GP43A-0790
Geodynamo, Core Energy, Precession, and Spheroids
Mantle precession and core oblateness have been suggested for support of geodynamo energy dissipation and fluid motions. Precession usually has been considered negligible. With a precession motion of 25,800 year/period and a period of 60x360 = 21,600 arc-minute, the motion is on the order of one arc-minute/year (little off by the sine of Earth's obliquity). The 'rigid' mantle changes its axis direction about one arc-minute each year. That is a major motion. Compare the sun's or the moon's apparent diameter of about 32 arc- minute. The CMB's oblateness is about (a-b)/a = 1/400. With (a-b) = 8.7 km, and estimates of its surface irregularities over 3 km, the CMB is neither smooth nor oblate. Between its 'calculated' oblate CMB and a 'calculated' included sphere, its very thin crescentoid interstice will generate turbulence and separation form drag with large dissipation energy rates. The actual core will not see the CMB but an effective smaller fluid sphere. Precession is an important feature of a geodynamo, but 1/400 oblateness is less pertinent. The core axis lags the precessing mantle axis by a small angle. This misalignment daily rubs the core against the mantle and produces major energy dissipation rates. The liquid core maintains its average lagging location by coupling drag and core internal flows. A correct analysis will use a 'rigid-sphere' model (1972 ref.) for energy, geodynamo, and coupling motion. The outer core is a melt whose temperature and heat are well known but not its cause. Some will be residual heat, but much of it will be generated by precession and radioactivity. Rigid-sphere energy (J. Appl. Mech. 1972, v39, 18-24). Geodynamo precession (Geo. Astro. Fluid Dyn. 1991, v59, 209-234). Turbulent laminar flow (Geophys. J. Intl., 1995, v121, 136-142). Concentric cylinders (Geophys. J. Intl., 2000, v142, 409-425). Core mantle coupling (Geophys. J. Intl., 2004, v158, 470-478). Theory and data (Rotating Fluids , 2001, Dover, Figs. 4.5, 4.10 and pp. 326, 397).
GP43A-0791
Fluctuation of Convection Pattern in Liquid Metal Under Uniform Magnetic Field
The convective flow in the outer core of the Earth is supposed to be extremely turbulent, because molten iron has very low viscosity and the spatial scale is large. It is important for the outer core dynamics that the flow behaves turbulently under the influence of rotation and magnetic field. In many numerical dynamo simulations, the values of Prandtl number and magnetic-Prandtl number are set around one, but these values for liquid metals are much smaller than one actually. Laboratory experiment using liquid metal is a useful way for studying highly turbulent flow system with such low Prandtl number, though it is difficult to realize self-sustained dynamo action. We use the Ultrasonic Velocity Profiler method to measure the fine- scale velocity field of the flow occurring in the liquid metal. We succeeded in the direct measurement of velocity profile for the Rayleigh-Benard convection in liquid gallium, with and without external uniform magnetic field. The geometry of the container is a square one, and the system is not rotating. Under no magnetic field, large-scale flow pattern is clearly observed, and it is interpreted as a kind of organized structure of turbulence. The remarkable feature of this large-scale flow is its fluctuation. It shows clearly regular periodic behavior, whose typical timescale is comparable to the circulation time of the mean flow. When we apply horizontal magnetic field, the large-scale flow is reorganized as two-dimensional roll with its axis to become parallel to the direction of the magnetic field. With the increase of the intensity of the applying magnetic field, the periodic components of the flow are reduced remarkably and the mean velocity of the roll-like flow pattern is increased. At the same time, fluctuation with much longer timescale is observed, which is characterized by the reversal of the flow direction of the two- dimensional roll. The reversal occurs randomly and it may give an insight to the outer core dynamics.
GP43A-0792
Boundary-modulated Thermal Convection Model in the Mantle
Analog experiments have played an important role in the constructing ideas of mantle dynamics. The series of experiments by H. Ramberg is one of the successful examples. Recently, however the realm of the analog experiments seems to be overwhelmed by steady progress of computer simulations. Is there still room for the analog experiments? This might be a main and hidden subject of this session. Here we propose a working hypothesis how the convecting mantle behaves based on the analog experiments in the system of viscous fluid and particles. The essential part is the interaction of convecting flow with heterogeneities existing in the boundaries. It is proposed the preexisting topographical heterogeneity in the boundary could control the flow pattern of convecting fluid. If this kind of heterogeneity can be formed as a consequence of convective motion and mobilized by the flow, the convection also can control the heterogeneity. We can expect interactions in two ways, by which the system behaves in a self-organize fashion. To explore the mutual interactions between convection flow and heterogeneity the system of viscous fluid and particles with slightly higher density is selected as 2D Rayleigh-Benard type convection. The basic structure consists of a basal particulate layer where permeable convection transports heat and an upper viscous fluid layer. By reducing the magnitude of the density difference the convective flow can mobilize the particles and can erode the basal layer. The condition of this erosion can be identified in the phase diagram of the particle Shieldsf and the Rayleigh numbers. At Ra greater than 107 the convection style drastically changed before and after the erosion. Before the erosion where the flat interface of the boundary is maintained small scaled turbulent convection pattern is dominant. After the erosion where the interface becomes bumpy the large scale convective motion is observed. The structure is coherent to that of the boundary. This is a good example of the consequence of mutual interactions between convective flow and the heterogeneity in boundary. We propose this is a basic framework of the mantle dynamics which can reconcile apparent discrepancy between observed seismic signatures and corresponding convective motion. As a conclusion we would like to emphasize the analog experiments is a useful tool for developing/breeding new ideas.
GP43A-0793
Quasi-Geostrophic Motions in the Earth's Core: in What Conditions are They Expected?
Geostrophic motions travelling as Alfvén waves have been shown recently (Jault, 2008) to
arise spontaneously among the transient axisymmetric motions generated by an impulsive forcing
in a rapidly rotating spherical cavity permeated by an axisymmetric magnetic field. We
generalize this result to the non axisymmetric case. We seek to give the range of length and
time scales in which quasi-geostrophic motions account for the main part of the Earh's
core
dynamics.
Assuming quasi-geostrophy, we write the 2D model that governs the evolution of the magnetic
potential and the velocity stream function. That gives insight in the 2D MHD turbulence that
takes place in the Earth's core.
http://www-lgit.obs.ujf-
grenoble.fr/~vsqg/
GP43A-0794
A Comparison of Experiments and Large Eddy Simulations of Spherical Couette Flow in Liquid Sodium
Fluid flow and magnetic field in the Earth's outer core are distributed over a vast range of length scales. Limits in computational capability prevent numerical simulations from including the full range of scales, so sub-grid scale (SGS) models are required to account for the effects of the unresolved fields on the large scale fields in geodynamo simulations. Verification of the SGS model is an important challenge because we cannot observe the fluid motion and small scale magnetic field in the outer core. In the present study, we compare the results of Couette experiments in liquid sodium with magnetohydrodynamic (MHD) simulations that employ a dynamic scale similarity SGS model. Our laboratory experiment is a spherical Couette cell, 60 cm in diameter, with a 20 cm inner sphere, yielding Earth-like geometry. Liquid sodium fills the gap, and fluid motions are driven by differential rotation of the two spheres. We impose an axial external magnetic field and measure the magnetic induction produced by those fluid motions using an array of 30 Hall probes outside the cell. Projecting their measurements onto the vector spherical harmonics, we produce Gauss coefficients up to degree four. In the numerical model, we perform a large eddy MHD simulation in a rotating spherical shell, based on the dimensions of the experiment. The dynamic scale similarity model is used for the relevant SGS terms: momentum flux, Lorentz force, and magnetic induction. We evaluate the gauss coefficients for the induced magnetic field outside the shell in the simulations with and without SGS model, and compare with the gauss coefficient obtained by the experiment to investigate contribution of the SGS terms to the behaviors of the large scale magnetic field.
GP43A-0795
Numerical simulation and modelling of experimental dynamos
The recent success of the VKS dynamo provides a new way to investigate dynamo action in turbulent conducting flows. We present results of 3D direct numerical simulations for different flow geometries used to try to generate experimental dynamos. In the case of the VKS experiment, we show how boundaries with a high magnetic permeability lead to a significant decrease of the critical magnetic Reynolds number, thus allowing the observation of dynamo action. We also understand the mechanism leading to experimentally observed geometries of the magnetic field without using any ad hoc mean field equation. In the case of the geometry of the Madison experiment, we show different mechanisms by which Cowling theorem can be by-passed, thus leading to a mean magnetic field with a strong axial dipolar component instead of the predicted equatorial dipole. This competition between axial and equatorial dipoles could also account for secular variations of the Earth magnetic field.
GP43A-0796
Laboratory Models of Librationally-Driven Flow in Planetary Core and Sub-Surface Oceans.
Many planetary bodies, including Mercury and the moon, undergo forced longitudinal librations. Yet few studies to date have investigated how longitudinal libration, the oscillatory motion of a planet around its rotation axis, couples with its interior planetary fluid dynamics. In the present study, we investigate, via laboratory experiments, the flow in a spherical rotating fluid cavity driven by an axial oscillation of the container. Here we consider the viscous coupling between the solid outer shell and the liquid interior, focussing on libration frequencies less than or equal to the planetary rotation frequency, moderate Ekman numbers (E=10-4 to 10-5) and Rossby numbers between 0.03 and 5. In addition, we model flow in three different core geometry: full sphere; rinner~eq0.6 router; and rinner~eq0.9 router. Direct flow visualizations in the laboratory experiment allows us to identify 3 distinct flow regimes: i) a stable regime dominated by inertial waves; ii) a longitudinal rolls instability regime; and iii) a boundary turbulence regime. The longitudinal rolls are initiated in the vicinity of the equator and are qualitatively similar to Taylor and Taylor-Görtler instabilities. Interior flow visualizations have shown that the longitudinal roll instability remains confined to a layer of fluid near the outer wall. In addition, we do not observe any noticeable effect of the inner core size. Extrapolating our results to planetary conditions suggest that librationaly driven turbulence may exist below the Moon and Mercury's core-mantle boundary (CMB) and Titan and Europa's ice-shell.
GP43A-0797
Laboratory geodynamo models: Effects of a soft iron inner core
An improved understanding of the geodynamo has fundamental importance in planetary science, with
relevance to geomagnetic forecasting as well as predicting behaviors of other planetary dynamos~---
Mercury, Ganymede, and newfound exoplanets, for example. One recent experiment (Bourgoin et~al.,
New J. Phys 8 12:329, 2006) achieved self-generation of magnetic fields after the addition of
ferromagnetic (soft iron) impellers. The geometry of that experiment greatly differs from that of a planet,
however, and the effects of soft iron are not well understood. We present experimental observations of
magnetic induction in an Earth-like geometry, both with a copper inner sphere and with a soft iron inner
sphere. Our experiment is a spherical Couette cell, 60~cm in diameter, with a 20~cm inner sphere, and liquid
sodium filling the gap. We drive fluid motions via differential rotation of the two spheres. Applying an axial
magnetic field, we observe the magnetic fields induced by those fluid motions. We find that some
characteristic behaviors, such as Coriolis-restored inertial modes, are present in both configurations. Other
behaviors arise only when a soft iron sphere is present, including sudden onsets of axisymmetric modes
causing large angular momentum fluxes. Our observations may suggest the mechanisms by which soft iron
can enable dynamo action. The support of NSF Earth Sciences is greatly acknowledged.
http://complex.umd.edu
GP43A-0798
Rapidly rotating experiments as laboratory models of planetary cores
Experiments using sodium or water can explore rapidly rotating flows in order to better understand the Earth's
outer core. Inertial modes and turbulent flows dominated by wave modes (such as MAC waves), are likely,
but unobserved, components or flows in the outer core. Local measurements of rotating flows in a 60 cm
rotating sodium experiment show Coriolis restored modes and the magnetic fields that they induce. We have
also observed these waves in water experiments in a rapidly rotating three meter experiment. While those
tests are being done in part to commission that system toward sodium experiments, measurements of the
fluctuating pressure and shear stress show wave mode dominated turbulent flows even in the absence of
magnetic fields. If the flows in planetary cores are dominated by large amplitude, fast time scale waves, those
would have an important causative effect but still be invisible on the surface. Implications on simulations via
the form of temporal and spatial spectra need to be understood if we hope to improve modeling toward
geomagnetic forecasting. The support of NSF Earth Sciences is greatly acknowledged.
http://complex.umd.edu