Comparison of the Effect of Horizontal Vibrations on Interfacial Waves in a Two-Layer System of Inviscid Liquids to Effective Gravity Inversion

• Published in: Microgravity science and technology Vol. 30; no. 1-2; pp. 1 - 10
• Main Authors: Pimenova, Anastasiya V., Goldobin, Denis S., Lyubimova, Tatyana P.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2018; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Boussinesq equations; Classical and Continuum Physics; Dynamic stability; Engineering; Gravitational waves; Gravity waves; Liquids; Mathematical analysis; Nonlinear equations; Original Article; Shallow water; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Thin films; Three dimensional flow; Topical Collection on Non-Equilibrium Processes in Continuous Media under Microgravity; Longitudinal vibrations; Boussinesq equation; Interfacial waves; Two-layer liquid system
• ISSN: 0938-0108; 1875-0494
• DOI: 10.1007/s12217-017-9567-4

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.