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Interface instabilities in Faraday waves of two-layer liquids with free surface

Published online by Cambridge University Press:  03 May 2022

Dongming Liu Open the ORCID record for Dongming Liu [Opens in a new window]  and
Pengzhi Lin Open the ORCID record for Pengzhi Lin [Opens in a new window]
Dongming Liu
Affiliation:
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, PR China
Pengzhi Lin*
Affiliation:
State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, PR China
*
†Email address for correspondence: [email protected]
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Abstract

For a fluid system with an interface between two-layer liquids and a free surface, there exist two series of natural frequencies. Under vertical excitations, the interface and the free surface can be excited separately or simultaneously. Laboratory experiments were conducted to excite the first- and second-mode Faraday waves on the free surface, which forced the in-phase motion of the interface. The experimental data were used to validate the extended numerical model NEWTANK. The secondary surface instability in the form of period tripling breaking occurred on the free surface when second-mode surface resonant response was large. Further numerical investigations were conducted to study the resonance of interface and in addition to the primary Faraday instability, the secondary interface instability occurred due to Rayleigh–Taylor (RT) instability. The analysis revealed that this was due to the contribution from the combined effects of vertical fluid acceleration and external excitation, which made the upper layer liquid essentially ‘heavier’ than the lower layer at certain instances, even when the amplitude of acceleration of the external excitation was lower than that of gravity at all times. A dimensionless parameter ‘normalised effective gravitational acceleration’ (NEGA) was proposed to quantify the occurrence criterion of RT instability in a dynamic fluid system. Furthermore, simultaneous resonances at both the interface and the free surface were studied and reverse flows could be formed across the interface as the upper Faraday waves and lower Faraday waves moved in opposite directions, which generated the secondary interface instability of Kelvin–Helmholtz (KH) type. When KH instability took place, more energy was transferred to higher frequency modes as time evolved.

JFM classification

Waves/Free-surface Flows: Faraday waves Instability: Instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A33
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Liu et al. Supplementary Movie 1

Resonant response of lower layer with Rayleigh-Taylor instability on the interface

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