We prove that the exact non local equation derived by the present authors for the temporal linear evolution of the surface of a viscous incompressible fluid reduces asymptotically for high viscosity to a second order Mathieu type equation proposed recently by Cerda and Tirapegui. The equation describes a strongly damped pendulum and the conditions of validity of the asymptotic regime are given in terms of the relevant physical parameters.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
T. B. Benjamin and F. Ursell, Proc. Roy. Soc. London A 225:505 (1954).
K. Kumar, Proc. Roy. Soc. London A 452:1113 (1996).
K. Kumar and L. S. Tuckerman, J. Fluid Mech. 279:49 (1994).
E. Cerda and E. Tirapegui, Phys. Rev. Lett. 78:859 (1997).
E. Cerda and E. Tirapegui, Journal of Fluid Mechanics 368:195 (1998).
E. Cerda and E. Tirapegui, Bull. Acad. R. Belgique 7:301 (1996).
H. W. Müller, H. Wittmer, C. Wagner, J. Albers, and K. Knorr, Phys. Rev. Lett. 78:2357 (1997).
V. P. Maslov and M. V. Fedorink, Semiclasical Approximation in Quantum Mechanics (Reidel, 1981).
J. Beyer and R. Friedrich, Phys. Rev. E 51:1162 (1995).
About this article
Cite this article
Cerda, E., Rojas, R. & Tirapegui, E. Asymptotic Description of a Viscous Fluid Layer. Journal of Statistical Physics 101, 553–565 (2000). https://doi.org/10.1023/A:1026411510531
- faraday instability
- viscous fluid