Abstract
The profiles of standing gravity waves of maximum height, parametrically excited on the free surface of a deep fluid in a vertically oscillating rectangular vessel (Faraday waves), are investigated experimentally. For a small modulation index of the excitation parameter, waves of three types are distinguished: regular, temporally periodic and symmetric about the vertical line passing through their crest; irregular but retaining the connectivity of the liquid volume; and breaking waves with drops separating from the free surface of the fluid. It is established that the profile of the maximum-height regular waves is smooth with a steepness of 0.255 and a limiting angle at the crest of less than 80°. Certain realizations of irregular and breaking waves, with profiles similar to those of regular waves but with much smaller steepnesses, 0288 and 0.429, respectively, are detected.
Similar content being viewed by others
References
G.B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
M. Perlin and W.W. Schultz, “Capillary Effects on Surface Waves,” Ann. Rev. Fluid. Mech. 32, 241–274 (2000).
W.G. Penney and A.T. Price, “Finite Periodic Stationary Gravity Waves in a Perfect Fluid,” Phil. Trans. Roy. Soc. London, Ser. A 224(882), 254–284 (1952).
G.N. Mercer and A.J. Roberts, “Standing Waves in Deep Water: Their Stability and Extreme Form,” Phys. Fluids. A 4(2), 259–269 (1992).
P.G. Saffman and H.C. Yuen, “A Note on Numerical Computations of Large Amplitude Standing Waves,” J. Fluid Mech. 95(Pt 4), 707–715 (1979).
G.I. Taylor, “An Experimental Study of Standing Waves,” Proc. Roy. Soc. London, Ser. A 218(1132) 44–59 (1953).
L. Jiang, C.L. Ting, and W.W. Schultz, “Moderate and Steep Faraday Waves: Instabilities, Modulation, and Temporal Asymmetries,” J. Fluid Mech. 329,275-307 (1996).
W.W. Schultz, J.M. Vanden-Broeck, L. Jiang, and M. Perlin, “Highly Nonlinear Standing Water Waves with Small Capillary Effect,” J. Fluid Mech. 369, 253–272 (1998).
H. Bredmose, M. Brocchini, D.H. Peregrine, and L. Thais, “Experimental Investigation and Numerical Modelling of Steep Forced Water Waves,” J. Fluid Mech. 490, 217–249 (2003).
M.S. Longuet-Higgins and D.A. Drazen, “On Steep Gravity Waves Meeting a Vertical Wall: a Triple Instability,” J. Fluid Mech. 466, 305–318 (2002).
H.E. Potts and D.A. Diver, “Large-Amplitude Ferrofluid Surface Waves and Jets,” New J. Phys. 3, 7.1–7.14 (2001).
V.A. Kalinichenko, S.V. Nesterov, S.Ya. Sekerzh-Zen’kovich, and A.V. Chaykovskii, Experimental Investigation of the Parametric Excitation of Surface Waves, Preprint No. 243 (Inst. for Problems in Mechanics, USSR Academy of Sciences, Moscow, 1985).
V.A. Kalinichenko, S.V. Nesterov, S.Ya. Sekerzh-Zen’kovich, and A.V. Chaykovskii, “Experimental Study of Surface Waves with Faraday Resonance Excitation,” Fluid Dynamics 30(1), 101–106 (1995).
Ya.I. Sekerz-Zen’kovich, “On the Theory of Standing Waves of Finite Amplitude on the Surface of a Heavy Fluid,” Dokl. Akad. Nauk SSSR 58(4), 551–553 (1947).
Additional information
Original Russian Text © V.A. Kalinichenko, S.Ya. Sekerzh-Zen’kovich, 2007, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2007, Vol. 42, No. 6, pp. 103–110.
Rights and permissions
About this article
Cite this article
Kalinichenko, V.A., Sekerzh-Zen’kovich, S.Y. Experimental investigation of Faraday waves of maximum height. Fluid Dyn 42, 959–965 (2007). https://doi.org/10.1134/S0015462807060117
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0015462807060117