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

Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model

We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ($Pr\in[10^{-2},10^{-1}]$). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds number of the flow is greater than $10^3$, and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed near the onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$.Comment: 30 pages, 16 figures, published in JF

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

Thermal convection in Earth's inner core with phase change at its boundary

Inner core translation, with solidification on one hemisphere and melting on the other, provides a promising basis for understanding the hemispherical dichotomy of the inner core, as well as the anomalous stable layer observed at the base of the outer core - the F-layer - which might be sustained by continuous melting of inner core material. In this paper, we study in details the dynamics of inner core thermal convection when dynamically induced melting and freezing of the inner core boundary (ICB) are taken into account. If the inner core is unstably stratified, linear stability analysis and numerical simulations consistently show that the translation mode dominates only if the viscosity $\eta$ is large enough, with a critical viscosity value, of order $3 10^{18}$ Pas, depending on the ability of outer core convection to supply or remove the latent heat of melting or solidification. If $\eta$ is smaller, the dynamical effect of melting and freezing is small. Convection takes a more classical form, with a one-cell axisymmetric mode at the onset and chaotic plume convection at large Rayleigh number. [...] Thermal convection requires that a superadiabatic temperature profile is maintained in the inner core, which depends on a competition between extraction of the inner core internal heat by conduction and cooling at the ICB. Inner core thermal convection appears very likely with the low thermal conductivity value proposed by Stacey & Davis (2007), but nearly impossible with the much higher thermal conductivity recently put forward. We argue however that the formation of an iron-rich layer above the ICB may have a positive feedback on inner core convection: it implies that the inner core crystallized from an increasingly iron-rich liquid, resulting in an unstable compositional stratification which could drive inner core convection, perhaps even if the inner core is subadiabatic.Comment: 25 pages, 12 figure

Quasi-geostrophic kinematic dynamos at low magnetic Prandtl number

International audienceRapidly rotating spherical kinematic dynamos at very low Ekman and Prandtl numbers 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. The QG flow is computed in the equatorial plane of the sphere; it corresponds to Rossby wave instabilities of a geostrophic internal shear layer produced by differential rotation. The induction equation is computed in the whole sphere after the QG flow has been expanded along the rotation axis. Differential rotation and Rossby wave propagation are the key ingredients of this dynamo which can be interpreted in terms of Parker-[Omega] dynamo. Taking into account the quasi-geostrophy of the velocity field enables us to increase time and space resolution to compute the dynamics. For the first time, we report on numerical dynamos with very low Ekman numbers (10- 8). Because the magnetic and velocity fields are computed on different grids, we compute dynamos for very low magnetic Prandtl numbers exhibiting a scale separation between magnetic and velocity field. These dynamos are asymptotically close to rapidly rotating, metallic planetary cores

On the reflection of Alfvén waves and its implication for Earth's core modelling

Alfvén waves propagate in electrically conducting fluids in the presence of a magnetic field. Their reflection properties depend on the ratio between the kinematic viscosity and the magnetic diffusivity of the fluid, also known as the magnetic Prandtl number Pm. In the special case, Pm = 1, there is no reflection on an insulating, no-slip boundary, and the incoming wave energy is entirely dissipated in the boundary layer. We investigate the consequences of this remarkable behaviour for the numerical modelling of torsional Alfvén waves (also known as torsional oscillations), which represent a special class of Alfvén waves, in rapidly rotating spherical shells. They consist of geostrophic motions and are thought to exist in the fluid cores of planets with internal magnetic field. In the geophysical limit Pm ≪ 1, these waves are reflected at the core equator, but they are entirely absorbed for Pm = 1. Our numerical calculations show that the reflection coefficient at the equator of these waves remains below 0.2 for Pm ≥ 0.3, which is the range of values for which geodynamo numerical models operate. As a result, geodynamo models with no-slip boundary conditions cannot exhibit torsional oscillation normal mode

Seismic response and anisotropy of a model hcp iron inner core

International audienceWe present a framework for simulating the measurement of seismic anisotropy in a model inner core by computing travel time residuals of synthetic seismic rays propagated through the model. The method is first tested on simple inner core structural models consisting of layers with distinct anisotropy, as often proposed in the literature. Those models are not consistent with geodynamics. Hence, we extend the method to a numerically grown inner core composed of ε-Fe with flow generated from an excess of crystallization in the equatorial belt, inducing polycrystalline textures. The global inner core anisotropy is 7 times smaller than that of the single crystal. Compositional stratification amplifies the global anisotropy by 15% while the addition of solidification textures reduces it by a factor of 2. As such, and within the tested geodynamical models, no published elastic model of ε-Fe at inner core conditions allows for reproducing the 3% cylindrical anisotropy reported in seismology publications. In addition, our models demonstrate that additional information such as the depth dependence and the spread of the observed anisotropy is a key for revealing the dynamics and history of the inner core

Magneto–Coriolis waves in a spherical Couette flow experiment

International audienceThe dynamics of fluctuations in a fast rotating spherical Couette flow experiment in the presence of a strong dipolar magnetic field is investigated in detail, through a thorough analysis of the experimental data as well as a numerical study. Fluctuations within the conducting fluid (liquid sodium) are characterized by the presence of several oscillation modes, identified as magneto-Coriolis (MC) modes, with definite symmetry and azimuthal number. A numerical simulation provides eigensolutions which exhibit oscillation frequencies and magnetic signature comparable to the observation. The main characteristics of these hydromagnetic modes is that the magnetic contribution has a fundamental influence on the dynamical properties through the Lorentz forces, although its importance remains weak in an energetical point of view. Another specificity is that the Lorentz forces are confined near the inner sphere where the dipolar magnetic field is the strongest, while the Coriolis forces are concentrated in the outer fluid volume close to the outer sphere

Towards a rapidly rotating liquid sodium dynamo experiment

The main characteristics of the Earth's dynamo are reviewed. The combined actions of Coriolisand Lorentz forces lead to the so--called ``magnetostrophic'' regime. We derive an estimate of the power needed to sustain the magnetic field in this regime. We show that an experimentwith liquid sodium can be designed to operate in the magnetostrophic regime. Such an experiment would bring most valuable informations on the mechanisms of planetary dynamos. In order toprepare this large--scale experiment and explore the magnetostrophic balance, a smaller scale liquid sodium set--up has been designed and is being built. It consists of a rapidly rotating spherical shell filled with liquid sodium, in which motions are set by spinning at a different rotation rate an inner core permeated by a strong magnetic field. We discuss the processes that can be explored with this new device

188: Prevalence of early repolarization in congenital long QT syndrome A combination of early and delayed repolarization

Introductionearly repolarization (ER) in Brugada or short QT syndrome is common and has been associated to a less favourable outcome. Even if apparently paradoxical, ER can also be seen in long QT (LQT) but prevalence and correlations to other variables are unknown.Methods12 lead ECG of 37 LQT pts (19 men, 39±21 yo) and 80 matched controls were reviewed. LQT pts were selected by a positive genetic testing (n=27) or by showing abnormal T wave and long QT interval (n=10) either spontaneously or during epinephrin infusion. ER was defined by >1mm J point elevation in the inferior or lateral leads with notch or slurring pattern. Presence of ER was correlated to the clinical and ECG characteristics and results genetic analysis.ResultsQT was 409±53 msec in pts and 372±24 in controls (p<0.0001) (QTc 476±52 vs 392±26 msec, p<0.0001). Two LQT pts presented with resuscitated sudden death and 4 with syncope at the time of diagnosis.14/37 LQT pts (38%) had ER compared to 17/80 (21%) controls (p=0.05).ER was more frequent in men (12/19, 63%) compared to women (2/18, 11%) (p=0.001) but was not correlated to age. Pts with ER had slower heart rate (63±10 vs 75±18 bpm, p=0.02).ER was not correlated to symptoms or cardiac events (no ER in the 2 pts with SD and in 2/4 pts with syncope).QT were longer in pts with ER (450±68 vs 397±54 msec in V2, p=0.01) but there was no correlations between ER and corrected QT intervals.ER was more often seen in pts with or without mutations although non significantly (8/27 vs 6/10, p=0.09), but there was a trend toward more frequent ER in case of HeRG mutations (6/12) than KCNQ1 or KCNJ2 mutations (2/11 and 0/4) (p=0.09).ConclusionER is very common in LQT pts and is related to the gender and to the heart rate but not to the corrected QT duration. ER does not seem to be correlated to cardiac events in this series but may be linked to some gene mutations. Further studies are needed for demonstrating additional mutations/ variants or the existence of an early transient voltage gradient due to altered kinetics in muted potassium channels with loss of function