Daniel Brito

A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium

Abstract Results of finite-amplitude convection experiments in a rotating spherical shell are presented. Water (Prandtl number P=7) and liquid gallium (P=0.027) have been used as working fluids. In both liquids, convective velocities could be measured in the equatorial plane using an ultrasonic Doppler velocimetry technique. The parameter space has been systematically explored, for values of the Ekman and Rayleigh numbers E>7×10−7 and Ra

Mechanics of inner core super-rotation

A mechanism is proposed to explain the seismologically-inferred prograde rotation of the Earths solid inner core in terms of the structure of convection in the fluid outer core. Numerical calculations of convection and dynamo action in the outer core exhibit excess temperatures inside the tangent cylinder surrounding the inner core. We show that this temperature difference generates a prograde thermal wind and a strong azimuthal magnetic field inside the tangent cylinder. Electromagnetic torques on the inner core derived from induced azimuthal magnetic fields and the ambient poloidal field equilibrate when the inner core angular velocity lags the nearby tangent cylinder fluid angular velocity by approximately 14%. The inferred prograde rotation of the inner core (1.1–3°/year relative to the mantle) can be produced by a very small (⋍ 0.001 K) temperature anomaly within the tangent cylinder and indicates strong toroidal magnetic fields with peak intensities of 24–66 mT in that region of the core.

Experimental study of super-rotation in a magnetostrophic spherical Couette flow

We report measurements of electric potentials at the surface of a spherical container of liquid sodium in which a magnetized inner core is differentially rotating. The azimuthal angular velocities inferred from these potentials reveal a strong super-rotation of the liquid sodium in the equatorial region, for small differential rotation. Super-rotation was observed in numerical simulations by Dormy et al. (Dormy, E., Cardin, P. and Jault, D., MHD flow in a slightly differentially rotating spherical shell, with conducting inner core, in a dipolar magnetic field, Earth Planet. Sci. Lett., 1998, 160, 15--30). We find that the latitudinal variation of the electric potentials in our experiments differs markedly from the predictions of a similar numerical model, suggesting that some of the assumptions used in the model – steadiness, equatorial symmetry, and linear treatment for the evolution of both the magnetic and velocity fields – are violated in the experiments. In addition, radial velocity measurements, using ultrasonic Doppler velocimetry, provide evidence of oscillatory motion near the outer sphere at low latitude: it is viewed as the signature of an instability of the super-rotating region.

Rotating spherical Couette flow in a dipolar magnetic field : experimental study of magneto-inertial waves

The magnetostrophic regime, in which Lorentz and Coriolis forces are in balance, has been investigated in a rapidly rotating spherical Couette flow experiment. The spherical shell is filled with liquid sodium and permeated by a strong imposed dipolar magnetic field. Azimuthally travelling hydromagnetic waves have been put in evidence through a detailed analysis of electric potential differences measured on the outer sphere, and their properties have been determined. Several types of waves have been identified depending on the relative rotation rates of the inner and outer spheres: they differ by their dispersion relation and by their selection of azimuthal wavenumbers. In addition, these waves constitute the largest contribution to the observed fluctuations, and all of them travel in the retrograde direction in the frame of reference bound to the fluid. We identify these waves as magneto-inertial waves by virtue of the close proximity of the magnetic and inertial characteristic time scales of relevance in our experiment.

Experimental evidence of inertial waves in a precessing spheroidal cavity

We have demonstrated experimentally the ex- istence of inertial waves in a slowly precessing spheroid of fluid. Although such oscillatory internal shear layers have been predicted theoretically and numerically, previous pre- cessionexperimentshadshownnoevidenceoftheirpresence. Using an ultrasonic Doppler velocimetry technique, proles of radial velocity have been measured in our precession ex- periment. Comparison of these proles with their synthetic counterparts obtained numerically, proves the presence of the predicted internal shear layers. They are emitted from the breakdown of the Ekman layer at the two critical lat- itudes of the fluid (around 30 and 30) and propagate through the entire volume on conical surfaces. The asymp- totic laws for these oscillatory layers, conrmed experimen- tally and numerically, lead us to predict an oscillatoryflow of 10 6 m/s along such characteristic cones in the Earths

Anomalous rotation of the inner core and the toroidal magnetic field

We use numerical calculations of magnetic induction by axisymmetric motions in a spherical shell of conducting fluid to investigate the relationship between the Earths toroidal magnetic field and the time-dependent anomalous rotation of the solid inner core. We compute the induced toroidal magnetic field and inner core rotation maintained by the interaction of time-independent, axisymmetric outer core fluid flow with models of the poloidal magnetic field. Three possible models of the azimuthal flow in the outer core are investigated: two thermal wind flows inside the tangent cylinder (predicted by some numerical models of the geodynamo) and a columnar flow outside the inner core tangent cylinder inferred from the geomagnetic westward drift. Results indicate that electromagnetic torques tightly couple the inner core rotation to the fluid motion. Electromagnetic spin-up of the inner core occurs through damped torsional oscillations with periodicity near 4 years depending on the strength of the poloidal magnetic field. In steady state the thermal winds inside the tangent cylinder generate a peak toroidal field of 25 mT accompanying a prograde inner core rotation rate of 1°/yr. In contrast, the columnar westward drift model generates toroidal field with peak intensity near 4 mT and a small, retrograde anomalous inner core rotation of −0.013°/yr. The weak retrograde motion of the inner core produced by electromagnetic coupling to the westward drift cannot explain the seismically inferred prograde anomalous rotation.

Rapidly rotating spherical Couette flow in a dipolar magnetic field: An experimental study of the mean axisymmetric flow

Abstract In order to explore the magnetostrophic regime expected for planetary cores, in which the Lorentz forces balance the Coriolis forces, experiments have been conducted in a rotating sphere filled with liquid sodium, with an imposed dipolar magnetic field (the DTS setup). The field is produced by a permanent magnet enclosed in an inner sphere, which can rotate at a separate rate, producing a spherical Couette flow. The flow properties are investigated by measuring electric potentials on the outer sphere, the induced magnetic field in the laboratory frame just above the rotating outer sphere, and velocity profiles inside the liquid sodium using ultrasonic Doppler velocimetry. This article focuses on the time-averaged axisymmetric part of the flow. The electric potential differences measured at several latitudes can be linked to azimuthal velocities, and are indeed found to be proportional to the azimuthal velocities measured by Doppler velocimetry. The Doppler profiles show that the angular velocity of the fluid is relatively uniform in most of the fluid shell, but rises near the inner sphere, revealing the presence of a “magnetic wind”, and gently drops towards the outer sphere. The transition from a magnetostrophic flow near the inner sphere to a geostrophic flow near the outer sphere is controlled by the local Elsasser number. For Rossby numbers up to order 1, the observed velocity profiles all show a similar shape. Numerical simulations in the linear regime are computed, and synthetic velocity profiles are compared with the measured ones. A good agreement is found for the angular velocity profiles. In the geostrophic region, a torque-balance model provides very good predictions. Radial velocities change sign with the Rossby number, as expected for an Ekman-pumping dominated flow. For a given Rossby number the amplitude of the measured angular velocity is found to vary by as much as a factor of 3. Comparison with numerical simulations suggests that this is due to variations in the electric coupling between liquid sodium and the inner copper sphere, implying an effect equivalent to a reduction of the inner sphere electric conductivity by as much as a factor 100. We show that the measured electric potential difference can be used as a proxy of the actual fluid velocity. Using this proxy in place of the imposed differential velocity, we find that the induced magnetic field varies in a consistent fashion, and displays a peculiar peak in the counter-rotating regime. This happens when the fluid rotation rate is almost equal and opposite to the outer sphere rotation rate. The fluid is then almost at rest in the laboratory frame, and the Proudman–Taylor constraint vanishes, enabling a strong meridional flow. We suggest that dynamo action might be favored in such a situation.

Can heterogeneous core–mantle electromagnetic coupling control geomagnetic reversals?

Abstract An analytical model is developed for the electromagnetic torques exerted on the mantle by the poloidal magnetic field of the core interacting with a laterally heterogeneous conducting layer at the base of the mantle. Torques due to changes in both orientation and intensity of a dipolar poloidal field are included. Contrary to earlier suggestions, our calculations predict that the trajectory of the magnetic pole during a polarity reversal is not strongly affected by heterogeneity in mantle electrical conductivity.

Experimental crystallization of gallium: ultrasonic measurements of elastic anisotropy and implications for the inner core

We present ultrasonic measurements of elastic anisotropy in gallium undergoing directional solidification in the presence of imposed thermal gradients, rotation, convection, turbulence, and magnetic fields. Simultaneous in situ measurements of temperature and compressional wave speed are used to track the crystallization front during solidification. We find that individual solidified gallium samples are always polycrystalline and elastically anisotropic, with grains elongated in the solidification direction. The measured compressional wave anisotropy in individual solid samples ranges from 20 to 80% of the single crystal values, depending on experimental conditions. We also find the amount of elastic anisotropy varies with position in an individual sample. Based on ensemble averages from multiple experiments made under similar environmental conditions, we find the direction of elastic anisotropy in the solid is sensitive to the thermal gradient direction, while the amount of anisotropy is most sensitive to the presence or absence of initial nucleation in the melt. Experiments that show average anisotropy have the ultrasonically fast axis aligned with gravity and the thermal gradient. Strongly anisotropic solids result when nucleation grains are present in the initial melt, whereas smaller or zero average anisotropy results when nucleation grains are initially absent. Other externally imposed factors we have examined, such as turbulence and magnetic fields, have either no measurable influence or tend to reduce the amount of anisotropy of the solid. Our results suggest that during crystallization of Earth’s inner core, the orientation of average anisotropy in the newly formed solid is controlled primarily by radial solidification, while the amount of anisotropy may be influenced by pre-existing inner core texture.

Experimental quantification of the seismoelectric transfer function and its dependence on conductivity and saturation in loose sand

ABSTRACT Under certain circumstances, seismic propagation within porous media may be associated to the conversion of mechanical energy to electromagnetic energy, which is known as a seismo‐electromagnetic phenomenon. The propagation of fast compressional P‐waves is more specifically associated to the manifestations of a seismoelectric field linked to the fluid flows within the pores. The analysis of seismoelectric phenomena, which requires the combination of the theory of electrokinetics and Biots theory of poroelasticity, provides us with transfer function Symbol that links the coseismic seismoelectric field E to the seismic acceleration Symbol. To measure the transfer function, we have developed an experimental setup enabling seismoelectric laboratory observation in unconsolidated quartz sand within the kilohertz range. The investigation focused on the impact of fluid conductivity and water saturation over the coseismic seismoelectric field. During the experiment, special attention was given to the accuracy of electric field measurements. We concluded that, to obtain a reliable estimate of the electric field amplitude, the dipole from which the potential differences are measured should be of much smaller length than the wavelength of the propagating seismic field. Time‐lapse monitoring of the seismic velocities and seismoelectric transfer functions were performed during imbibition and drainage experiments. In all cases, the quantitative analysis of the seismoelectric transfer function Symbol was in good agreement with theoretical predictions. While investigating saturation variations from full to residual water saturation, we showed that the Symbol ratio undergoes a switch in polarity at a particular saturation Symbol, which also implies a sign change of the filtration, traducing a reversal of the relative fluid displacement with respect to the frame. This sign change at critical saturation Symbol stresses a particular behaviour of the poroelastic medium: the dropping of the coseismic electric field to zero traduces the absence of relative pore/fluid displacements representative of a Biot dynamically compatible medium. We concluded from our experimental study in loose sand that the measurements of the coseismic seismoelectric coupling may provide information on fluid distribution within the pores and that the reversal of the seismoelectric field may be used as an indicator of the dynamically compatible state of the medium. Symbol. No Caption available. Symbol. No Caption available. Symbol. No Caption available. Symbol. No Caption available. Symbol. No Caption available. Symbol. No Caption available.