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Instabilities, Waves and Turbulence

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Natural and industrial flows, in geophysics, aeronautics or process engineering, are complex, unsteady, sometimes multiphase, and most often turbulent. Understanding and modeling these flows is a real challenge for both fundamental and practical reasons.

On a global scale, atmospheric and oceanic flows are subject to stratification and background rotation effects. These lead to the generation of internal waves, which have a profound influence on the flow dynamics, such as the emergence of eddies or coherent jets that can influence the mixing properties (heat, pollutants ...)

On a smaller scale, flows with interfaces (either between two liquids or between a liquid and a gas) provide other examples of such complex flows. The formation of ocean waves illustrates the wide range of open issues, from the origin of the first ripples generated by wind to their amplification to the mechanism of saturation and dissipation by wave breaking. Other examples are the coiling instability of "liquid ropes" that fall on a surface and the surprising morphology of the "liquid curtains" that form at the exit of a horizontal pipe.

In this research group, we develop model experiments in simple and controlled configurations that aim to reproduce these complex flows from the first stages of instability to fully turbulent situations.

Permanent members:

P. Carles, P.-P. Cortet, F. Moisy, M. Rabaud, N. Ribe

Non Permanent members:

N. Lanchon (PhD), L. Martin-Witkowski (AP Sorbonne U), D. Mora-Paiba (PostDoc), J. Zhang (PostDoc)

Former Members:

M. Aulnette (PhD, 2022), M. Brunet (PhD, 2021), M. Leang (PhD, 2018), E. Monsalve (PostDoc, 2021), C. Nové-Josserand (PostDoc, 2020), S. Perrard (PostDoc, 2018), A. Sibrant (PostDoc, 2017)

How do colonial micro-algae swim towards light?

F. Moisy

Collaboration: H. de Maleprade and R. Goldstein (DAMTP Cambridge), T. Ishikawa (Tohoku University)

Unicellular flagellate microalgae like Chlamydomonas are able to swim in the direction of light in order to optimize photosynthesis: this is phototaxis . This biased swimming towards light is performed thanks to a differential action of the flagella according to the perceived light incidence. How is this property transmitted to its close relative Gonium , a small colony made of 8 to 16 cells assembled as a plate, capable of swimming along intriguing helical trajectories towards the light? We have developed a hydrodynamic model that relates the individual cell behavior to the apparently coordinated swimming of the colony.

Photo: D. Voisin (2008)

H. de Maleprade, F. Moisy, T. Ishikawa, R.E. Goldstein, Phys. Rev. E 101, 022416 (2020).
[Abstract | PDF | arXiv | bioRxiv]

Torricelli's curtain: Morphology of laminar jets under gravity

M. Rabaud, N. Ribe

While the form of a fluid jet issuing horizontally from an orifice was first studied by Torricelli (1643), this classic problem in fluid mechanics still holds surprises. When a laminar jet issues from the end of a pipe, it divides into primary and secondary jets with a thin vertical curtain of fluid connecting them. We are currently using laboratory experiments and numerical simulations to study this unexpected behavior.

O. Tramis, E. Merlin-Anglade, G. Paternoster, M. Rabaud, and N. M. Ribe, Phys. Fluids 33, 062116 (2021).
[ Abstract |[ PDF]

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Strange rotation in an orbitally shaken glass of beer

F. Moisy, J. Bouvard

Collaboration: W. Herreman (LIMSI, Universite Paris-Sud)

Swirling a glass of wine induces a rotating gravity wave along with a mean flow rotating in the direction of the applied swirl. Surprisingly, when the liquid is covered by a floating cohesive material, for instance a thin layer of foam in a glass of beer, the mean rotation at the surface can reverse. This intriguing counter-rotation can also be observed with coffee cream, tea scum, cohesive powder, provided that the wave amplitude is small and the surface covering fraction is large..

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F. Moisy, J. Bouvard, W. Herreman, EPL 122, 34002 (2018)

Liquid rope coiling

N. Ribe
Collaborations: M. Habibi and D. Bonn

If you like honey on your toast at breakfast, you are ready to perform a simple and beautiful fluid mechanics experiment. Plunge a spoon into the honey jar, and then hold it vertically several inches above the toast. The falling honey builds a whirling corkscrew-shaped structure - a phenomenon called "liquid rope coiling".

(Photo H. Hosseini)

N. Ribe, J. Fluid Mech. 812, R2 (2017).

Making folds by blowing on a liquid

M. Aulnette, J. Zhang, F. Moisy, M. Rabaud

When the wind blows on the surface of a liquid, it is well known that, above a critical wind velocity, a propagative wave is formed. But what happens when the fluid is very viscous (100 to 1000 times more viscous than water), to the point that these propagative waves become critically damped? Experimentally, we observe that the waves are violently destabilized in the form of sharp "liquid folds", like a fabric forming folds in front of an iron. These liquid folds then advance at high speed, pushed by the wind, and can interact with each other.

M. Aulnette, J. Zhang, M. Rabaud, F. Moisy, Phys. Rev. Fluids 7, 014003 (2022).
[Abstract | PDF]

Turbulent windprint on a liquid surface

C. Nové-Josserand, S. Perrard, A. Paquier, F. Moisy, M. Rabaud

Collaborations : M. Benzaquen (Ecole Polytechnique), A. Lozano-Duran (Stanford University)

As soon as a light breeze blows on the surface of the water, well before the threshold of formation of the first capillary waves, we notice that the surface is not perfectly smooth like a mirror. Very small deformations (in the order of a few microns) appear, called wrinkles. We have shown that these wrinkles are the imprint of pressure fluctuations travelling in the turbulent boundary layer generated by the wind, which stripe the surface of small unsteady wakes. We study these wrinkles using wind tunnel experiments based on a highly sensitive optical method (Synthetic Schlieren) and numerical simulations.

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S. Perrard, A. Lozano-Duran, M. Rabaud, M. Benzaquen, F. Moisy, J. Fluid Mech. 873, 1020-1054 (2019).

C. Nové-Josserand, S. Perrard, A. Lozano-Duran, M. Rabaud, M. Benzaquen, F. Moisy, Phys. Rev. Fluids 5, 124801 (2020).

Internal wave turbulence in rotating and stratified fluids

M. Brunet, E. Monsalve, D.O. Mora, P.-P. Cortet

Collaboration : B. Gallet (CEA Saclay)

Density stratification and the Earth's rotation are two key ingredients of the dynamics of the oceans and the atmosphere. These ingredients deeply modify the physics of hydrodynamic turbulence by allowing the propagation of internal waves in the volume of the fluid. The "Weak Turbulence Theory" aims to describe the regimes of rotating or "stratified" turbulence for which internal waves dominate the flow. In the framework of the " Simons Collaboration on Wave Turbulence " (2019-2023) and of the ANR project DisET (2018-2022), we carried out in 2020 the first quantitative experimental observation of the weak turbulence of inertial waves in a rotating fluid. We now explore the limits of applicability of the theory in rotating fluids and the possibility of achieving in the lab the weak turbulence regime in the case of internal gravity waves in a stratified fluid.

E. Monsalve, M. Brunet, B. Gallet, P.-P. Cortet, Phys. Rev. Lett. 125, 254502 (2020) [PDF]

M. Brunet, B. Gallet, P.-P. Cortet, Phys. Rev. Lett. 124, 124501 (2020) [PDF]

Linear and nonlinear regimes of an inertial wave attractor

M. Brunet, P.-P. Cortet

Collaboration: T. Dauxois (Laboratoire de Physique de l'ENS de Lyon)

Fluids subjected to a global rotation allow the propagation of a specific class of waves, called inertial waves, found in geophysical and astrophysical flows (ocean, atmosphere, liquid core of planets ...). As a result of the anomalous reflection laws of these waves, which keep their inclination constant with respect to the horizontal, these systems can lead in closed domains to singular modes, called wave attractors, focusing the energy on a limit cycle. We report an experimental study of the non-linear regime of an inertial wave attractor revealing the emergence of a triadic resonance instability with singular features. The scaling laws of the attractor wavelength and amplitude are shown to be quantitatively described by introducing a turbulent viscosity in the linear attractor model, a result that could help in extrapolating attractor theory to geophysically and astrophysically relevant situations.

M. Brunet, T. Dauxois, P.-P. Cortet, Phys. Rev. Fluids 4 034801 (2019) [PDF]

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