Abstract
The nonlinear capillary wave motion in a two-layer liquid with a free surface is analytically investigated accurate to the second order of smallness in ratio of the wave amplitude to the layer thickness. The layers differ in physicochemical properties. A capillary analogue to the “dead water” effect is observed in the system in both linear and quadratic approximations. In the absence of an electric charge at the interfaces, internal nonlinear resonance interaction between capillary waves is also absent regardless of the place of their origination. When there is a charge at the interlayer boundary, capillary waves resonantly interact with each other.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. A. Grigor’ev, S. O. Shiryaeva, and A. I. Grigor’ev, Pis’ma Zh. Tekh. Fiz. 21(12), 36 (1995) [Tech. Phys. Lett. 21, 458 (1995)].
S. O. Shiryaeva, O. A. Grigor’ev, and A. I. Grigor’ev, Zh. Tekh. Fiz. 66(10), 31 (1996) [Tech. Phys. 41, 989 (1996)].
S. O. Shiryaeva and O. A. Grigor’ev, Zh. Tekh. Fiz. 70(6), 31 (2000) [Tech. Phys. 45, 698 (2000)].
V. M. Kozhevnikov, I. Yu. Chuenkova, M. I. Danilov, and S. S. Yastrebov, Pis’ma Zh. Tekh. Fiz. 31(21), 64 (2005) [Tech. Phys. Lett. 31, 932 (2005)].
V. M. Kozhevnikov, I. Yu. Chuenkova, M. I. Danilov, and S. S. Yastrebov, Zh. Tekh. Fiz. 76(7), 129 (2006) [Tech. Phys. 51, 946 (2006)].
V. M. Kozhevnikov, I. Yu. Chuenkova, M. I. Danilov, and S. S. Yastrebov, Zh. Tekh. Fiz. 78(2), 51 (2008) [Tech. Phys. 53, 192 (2008)].
B. V. Deryagin, Theory of Stability of Colloids and Thin Films (Nauka, Moscow, 1986) [in Russian].
A. I. Grigor’ev, M. I. Munichev, and S. O. Shiryaeva, J. Colloid Interface Sci. 166, 267 (1994).
A. I. Grigor’ev, Zh. Tekh. Fiz. 80(6), 36 (2010) [Tech. Phys. 55, 789 (2010)].
B. A. Altoiz, S. V. Kiriyan, and E. A. Shatagina, Zh. Tekh. Fiz. 80(10), 37 (2010) [Tech. Phys. 55, 1426 (2010)].
A. O. Grigor’ev, S. O. Shiryaeva, and M. S. Fedorov, Zh. Tekh. Fiz. 80(7), 8 (2010) [Tech. Phys. 55, 920 (2010)].
L. N. Sretenskii, Theory of Wave Motions of Fluids (Nauka, Moscow, 1977) [in Russian].
A. I. Grigor’ev, M. S. Federov, and S. O. Shiryaeva, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 130 (2010).
A. N. Nayfeh, J. Fluid Mech. 48, 463 (1971).
S. A. Kurochkin and A. I. Grigor’ev, Zh. Tekh. Fiz. 75(11), 44 (2005) [Tech. Phys. 50, 727 (2005)].
L. N. Sretenskii, Geofiz. Zh. 4, 332 (1934).
M. V. Rybakova, S. O. Shiryaeva, and A. I. Grigor’eva, Zh. Tekh. Fiz. 74(1), 24 (2004) [Tech. Phys. 49, 22 (2004)].
S. O. Shiryaeva, D. F. Belonozhko, and A. I. Grigor’ev, Zh. Tekh. Fiz. 75(2), 45 (2005) [Tech. Phys. 50, 185 (2005)].
A. N. Zharov, A. I. Grigor’ev, and S. O. Shiryaeva, Zh. Tekh. Fiz. 75(7), 19 (2005) [Tech. Phys. 50, 635 (2005)].
O. M. Phillips, in Nonlinear Waves, Ed. by S. Leibovich and A. Sibass (Cornell Univ., Ithaca-New York-London, 1974; Mir, Moscow, 1977), pp. 197–220.
R. C. Reid and T. K. Sherwood, Properties of Gases and Liquids (McGraw-Hill, New York, 1966; Khimiya, Moscow, 1971).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.I. Grigor’ev, M.S. Fedorov, S.O. Shiryaeva, 2011, published in Zhurnal Tekhnicheskoi Fiziki, 2011, Vol. 81, No. 11, pp. 31–39.
Rights and permissions
About this article
Cite this article
Grigor’ev, A.I., Fedorov, M.S. & Shiryaeva, S.O. Nonlinear analysis of interaction between finite-amplitude capillary waves in a layered inhomogeneous liquid. Tech. Phys. 56, 1570–1578 (2011). https://doi.org/10.1134/S1063784211110119
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063784211110119