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Physics of Fluids / Volume 19 / Issue 8 / ARTICLES / Interfacial Flows

Phys. Fluids 19, 082105 (2007); http://dx.doi.org/10.1063/1.2760244 (6 pages)

Correction of Lamb’s dissipation calculation for the effects of viscosity on capillary-gravity waves

J. C. Padrino and D. D. Joseph

Aerospace Engineering and Mechanics Department, University of Minnesota, Minneapolis, Minnesota 55455, USA

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(Received 20 January 2007; accepted 19 June 2007; published online 21 August 2007)

Purely irrotational theories of the flow of a viscous liquid are applied to model the effect of viscosity on the decay and oscillation of capillary-gravity waves. In particular, the dissipation approximation used in this analysis gives rise to a viscous correction of the frequency of the oscillations which was not obtained by Lamb’s [ H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, UK, 1932) (reprinted in 1993) ] dissipation calculation. Moreover, our dissipation method goes beyond Lamb’s in the sense that it yields an eigenvalue relation valid for the entire continuous spectrum of wave numbers. Comparisons are presented between the purely irrotational theories and Lamb’s exact solution, showing good to reasonable agreement for long, progressive waves and for short, standing waves, even for very viscous liquids. The performance of the irrotational approximations deteriorates within an interval of wave numbers containing the cutoff where traveling waves become standing ones.

© 2007 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. VISCOUS POTENTIAL FLOW ANALYSIS (VPF)
  3. DISSIPATION METHOD (DM)
  4. DISCUSSION

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KEYWORDS and PACS

Keywords

capillary waves, gravity waves, viscosity

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2760244

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    J. Wang, D. D. Joseph, and T. Funada, “Viscous contributions to the pressure for potential flow analysis of capillary instability of two viscous fluids,” Phys. Fluids 17, 052105 (2005)PHFLE6000017000005052105000001.

    A. Prosperetti, “Viscous effects on small-amplitude surface waves,” Phys. Fluids 19, 195 (1976)PFLDAS000019000002000195000001.


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