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 isovelocity 17% (parameters: 2.5
rotations, equatorial axes ratio b/a=0.72, polar axis c=0.65,
E=6.66e4).
 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 isovelocity 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, 45. PDF
 D. Cebron, P.
Maubert,
M. Le Bars, 2010. Tidal
instability in a rotating and differentially heated ellipsoidal shell.
Geophys. J. Int., 182,
13111318. 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,
119128. 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 nonaxisymmetric 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
 D.
Cebron, M. Le Bars, P.
Meunier, 2010. Tiltover
mode in a
precessing triaxial ellipsoid. Phys.
Fluids, 22, 116601. PDF
Libration driven flows
Collaborators: J.
Noir (ETH Zürich), J.M. Aurnou (UCLA), A. Sauret, S. Le Dizès (IRPHE), M. Le Bars (PhD Advisors,
IRPHE), C. Morize (FAST, Orsay), W. Herreman (LIMSI).
The longitudinal
libration of a socalled 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 librationdriven flows in nonaxisymmetric containers. Phys. Earth Planet.
Int., 204205, 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. 260268. 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, CoRoT7b et GJ1214b). Finally, the possible
development of the instability in extrasolar HotJupiters systems has
been considered, showing its possible relevance for some of them, such
as the system of Tauboo.
References
 D. Cebron,
M.
Le Bars, P. Le Gal, C. Moutou, J. Leconte, A. Sauret. Elliptical instability in Hotjupiter 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 impactdriven dynamo for
the early Moon. Nature, 479,
215218.
MAGNETOHYDRODYNAMICS (MHD)
Collaborators: W. Herreman (LIMSI), M. Le Bars, P. Le Gal, P. Maubert (PhD Advisors, IRPHE), S. Le Dizès (IRPHE)
The elliptical
instability can take place in planetary cores and stars elliptically
deformed by gravitational effects, where it generates largescale
threedimensional 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 nonlinear 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
isovelocity 23% (parameters: 2.5 rotations, equatorial axes ratio
b/a=0.72, polar axis c=0.65, E=6.66e4, Pm=0.1 and Elsasser number of
1e3).
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, 45. 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. 130158. 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 socalled megatsunamis, 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 twophase finitevolume
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, 747762. PDF
 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 socalled 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 DDYNA
explicit code, offer some functionality to deal with the slamming
problem; the underlying methodology is based on the
socalled ArbitraryLagrangianEulerian (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 opensource 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
halffull 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, 747762. PDF
 D. Cebron, JF. Sigrist,
2008. Toward a 2D SPH
multiphysic code with solidsolid & fluid interactions for
industrial related problems. Proceedings
of the 8th Int. Conf. on Hydrodynamics. Nantes, France. PDF