The subcritical transition to turbulence of Faraday waves in miscible fluids

Cavelier, Mathilde; Gréa, Benoît-Joseph; Briard, Antoine; Gostiaux, Louis

doi:10.1017/jfm.2021.1124

Cited by 4 publications

(2 citation statements)

References 67 publications

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“…Here, we used the assumption of small density contrast A ≈ 0.01, g 0 ≈ 10 ms −2 which gives 2Ag 0 = 0.2 ms −2 . We can verify the approximation L 0 f 2 2Ag 0 by taking L 0 = 0.003 m from the experimental data of Cavelier et al (2022) and f = 0.322 s −1 from the present numerical simulations (see table 1 for case F075f/ω48), which yields L 0 f 2 ≈ 0.0003 ms −2 . This implies that L 0 f 2 2Ag 0 (0.0003 0.2) and we can neglect L 0 f 2 compared with 2Ag 0 .…”

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confidence: 60%

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The onset and saturation of the Faraday instability in miscible fluids in a rotating environment

Singh,

Pal

2023

J. Fluid Mech.

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We investigate the influence of rotation on the onset and saturation of the Faraday instability in a vertically oscillating two-layer miscible fluid using a theoretical model and direct numerical simulations (DNS). Our analytical approach utilizes Floquet analysis to solve a set of the Mathieu equations obtained from the linear stability analysis. The solution of the Mathieu equations comprises stable and harmonic, and subharmonic unstable regions in a three-dimensional stability diagram. We find that the Coriolis force delays the onset of the subharmonic instability responsible for the growth of the mixing zone size at lower forcing amplitudes. However, at higher forcing amplitudes, the flow is energetic enough to mitigate the instability delaying effect of rotation, and the evolution of the mixing zone size is similar in both rotating and non-rotating environments. These results are corroborated by DNS at different Coriolis frequencies and forcing amplitudes. We also observe that for $(\,f/\omega )^2<0.25$ , where $f$ is the Coriolis frequency, and $\omega$ is the forcing frequency, the instability and the turbulent mixing zone size- $L$ saturates. When $(\,f/\omega )^2\geq 0.25$ , the turbulent mixing zone size- $L$ never saturates and continues to grow.

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Section: Discussionsupporting

confidence: 60%

“…We can verify the approximation by taking from the experimental data of Cavelier et al. (2022) and from the present numerical simulations (see table 1 for case F075f/48), which yields . This implies that and we can neglect compared with .…”

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confidence: 75%

The onset and saturation of the Faraday instability in miscible fluids in a rotating environment

Singh,

Pal

2023

J. Fluid Mech.

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Faraday instability of non-Newtonian fluids under low-frequency vertical harmonic vibration

Huo

Wang

2022

Physics of Fluids

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Resonance Acoustic Mixing® (RAM) technology applies an external low-frequency vertical harmonic vibration to convey and mix the non-Newtonian fluid across space. However, although this method is used for various applications, its mechanism is yet not well understood. In this paper, we investigate the Faraday instability of power-law non-Newtonian fluids in RAM utilizing theory and simulations. According to the Floquet analysis and the dimensionless Mathieu equation, the critical stable region besides the stable region and the unstable region is discovered. Based on the numerical solutions of the two-dimensional incompressible Euler equations for a prototype Faraday instability flow, the temporal evolution of the surface displacement and the mechanism of Faraday waves for two cases are explored physically. For the low forcing displacement, there are only stable and critical stable regions. The surface deformation increases linearly and then enters the steady-state in which the fluctuation frequency is twice the vertical harmonic vibration. For the large forcing displacement, there are only stable and unstable regions. Under the effect of the inertial force, both cases have a sudden variation after the brief stabilization period. Furthermore, a ligament structure is observed, which signals that the surface is destabilized. In addition, a band-like pressure minimum distribution below the interface is formed. The fluid flows from the bottom to the crest portion to balance the pressure difference, which raises the crest.

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Quantifying the turbulent mixing driven by the Faraday instability in rotating miscible fluids

Singh,

Pal

2024

Physics of Fluids

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The effect of the rotation on the turbulent mixing of two miscible fluids of small contrasting density, induced by Faraday instability, is investigated using direct numerical simulations. We quantify the irreversible mixing, which depicts the conversion of the available potential energy (APE) to the background potential energy (BPE) through the irreversible mixing rate M. We demonstrate that at lower forcing amplitudes, the turbulent kinetic energy (t.k.e.) increases with an increase in the Coriolis frequency f till (f/ω)2<0.25, where ω is the forcing frequency, during the sub-harmonic instability phase. This enhancement of t.k.e. is attributed to the excitement of more unstable modes. The irreversible mixing sustains for an extended period with increasing (f/ω)2 till 0.25 owing to the prolonged sub-harmonic instability phase and eventually ceases with instability saturation. When (f/ω)2>0.25, the Coriolis force significantly delays the onset of the sub-harmonic instabilities. The strong rotational effects result in lower turbulence because the bulk of the APE expends to BPE, decreasing APE that converts back to t.k.e. reservoir for (f/ω)2>0.25. Therefore, in the subsequent oscillation, the t.k.e. available to contribute to the external energy input from periodic forcing is small. Since the instability never saturates for (f/ω)2>0.25, the conversion of APE to BPE via M continues, and we find prolonged irreversible mixing. At higher forcing amplitudes, the instability delaying effect of rotation is negligible, and the turbulence is less intense and short-lived. Therefore, the irreversible mixing phenomenon also ends quickly for (f/ω)2<0.25. However, when (f/ω)2>0.25, a continuous irreversible mixing is observed. We also examine the mixing efficiency in terms of M and find that the mixing is efficient at lower forcing amplitudes and rotation rates of (f/ω)2>0.25 because the major portion of APE expends to BPE.

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The subcritical transition to turbulence of Faraday waves in miscible fluids

Cited by 4 publications

References 67 publications

The onset and saturation of the Faraday instability in miscible fluids in a rotating environment

The onset and saturation of the Faraday instability in miscible fluids in a rotating environment

Faraday instability of non-Newtonian fluids under low-frequency vertical harmonic vibration

Quantifying the turbulent mixing driven by the Faraday instability in rotating miscible fluids

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