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Viscous effects in Rayleigh-Taylor instability

Plesset, Milton S. and Whipple, Christopher G. (1974) Viscous effects in Rayleigh-Taylor instability. Physics of Fluids, 17 (1). pp. 1-7. ISSN 1070-6631. doi:10.1063/1.1694570.

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A simple, physical approximation is developed for the effect of viscosity for stable interfacial waves and for the unstable interfacial waves which correspond to Rayleigh‐Taylor instability. The approximate picture is rigorously justified for the interface between a heavy fluid (e.g., water) and a light fluid (e.g., air) with negligible dynamic effect. The approximate picture may also be rigorously justified for the case of two fluids for which the differences in density and viscosity are small. The treatment of the interfacial waves may easily be extended to the case where one of the fluids has a small thickness; that is, the case in which one of the fluids is bounded by a free surface or by a rigid wall. The theory is used to give an explanation of the bioconvective patterns which have been observed with cultures of microorganisms which have negative geotaxis. Since such organisms tend to collect at the surface of a culture and since they are heavier than water, the conditions for Rayleigh‐Taylor instability are met. It is shown that the observed patterns are quite accurately explained by the theory. Similar observations with a viscous liquid loaded with small glass spheres are described. A behavior similar to the bioconvective patterns with microorganisms is found and the results are also explained quantitatively by Rayleigh‐Taylor instability theory for a continuous medium with viscosity.

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Additional Information:© 1974 American Institute of Physics. Received 23 May 1973. We wish to acknowledge the support of the Office of Naval Research under Contract No. N00014-67-A-0094-0009 and the National Science Foundation under Grant GK 31161X.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-67-A-0094-0009
NSFGK 31161X
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33065
Deposited By: Tony Diaz
Deposited On:09 Aug 2012 23:17
Last Modified:09 Nov 2021 21:32

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