David CEBRON

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Numerical simulation of a rotating flow in an ellipsoid.

spinup
  Iso-velocity 13% during 86 rotations (equatorial axes ratio b/a=0.72, polar axis c=(a+b)/2, Ekman E=0.002).

After the spin-up, the rotation axis is tilted by the tidal instability: this is the spinover mode.




Thermal convection : case 0 of the benchmark of Christensen et al. (2001).
christensenIn the rotating frame,  cylindrical radial velocity between -15.6 & 12.7 (Christensen et al. (2001) for details).

The Busse columns (above) is a base flow able to drive a dynamo.




Interaction between tides & precession : a 1st step.

precession_manip
A sphere filled with liquid is deformed by 2 rollers (in gray) into an ellipsoid and set in rotation (motor in black). The whole setup is then tilted and fixed on a rotating table.

This setup has been studied theoretically & numerically (see pdf).












Early lunar dynamo due to an impact?

Moon-dynamo
The impact changes the early Moon rotation rate, which excite an elliptical instability, able to drive a dynamo magnetic field.










MHD experiment IMAGINE (Gallinstan)

Imagine
The induced magnetic field of the elliptical instability is studied with this setup.



Kinematic VKS dynamo

VKS
The velocity field of Gissinger (2009) provides a benchmark dynamo case.








Landslides generated waves

Landslide_waves
The experimental free surface  (top) is in good agreement with the SPH simulation (bottom).








Impact of a buoyant sphere in a 2D water box.

impact_ball
No-slip boundary conditions & no surface tension.

A very rough simulation which shows the abilities of the numerical code.





PHYSICS OF ROTATING FLUIDS

   
    The elliptical instability
Collaborators: M. Le Bars, P. Le Gal, P. Maubert (PhD Advisors, IRPHE), J. Leontini (Monash Univ.)

    The elliptical instability is a generic instability which takes place in any rotating flow whose streamlines are elliptically deformed enough. Its existence in geo- or astrophysical flows raises many issues. This is the starting point of my theoretical, numerical and experimental work. With the first simulations of the elliptical instability in an ellipsoidal geometry, we obtain the scaling laws needed to bridge the gap between numerics and planetary applications. We also investigate the interaction between the elliptical instability and a thermal field, showing that the instability can grow over established convective motions as well as in a thermally stably stratified layer.

Supplementary videos:

- the mode (1,3), with an eigenfrequency of 2, of the tidal instability can be selected in changing the oblateness. We can see on the slice the dimensionless vertical velocity and the surface of iso-velocity 17% (parameters: 2.5 rotations, equatorial axes ratio b/a=0.72, polar axis c=0.65, E=6.66e-4).
- Tidal instability vs. Convection : the usual Busse columns (convection patterns in rotating flows) are totally disrupted by the tidal instability. We can see on the slices the dimensionless vertical velocity and the surface of iso-velocity 19% (parameters: 74 rotations, equatorial axes ratio b/a=0.72, polar axis c=(a+b)/2, E=0.003, Ra=18762, differentially heated autogravitating ellipsoidal shell of ratio 0.3). 

References
- D. Cebron, M. Le Bars, P. Maubert, P. Le Gal, 2012. Magnetohydrodynamic simulations of the elliptical instability in triaxial ellipsoids. Geophys. Astrophys. Fluid Dyn., 106, 4-5. PDF
- D. Cebron, P. Maubert, M. Le Bars, 2010. Tidal instability in a rotating and differentially heated ellipsoidal shell. Geophys. J. Int., 182, 1311-1318. PDF
- D. Cebron, M. Le Bars, J. Leontini, P. Maubert, P. Le Gal, 2010. A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid. Phys. Earth Planet. Int., 182, 119-128. PDF


    Precession driven flows
Collaborators: P. Meunier (IRPHE), F. Moisy, P.P. Cortet (FAST, Orsay), J. Boisson (ENSTA, Paris), M. Le Bars (PhD Advisor, IRPHE)

    Precession is a change in the orientation of the rotational axis of a rotating body (change in direction of the rotation axis in which the second Euler angle, ie. nutation, is constant). The flow of a rotating fluid in a precessing container has been studied for over one century because of its multiple applications, such as the motions in planetary liquid cores and the generation of planetary magnetic fields. We have extended previous theories and simulations  to triaxial ellipsoids (in the precessing frame) to investigate the interaction of tides and precession. We have also shown that the Earth rotation is a precession forcing which prevents exact solid body rotation of fluids in the laboratory (unless by tilting the rotation axis of the experiment parallel to the Earth rotation axis).

References
J. Noir & D. Cebron. Prcession driven flows in non-axisymmetric ellipsoids. In review for J. Fluid. Mech.
- J. Boisson, D. Cebron, F. Moisy, P.P. Cortet, 2012. Earth rotation prevents exact solid body rotation of fluids in the laboratory. Eur. Phys. Let., 98, 59002. PDF
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D. Cebron, M. Le Bars, P. Meunier, 2010. Tilt-over mode in a precessing triaxial ellipsoid. Phys. Fluids, 22, 116601. PDF


  Libration driven flows
Collaborators: J. Noir (ETH Zrich), J.M. Aurnou (UCLA), A. Sauret, S. Le Dizs (IRPHE), M. Le Bars (PhD Advisors, IRPHE), C. Morize (FAST, Orsay), W. Herreman (LIMSI).

    The longitudinal libration of a so-called synchronized planet or moon, i.e., the oscillation of its axial rotation rate whose mean value is otherwise equal to the orbital rotation rate, arises through its gravitational coupling with its closest neighbors. We have studied theoretically, experimentally and numerically the flow driven by this harmonic oscillation of the rotation rate in axisymmetric containers (spheres, cylindres) to investigate the role of the viscous coupling. Although practical to isolate the effect of viscous coupling, the axisymmetric containers are very restrictive from a fluid dynamics standpoint, and we have thus studied containers with an elliptical cross section. We have extended previous analytical studies and reported the first numerical and experimental evidence that elliptical instability can also be driven by libration, i.e., periodic oscillations of the differential rotation between the fluid and the elliptical distortion, with a zero mean value.

References
- D. Cebron, S. Vantieghem, W. Herreman. Libration  driven multipolar instability. In review for J. Fluid. Mech.
- D. Cebron, M. Le Bars, J. Noir, J.M. Aurnou, 2012. Libration driven elliptical instability. Phys. Fluids, 24, 061703. PDF
- J. Noir, D. Cebron, M. Le Bars, A. Sauret, J.M. Aurnou, 2012. Experimental study of libration-driven flows in non-axisymmetric containers. Phys. Earth Planet. Int., 204-205, 1.
- A. Sauret, D. Cebron, M. Le Bars, S. Le Dizes, 2012. Fluid flows in a librating cylinder. Phys. Fluids, 24, 026603. PDF
- A. Sauret, D. Cebron, C. Morize, M. Le Bars, 2010. Experimental and numerical study of mean zonal flows generated by librations of a rotating spherical cavity. J. Fluid Mech., vol. 662, pp. 260-268. PDF




GEOPHYSICAL/ASTROPHYSICAL TIDES DRIVEN FLOWS

Collaborators: C. Moutou (LAM, Marseille), J. Leconte (LMD, Paris), M. Le Bars, P. Le Gal (PhD Advisors, IRPHE), M.A. Wieczorek (IPG Paris), O. Karatekin (Royal Obs. of Belgium).

    The results obtained in our fluid dynamics studies are used to to study the presence of the elliptical instability in known planets, moons, and stars. The particular case of the Moon has been considered and a scenario, based on the elliptical instability, is proposed and evaluated to explain the early lunar dynamo. Telluric bodies have also been considered in a more general context, and a stability analysis adapted to this context shows that the instability can be expected in the Early Earth, Europa and three exoplanets (55CnCe, CoRoT-7b et GJ1214b). Finally, the possible development of the instability in extra-solar Hot-Jupiters systems has been considered, showing its possible relevance for some of them, such as the system of Tau-boo.
 
References
- D. Cebron, M. Le Bars, P. Le Gal, C. Moutou, J. Leconte, A. Sauret. Elliptical instability in Hot-jupiter systems. Icarus. In press. PDF
- D. Cebron, M. Le Bars, C. Moutou, P. Le Gal, 2012. Elliptical instability in terrestrial planets and moons. Astronomy & Astrophysics, 539, A78. PDF
- M. Le Bars, M. A. Wieczorek, O. Karatekin, D. Cebron, M. Laneuville, 2011. An impact-driven dynamo for the early Moon. Nature, 479, 215-218.




MAGNETOHYDRODYNAMICS (MHD)

Collaborators: W. Herreman (LIMSI), M. Le Bars, P. Le Gal, P. Maubert (PhD Advisors, IRPHE), S. Le Dizs (IRPHE)

    The elliptical instability can take place in planetary cores and stars elliptically deformed by gravitational effects, where it generates large-scale three-dimensional flows, able to generate induced magnetic field, or assumed to generate a magnetic field by dynamo effect. Using a MHD setup, we have experimentally studied the induced magnetic field driven by the non-linear dynamics of the instability in an elliptically deformed cylinder. Using the first MHD simulations of such flows, we first validate the model against kinematic and dynamic dynamos benchmarks of the literature. Then, we study the magnetic field induced by various modes of the elliptical instability from an imposed external field in a triaxial ellipsoidal geometry, relevant in a geo- and astrophysical context.

Supplementary videos : in presence of a uniform magnetic field along the rotation axis, the induction of the mode (1,3) of the tidal instability can be studied in changing the oblateness. We can see on the slice the norm of the magnetic field and the surface of iso-velocity 23% (parameters: 2.5 rotations, equatorial axes ratio b/a=0.72, polar axis c=0.65, E=6.66e-4, Pm=0.1 and Elsasser number of 1e-3).
 
References
- D. Cebron, M. Le Bars, P. Maubert, P. Le Gal, 2012. Magnetohydrodynamic simulations of the elliptical instability in triaxial ellipsoids. Geophys. Astrophys. Fluid Dyn., 106, 4-5. PDF
- W. Herreman, D. Cebron, S. Le Dizes, P. Le Gal, 2010. Elliptical instability in rotating cylinders: liquid metal experiments under imposed magnetic field. J. Fluid Mech., vol. 661, pp. 130-158. PDF




FREE SURFACE FLOWS


    Landslides generated tsunamis
Collaborators: S. Viroulet, O. Kimmoun, C. Kharif (IRPHE)

    Problem of waves generated by submarine landslides is in the focus of attention of tsunami society. The danger of tsunami caused by the earthquake of moderate magnitude is related with strong landslide generated on the bottom slopes during the earthquake. Tsunamis generated by landslides are rarer but can be locally more dangerous since they form near the coast and sometimes may generate so-called mega-tsunamis, which are characterized by localized extreme runup heights leading to a significant hazard for the population [Lituya Bay 1958, Alaska, (Fritz et al. 2009), Spirit Lake 1980, Washington USA (Glicken et al. 1989) and maybe Cumbre Vieja, Canary Islands, (Ward & Day 2001; Lovholt et al. 2008; Abadie et al. 2012)]. However, modeling the landslide motion remains challenging because the interactions between the slide and the water as well as the influence of the rheology are difficult to capture as we will see below. In addition, the time evolution of the associated waves remains intricate to forecast.
    In order to get insights into the problem of subaerial landslide generated tsunamis and to further validate the codes for this case of landslides, a series of experiments have been conducted in a water wave tank and successfully compared with the results of two codes : Geris, based on a two-phase finite-volume method, and a SPH code. Based on a simplified approach we derive different scaling laws in excellent agreement with the experiments and numerical simulations.

References

- S. Viroulet, D. Cebron, O. Kimmoun, C. Kharif. Shallow water waves generated by subaerial solid landslides. Geophys. J. Int. 193,2, 747-762. PDF
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S. Viroulet, D. Cebron, O. Kimmoun, C. Kharif, 2012. Evolution of water waves generated by subaerial solid landslide. 27th International Workshop and Water Waves and Floating Bodies (IWWWFB), Copenhagen, Denmark. PDF


 
    Smoothed Particles Hydrodynamics (SPH) method

    Impact of a structure on a fluid is an academic problem of major interest in naval shipbuilding since it is a representative case of the so-called slamming situation, which occurs for a surface ship in various operational conditions. The slamming problem has therefore been extensively studied over the past years, both from the experimental as well as from the numerical points of view, see Donguy (2001) and Peseux et al. (2005), among many others on the matter. Some industrial codes, such as the LS D-DYNA explicit code, offer some functionality to deal with the slamming problem; the underlying methodology is based on the so-called Arbitrary-Lagrangian-Eulerian (ALE) method (Aquelet, 2004; Aquelet et al., 2005).
    Meshfree methods as the Smoothed Particle Hydrodynamic (SPH) method is of particular interest for this kind of problem. Starting from the open-source SPH code SPHYSICS (Crespo et al., 2007 ; Dalrymple & Rogers, 2007), we have undertaken some numerical developments to perform some industrial applications with Fluid/Solid interactions.

Supplementary videos : motion of a rolling half-full Beer Can as it rolls down an incline.

References
- S. Viroulet, D. Cebron, O. Kimmoun, C. Kharif. Shallow water waves generated by subaerial solid landslides. Geophys. J. Int. 193,2, 747-762. PDF
- D. Cebron, J-F. Sigrist, 2008. Toward a 2D SPH multiphysic code with solid-solid & fluid interactions for industrial related problems. Proceedings of the 8th Int. Conf. on Hydrodynamics. Nantes, France. PDF