PhD position : Dynamo capable flows driven by coupled mechanical forcings and topographic effect

– Grant : Allocation MRE
– Fields : Geophysics, Fluid Mechanics
– Openings : Academia, applied research

It is a commonly accepted hypothesis that buoyancy drives planetary dynamos. Indeed, on Earth, the prevalent model is that the current magnetic field comes from thermochemical convective motions within the conducting liquid core. However, the validity of this model in certain planets can be questioned, as for instance the Early Moon or Earth, Ganymede, Mercury and certain asteroid such as Vesta. Moreover, the short magnetic cycle observed in certain hot-Jupiter systems, as -boo, are thought to be due to tidal forces, but the underlying physical mechanism remains unclear.

Alternative mechanisms, based on mechanical forcings (precession/nutation, libration, or tides), have been proposed (e.g. Malkus 1968), but their dynamo capabilities remains unknown. . Besides, even in planets where the dynamo is of convective origin, additional driving mechanisms may significantly modify the organization of fluid motions, and then heat transport or intern dissipation. In particular, topographic effects (i.e. pressure torques generated by boundaries on a fluid layer) are expected to play a key role in planetary liquid cores and subsurface oceans flow dynamics. However, their study requires to consider a non-spherical fluid layer, which is a real difficulty for theoretical calculations, as well as efficient numerical simulations (spectral code). Even a small departure from sphere can lead to vigorous large scale flows, which remains thus badly known.

We propose here to tackle this problem by considering two cases : (i) fluid layers of terrestrial planets, where the core-mantle boundary is rather ellipsoidal than spherical, and (ii) the stars, or gaseous planets, where the boundary is a free surface. We aim at combining theoretical approaches, allowing the study of the linear regime of the considered flows, with numerical simulations, allowing to characterize the fate of these flows in the non-linear, or even turbulent, regime.

The theoretical approach relies on both local and global stability methods. Generalizing the recent work of Hattori&Fukumoto (2012), the local analysis will extend these works to arbitrary unsteady 3D flows. The global stability study will first rely on polynomial modes (large deformation of ellipsoidal celestial bodies), and then on gravito-inertial modes (small deformations of arbitrary shape). The formers will allow to revisit the classical results of ellipsoidal figures of equilibrium (Chandrasekhar, 1969) in a dynamical framework, whereas the latters will allow to predict possible triadic resonances on a weakly deformed free surface. These calculations may lead to collaborations with W. Herreman (LIMSI, Orsay) or M. Rieutord (IRAP, Toulouse).

Concerning the numerical simulations, we will rely on the code XSHELLS (spherical), developed at ISTerre by N. Schaeffer (Schaeffer, 2013). Extending XSHELLS to ellipsoids will allow to benefit from its tremendous efficiency to study flows well beyond the laminar regime considered by the few existing studies (Ernst-Hullerman et al. 2013 ; Cébron&Hollerbach 2014), i.e. flows closer from the geophysical and astrophysical regimes. This is an important challenging extension given that no code can currently solve efficiently this kind of flows in such geometries, which are much closer from planets and stars. Two approaches are envisaged. First, we can describe a simple deformation of the sphere using a metric (and then rewrite the equations in this new generalized coordinates system). Second, we can keep the spherical shape and perturbate the flow to mimic an arbitrary topography.

This PhD thesis is directly linked with the general topic “topographic coupling” currently investigated within the group Geodynamo. It will thus be possible, for the PhD student, to collaborate on various projects currently developed in the group, either theoretical ones (with D. Jault) or experimental ones (EDEN project, with H.-C. Nataf).

At the frontier between fluid mechanics and geophysics, this work will lead the PhD student to code in C/C++ and/or Python, and to use computer algebra code ; the required skills range thus from code development to the use of mathematical methods used in fluid mechanics.

**References

– Cébron & Hollerbach, 2014. Elliptical instability driven dynamo in sphere. In prep.
– Chandrasekhar, 1969. Ellipsoidal figures of equilibrium. Yale University Press ; 1st edition : 253p.
– Ernst-Hullermann, Harder, Hansen, 2013. Finite volume simulations of dynamos in ellipsoidal planets. Geophys. J. Int. 195:1395-1405.
– Hattori&Fukumoto, 2012. Effects of axial flow on the stability of a helical vortex tube. Phys. Fluids. 24, 054102.
– Malkus, 1968. Precession of the Earth as the cause of geomagnetism. Science 160:259-264.
– Schaeffer, 2013. Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations. Geochem. Geophys. Geosyst., 14, 751–758.