Nov 25 2002

Faraday waves literature

0 Faraday instability, T. Cvitanovic' notes (Nov 26 2002) - tex - bib

A summary of the derivation of the equations.

1 On a peculiar class of Acoustical Figures, M. Faraday, Philos. Trans. R.Soc. London 52 (1831)

Careful experimentation, but absolutely clueless about mathematical mode of description - this kind of English empiricism must have driven French mathematicians cookoo.

2 The Stability of the Plane Free Surface of a Liquid in Vertical Periodic Motion, T. B. Benjamin, F. Ursell, Proc Royal Society of London. Series A, Math Phys 225 (1954), pp. 505-515.

A pedagogical exposition of the Mathieu function stability analysis in the ideal Euler fluid approximation.

3 Linear Theory of Faraday Instability in Viscous Liquids, Krishna Kumar, Proc Royal Society of London. Series A, Math Phys 452, (1996), pp. 1113-1126.

4 Parametric instability of the interface between two fluids, K. Kumar and L.S. Tuckerman, J. Fluid Mech. 279, 49-68 (1994) (file not available)

5 Patterns and quasi-patterns in the Faraday experiment, W.S. Edwards and S. Fauve, J. Fluid Mech. 278, 123-148 (1994) (file not available)

6 Two-frequency parametric excitation of surface waves Phys. Rev. E 54, 507-513 (1996), T Besson, WS Edwards and LS Tuckerman

7 Theoretical Model for Faraday Waves with Multiple-Frequency Forcing, Ron Lifshitz, Dean M. Petrich

8 A Simple Model for Faraday Waves, J Bechhoefer and B Johnson

9 Pattern selection in Faraday waves, P. Chen and J. Viñals, Phys. Rev. Lett. 79, 2670 (1997).

10 Amplitude equations and pattern selection in Faraday waves, P. Chen and J. Viñals, Phys. Rev. E. 60, 551 (1999).

12 Faraday patterns in Bose-Einstein condensates, K. Staliunas, S. Longhi, G. J. de Valcarcel

Mike Schatz recommendatios:

Parametrically Forced Surface Waves, J Miles and D Henderson, Annu. Rev. Fluid Mech. 1990, Vol. 22: 143-165 . (file not available)
--rather dated but good overview (not much on pattern formation).

patterns article by Douady

Journal of Fluid Mechanics

from early 90's---very clear exposition on basic pattern forming aspects (no fancy stuff like quasipatterns)