Abstract
This is a study of the evolution of finite amplitude wave packets at the contact surface between a semi-infinite liquid medium and a liquid located above it near a solid lid. The limiting case of near-critical wave numbers for propagation of wave packets in the liquid system is discussed. Perturbation expansions are obtained for the deviation of the contact surface from its unperturbed position and for wave numbers near the critical value. This is compared with the solution for the analogous limiting cases of one or two semi-infinite liquids. A version in which the wave numbers are far from critical is examined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
H. Hasimoto and H. Ono, “Nonlinear modulation of gravity waves, ” J. Phys. Soc., Japan, 33, 805–811 (1972).
A. Nayfeh, “Nonlinear propagation of wave-packets on fluid interface, ” Trans. ASME J. Appl. Mech. Ser. E, 43, 584–588 (1976).
O. V. Avramenko and I. T. Selezov, “Nonlinear wave propagation in a fluid layer based on semi-infinite fluid, ” Dop. NANU, No. 10, 61–66 (1997).
R. L. Kiang, “Nonlinear theory of inviscid Taylor instability near the cutoff wave number, ” Phys. Fluids, 12, 1333–1339 (1969).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Selezov, I.T., Avramenko, O.V. Nonlinear Propagation of Wave Packets for Near-Critical Wave Numbers in a Liquid that Is Piecewise Nonuniform with Depth. Journal of Mathematical Sciences 103, 409–413 (2001). https://doi.org/10.1023/A:1011386917466
Issue Date:
DOI: https://doi.org/10.1023/A:1011386917466