhancements On Off] (What's this?)

  • [1] W. J. Harrison, The Influence of Viscosity on the Oscillations of Superposed Fluids, Proc. London Math. Soc. (2) 6 (1908), 396–405. MR 1575134, https://doi.org/10.1112/plms/s2-6.1.396
  • [2] H. Lamb, Hydrodynamics, 6th Ed., Cambridge, 1932, pp. 370, 456, and 625.
  • [3] D. J. Lewis, Proc. Roy. Soc. (A) 202, 81 (1950).
  • [4] G. I. Taylor, Proc. Roy. Soc. (A) 201, 192 (1950).

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DOI: https://doi.org/10.1090/qam/63198
Article copyright: © Copyright 1954 American Mathematical Society

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