Quasi-geostrophic kinematic dynamos at low magnetic Prandtl number

Rapidly rotating spherical kinematic dynamos are computed using the combination of a quasi geostrophic (QG) model for the velocity field and a classical spectral 3D code for the magnetic field. On one hand, the QG flow is computed in the equatorial plane of a sphere and corresponds to Rossby wave instabilities of a geostrophic internal shear layer produced by differential rotation. On the other hand, the induction equation is computed in the full sphere after a continuation of the QG flow along the rotation axis. Differential rotation and Rossby-wave propagation are the key ingredients of the dynamo process which can be interpreted in terms of $\alpha\Omega$ dynamo. Taking into account the quasi geostrophy of the velocity field to increase its time and space resolution enables us to exhibit numerical dynamos with very low Ekman (rapidly rotating) and Prandtl numbers (liquid metals) which are asymptotically relevant to model planetary core dynamos

Quasi-geostrophic model of the instabilities of the Stewartson layer

We study the destabilization of a shear layer, produced by differential rotation of a rotating axisymmetric container. For small forcing, this produces a shear layer, which has been studied by Stewartson and is almost invariant along the rotation axis. When the forcing increases, instabilities develop. To study the asymptotic regime (very low Ekman number $E$), we develop a quasi-geostrophic two-dimensional model, whose main original feature is to handle the mass conservation correctly, resulting in a divergent two-dimensional flow, and valid for any container provided that the top and bottom have finite slopes. We use it to derive scalings and asymptotic laws by a simple linear theory, extending the previous analyses to large slopes (as in a sphere), for which we find different scaling laws. For a flat container, the critical Rossby number for the onset of instability evolves as $E^{3/4}$ and may be understood as a Kelvin-Helmoltz shear instability. For a sloping container, the instability is a Rossby wave with a critical Rossby number proportional to $\beta E^{1/2}$, where $\beta$ is related to the slope. We also investigate the asymmetry between positive and negative differential rotation and propose corrections for finite Ekman and Rossby numbers. Implemented in a numerical code, our model allows us to study the onset over a broad range of parameters, determining the threshold but also other features such as the spatial structure. We also present a few experimental results, validating our model and showing its limits.Comment: 28 pages, 15 figures. * New version including discussion of the recent work of Hollerbach, and much more. * A sign error in the Ekman pumping has been corrected. This has almost no influence on the results presented in the previous versio

A versatile biomimetic controller for contact tooling and haptic exploration

International audienceThis article presents a versatile controller that enables various contact tooling tasks with minimal prior knowledge of the tooled surface. The controller is derived from results of neuroscience studies that investigated the neural mechanisms utilized by humans to control and learn complex interactions with the environment. We demonstrate here the versatility of this controller in simulations of cutting, drilling and surface exploration tasks, which would normally require different control paradigms. We also present results on the exploration of an unknown surface with a 7-DOF manipulator, where the robot builds a 3D surface map of the surface profile and texture while applying constant force during motion. Our controller provides a unified control framework encompassing behaviors expected from the different specialized control paradigms like position control, force control and impedance control

The EU Center of Excellence for Exascale in Solid Earth (ChEESE): Implementation, results, and roadmap for the second phase

publishedVersio

S2 magnetic field movie

Magnetic field in a 3D turbulent geodynamo simulation (intensity in the core and radial field at the surface).</p

S2 temperature movie

Temperature anomaly in a 3D turbulent geodynamo simulation.</p

Simulations of the Earth's magnetic field and length-of-day variations

The Earth's core, mostly made of liquid iron, is stirred by convection which leads to our magnetic field.<br>These movements can also transport angular momentum and exchange it with the solid mantle, inducing variations in the length of day.<br>I will present recent simulations of the dynamics of the core and of the magnetic field, and the implications for the both the core-mantle boundary and the length-of-day variations.<br

Temperature field in the equatorial plane of the Earth's core from a high resolution numerical simulation

Snapshot of temperature field in the equatorial plane of the Earth's core, from a high resolution simulation employing spherical harmonics up to degree 893 and 1024 radial levels.<br>The Ekman number is E=nu/(D^2.Omega) = 10^(-7) and the magnetic Prandtl number is Pm=nu/eta=0.

Inertial waves propagation associated to a localized radial force

<p>This movie shows the vertical velocity (along the rotation axis, which is the vertical axis on the left hand side of the figure)</p> <p>In a spherical shell filled with fluid, a localized body force (gaussian profile) is applied where the column starts. It appears that inertial waves propagate from this point, and as time passes, only the lowest frequency inertial waves are left, which form a Taylor column.</p> <p>See the link below for another viewpoint.</p