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The subcritical transition to turbulence of Faraday waves in miscible fluids

Published online by Cambridge University Press:  19 January 2022

M. Cavelier ,
B.-J. Gréa Open the ORCID record for B.-J. Gréa [Opens in a new window] ,
A. Briard Open the ORCID record for A. Briard [Opens in a new window]  and
L. Gostiaux Open the ORCID record for L. Gostiaux [Opens in a new window]
M. Cavelier
Affiliation:
CEA, DAM, DIF, F-91297Arpajon, France Univ Lyon, CNRS, École Centrale de Lyon, INSA Lyon, Univ Claude Bernard Lyon 1, LMFA, UMR5509, F-69134Écully, France
B.-J. Gréa*
Affiliation:
CEA, DAM, DIF, F-91297Arpajon, France
A. Briard
Affiliation:
CEA, DAM, DIF, F-91297Arpajon, France
L. Gostiaux
Affiliation:
Univ Lyon, CNRS, École Centrale de Lyon, INSA Lyon, Univ Claude Bernard Lyon 1, LMFA, UMR5509, F-69134Écully, France
*
†Email address for correspondence: benoit-joseph.grea@cea.fr
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Abstract

We study the development and the breaking process of standing waves at the interface between two miscible fluids of small density contrast. In our experiment, a subharmonic wave is generated by a time-periodic vertical acceleration via the Faraday instability. It is shown that its wavelength may be selected not only by the linear process predicted by the Floquet theory and favouring the most unstable modes allowed by the tank geometry, but also by a nonlinear mode competition mechanism giving the preference to subcritical modes. Subsequently, as the standing wave amplitude grows, a secondary destabilization process occurs at smaller scales and produces turbulent mixing at the nodes. We explain this phenomenon as a subcritical parametric resonance instability. Different approaches derived from local and global stability analysis are proposed to predict the critical wave steepness. These theories are then assessed against various numerical and experimental data varying the frequencies and amplitudes of the forcing acceleration.

JFM classification

Instability: Parametric instability Instability: Transition to turbulence Waves/Free-surface Flows: Faraday waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A34
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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Cavelier et al. supplementary movie 1

Movie of experiment EXPa1 (see parameters in table 1).

Download Cavelier et al. supplementary movie 1(Video)
Video 2.3 MB

Cavelier et al. supplementary movie 2

Movie of experiment EXPb1 (see parameters in table 1).

Download Cavelier et al. supplementary movie 2(Video)
Video 2.3 MB

Cavelier et al. supplementary movie 3

Movie of a vertical slice of the concentration eld extracted from simulation DNSa2 (see parameters in table 2).

Download Cavelier et al. supplementary movie 3(Video)
Video 1 MB

Cavelier et al. supplementary movie 4

Movie of a vertical slice of the concentration eld extracted from simulation DNSa3 (see parameters in table 2).

Download Cavelier et al. supplementary movie 4(Video)
Video 1.5 MB

Cavelier et al. supplementary movie 5

Movie of a vertical slice of the concentration eld extracted from simulation DNSa8 (see parameters in table 2).

Download Cavelier et al. supplementary movie 5(Video)
Video 5.1 MB

Cavelier et al. supplementary movie 6

Movie of the interface extracted from simulation DNSf (see pa- rameters in table 2).

Download Cavelier et al. supplementary movie 6(Video)
Video 12.3 MB