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What is the final size of turbulent mixing zones driven by the Faraday instability?

Published online by Cambridge University Press:  21 December 2017

B.-J. Gréa Open the ORCID record for B.-J. Gréa [Opens in a new window]  and
A. Ebo Adou
B.-J. Gréa*
Affiliation:
CEA, DAM, DIF, F-91297 Arpajon, France
A. Ebo Adou
Affiliation:
CMLA, ENS Cachan, France
*
†Email address for correspondence: [email protected]
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Abstract

Miscible fluids of different densities subjected to strong time-periodic accelerations normal to their interface can mix due to Faraday instability effects. Turbulent fluctuations generated by this mechanism lead to the emergence and the growth of a mixing layer. Its enlargement is gradually slowed down as the resonance conditions driving the instability cease to be fulfilled. The final state corresponds to a saturated mixing zone in which the turbulence intensity progressively decays. A new formalism based on second-order correlation spectra for the turbulent quantities is introduced for this problem. This method allows for the prediction of the final mixing zone size and extends results from classical stability analysis limited to weakly nonlinear regimes. We perform at various forcing frequencies and amplitudes a large set of homogeneous and inhomogeneous numerical simulations, extensively exploring the influence of initial conditions. The mixing zone widths, measured at the end of the simulations, are satisfactorily compared to the predictions, and bring a strong support to the proposed theory. The flow dynamics is also studied and reveals the presence of sub-harmonic as well as harmonic modes depending on the initial parameters in the Mathieu phase diagram. Important changes in the flow anisotropy, corresponding to the large scale structures of turbulence, occur. This phenomenon appears directly related to the orientation of the most amplified gravity waves excited in the system, evolving due to the enlargement of the mixing zone.

JFM classification

Convection: Buoyancy-driven instability Turbulent Flows: Stratified turbulence Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 293 - 319
Copyright
© 2017 Cambridge University Press 

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Gréa et al. supplementary movie 1

SHT 512^3 simulation with F=1: (Top) Time evolution of the mixing layer. (Bottom) Turbulent fluctuations of concentration in the periodic domain.

Download Gréa et al. supplementary movie 1(Video)
Video 36.6 MB

Gréa et al. supplementary movie 2

SHT 1024^3 simulation with F=1: (Top) Time evolution of the mixing layer. (Bottom left) Turbulent fluctuations of concentration in the periodic domain. (Bottom right) Spectra of kinetic energy and concentration.

Download Gréa et al. supplementary movie 2(Video)
Video 26.4 MB

Gréa et al. supplementary movie 3

MZ 512^3 simulation: (Top) time evolution of the mixing layer. (Bottom) Density field.

Download Gréa et al. supplementary movie 3(Video)
Video 4.8 MB