GP33A-0914
Precessionally-Driven Dynamo in a Spheroid
More than a half century ago, Bullard conjectured that the motions necessary to generate the Earth's magnetic field in the Earth's electrically-conducting fluid core might be driven by the luni-solar precession. All that has been unequivocally established in the intervening 55 years is that precession can in principle supply the geodynamo with abundant power. The question of whether the geodynamo can draw on this power is still unanswered, though it seems probable from the work of Tilgner [Physics Fluids 17 (3): Art. No. 034104, 2005] that it can do so. Two types of precession-driven flows may be distinguished: in spherical precession, the mantle transmits motion to the core by viscous coupling; in non-spherical precession, the oblateness of the core-mantle boundary creates core motion through pressure differences. Non-spherical precession is geophysically the more relevant and is being studied in a spheroid using a computer code for solving the time-dependent incompressible dissipative MHD equations with finite differences on overlapping grids. As in the study of Kerswell [Geophys. Astrophys. Fluid Dynamics, 72, 107-144, 1993], Poincaré's basic solution in a precessing spheroid is found to be linearly unstable. Furthermore, it is shown that the nonlinear evolution of the flow can lead to dynamo action. These results will be reported.
GP33A-0915
Numerical Investigation of a Reduced One-dimensional Model for the Geodynamo
Many simplified dynamical models can be constructed to investigate dynamo action. On the one hand, these models allow much longer simulations than three-dimensional (3D) models. They are often used to study polarity reversals and their statistics. On the other hand, they are very remote from the dynamics of the Earth outer core. We present non-linear numerical results obtained with an original one-dimensional (1D) model. This model is obtained from a truncation of the governing equations for the geodynamo written under the quasi-geostrophic formalism. The resulting model, although very simplified, relies on the same non-dimensional parameters as fully 3D simulations (i.e. Ekman, Prandtl, magnetic Prandtl and Rayleigh numbers). The spatial description is limited to a few modes, explicitly coupled, so that the integration time is much less constrained as well as the accessible parameter range. We compare the results of our 1D model of the geodynamo to those of 3D simulations, discuss dynamical and statistical properties of these models, and their applicability to investigate the dynamics of the Earth core.
GP33A-0916
Zonal Flow Dynamos
The magnetic fields of the ice giants have signature characteristics that set them apart from other planetary dynamos. Unlike the magnetic fields of Earth, Jupiter and Saturn, which are dipolar and more or less axially aligned, Uranus and Neptune exhibit non-dipolar and non-axisymmetric magnetic fields. Using numerical models of dynamo action driven by strong convection in a spherical shell, we show that magnetic field generation in a fluid of low electrical conductivity (such as the proposed electrolytic liquid layer of the ice giants) can result in magnetic fields similar to those found by Voyager II in its flybys of Uranus and Neptune. We present numerical simulations of self-sustained dynamos using relatively low magnetic Prandtl numbers (Pm=0.1 and Pm=0.3). The flow outside the tangent cylinder develops a strong azimuthal prograde jet. Coriolis forces are stronger than convective forces (the convective Rossby number is less than unity). These flows sustain highly time variable magnetic fields with strong non-axisymmetric and non- dipolar components. In our models the toroidal kinetic energies dominate over magnetic and poloidal kinetic energies. Thus, the relatively weak magnetic field has little effect on the flow, resulting in Alfvén numbers as low as A=0.07. These simulations also lead to low Elsasser numbers (Λ=0.03-0.43). Our results suggest that a geostrophic (rather than magnetostrophic) force balance may be present in the dynamo region of the ice giants.
GP33A-0917
Torsional Oscillations in a Numerical Geodynamo Model
In a first approximation, the Earth's core is in a Taylor state, where viscous and inertial forces are negligibly small compared with Coriolis and Lorentz forces. To decrease viscous effects in a numerical geodynamo, the Ekman number, E = ν/Ømega L2, should be small, where ν is kinematic viscosity, Ømega is angular velocity of the core and L is the core size. To decrease inertial effects, the ratio of kinetic to magnetic energy densities should be smaller than unity, implying that the magnetic Ekman number, Em = η/Ømega L2, where η is magnetic diffusivity, should be small, assuming that that the magnetic Reynolds number and the Elsasser number are close to those expected for the Earth's core. Deviations from the Taylor state are believed to propagate as torsional waves inside the core with timescales of some decades. Torsional oscillations are of particular interest for the angular momentum balance in the Earth system. They might also be related to abrupt changes in the geomagnetic field such as magnetic jerks. Torsional waves can exist when the viscous diffusion timescale is much longer than the magnetic one, i.e., E \ll Em. Early dynamo models succeeded in creating dynamos with both E and Em smaller than unity (typically 10-5 ~ 10-6) but with E ≥ Em. For a better understanding of torsional oscillations, numerical calculations with E < Em, i.e., small magnetic Prandtl number, are desirable. We attempted to simulate Earth-type dynamos with E < Em < 10-5 and to analyze the torques on axial cylinders and the propagation of torsional waves. We paid particular attention to the effect of the freely rotating conductive inner core. Since the computation is demanding even on super-parallel computers, we approximated the magnetic field in the inner and outer cores by using the same number of Chebyshev spectral modes as those used for the velocity in the outer core. As a result, we could integrate the dynamo with the conductive inner core without increasing the computation time. This treatment is reasonable when E < Em and the magnetic length scale exceeds the velocity length scale.
GP33A-0918
A dynamic large eddy dynamo simulation in a rotating spherical shell
Flow and magnetic field in the outer core are distributed over a vast range of length scale from the size of the outer core to the thickness of the boundary layers. Numerical simulations cannot include 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. We previously performed a large-eddy simulation (LES) of a dynamo in a rotating plane layer model using the dynamic scale-similarity SGS model, In the present study, we implement the dynamic similarity model in a dynamo simulation in a rotating spherical shell. We include terms for the SGS momentum and heat flux, the SGS Lorentz force, and the SGS magnetic induction. We also correct the commutation error caused by interchanging the order of the spatial differentiations and filtering operation. The amplitudes of the SGS term and commutation error correction are adjusted using model coefficients, which are evaluated automatically with a dynamic scheme, based on the Germano identity. In the present study, we use a snapshot of the dynamo simulation without SGS model as an initial value. This simulation is performed using 5.2 million elements. The fluid region of the domain has 288 and 96 element in the zonal and radial direction. The initial solution is interpolated onto a coarser grid with half of the spatial resolution in each direction. We perform dynamo simulations with the SGS models (e.g. LES), and compare these results with the simulation on the original fine grid without the SGS model (e.g. resolved DNS). The predicted model coefficients for each SGS term increase gradually with the radius in the convective region, and decrease rapidly in the boundary layers, consistent with theoretical expectations. We also obtain preliminary estimates for the energetics of the simulations. We find that the buoyancy flux in the LES is significantly smaller than that in the resolved DNS case. This result suggests that the SGS heat flux reduces the variance in temperature perturbations in the LES. The SGS Lorentz force and SGS induction term also have an important role transferring the kinetic energy and magnetic energy from the resolved components to unresolved components. The SGS momentum flux also transfers the kinetic energy from the resolved components to unresolved components, but the amplitude of the energy flux of the SGS momentum flux is smaller than that of the SGS Lorentz force. Further tests and more quantitative investigations will be presented.
GP33A-0919
The reliability of paleomagnetic directions
Reliable paleomagnetic poles are vital for plate tectonic reconstructions. Several authors have proposed reliability criteria for paleomagnetic data but the most commonly used were proposed by van der Voo (1990) who introduced seven criteria to reliable determine a paleomagnetic pole. To average paleosecular variation (PSV) of the geomagnetic field van der Voo proposed to average at least 24 samples with a precision parameter, k (or K for virtual geomagnetic poles (VGPs)) of at least 10.0 and a maximum of 16 degrees for the a95 (or A95). These criteria apply for statistics derived from sets of directions as well as from VGPs. A problem that is largely ignored in paleomagnetism is the use of Fisher statistics (Fisher, 1953) on directions (a95 and k) instead of on VGPs (A95 and K). As was proposed decades ago and recently stressed by Tauxe and Kent (2004), the observed geomagnetic field behaviour fits better with the Virtual Geomagnetic Poles (VGPs) to be Fisherian rather than distributions of measured directions, which are consequently elongated in a north-south direction, especially at low and mid latitudes. We argue that it is more correct to use general Fisher statistics on the VGPs, and so consequently look at deviations from the mean in declination and inclination separately. Furthermore, we use a modified statistical model for the geomagnetic field for the last 5 Ma from Tauxe and Kent (2004) and a set of purely Fisherian VGPs to predict reasonable values for A95 and K as a function of N (amount of samples/sites). These simulations are used as well to give restrictions on the number of samples needed to average out PSV of the geomagnetic field within a certain error. R.van der Voo, 1990. The reliability of paleomagnetic data. Tectonophysics, 184: 1-9 L. Tauxe, D.V. Kent, 2004. A simplified statistical model for the geomagnetic field and the detection of shallow bias in paleomagnetic inclinations: was the ancient magnetic field dipolar? Timescales of the Paleomagnetic Field. Geophys. Monogr. Am. Geophys. Union, 145: 101- 115.
GP33A-0920
Polarity Reversal Statistics in Geodynamo Simulations
We present 45 simulations of the geodynamo using a gravitational dynamo model driven by compositional convection in an electrically conducting 3-D fluid shell. By varying the relative effects of buoyancy and rotation these simulations span a range of dynamo behavior from strongly dipolar, non-reversing, superchron-like models to multi-polar, frequently reversing models. A transition region is found where the models have strongly dipolar fields and moderate (Earth-like) reversal frequencies of approximately 1 reversal per 12.5 dipole diffusion times. The shape of the transition region is non-monotonic as a function of the Rayleigh and Ekman input parameters. Secular changes in the relative effects of buoyancy and rotation in the Earth may be used to explain secular changes in the geodynamo reversal frequency. We investigate correlations between model statistics such as reversal frequency, dipolarity, time variations of dipole strength, local Rossby number, and magnetic and kinetic energies. We also investigate the dependence of these statistics on the Rayleigh and Ekman input parameters.
GP33A-0921
Statistical properites and clustering of dynamo reversals observed from paleomagnetic records, experimental dynamo, numerical simulations and simplified models
The statistical properites of the time sequence of the geodynamo reversals show interesting features, such as non-poisson statistics indicating presence of correlations, and clustering in time. Such properties can be used to compare the observed reversals sequence with different dynamos, both experimental and numerical. In this work an experimental Bullard-Von Karman dynamo, which reproduces the field reversal, is studied in comparison with the paleomagnetic data. Moreover, some numerical models (namely an alpha-alpha dynamo, a turbulent dynamo, a dissipative Rikitake dynamo, and a shell model MHD dynamo) are characaterized, and their capacity of reproducing the observed clustering properties are discussed, also allowing the fine tuning of the models parameters.
GP33A-0922
Simulation Study Of The Symmetry-Breaking Instability And The Dipole Field Reversal In A Rotating Spherical Shell Dynamo
It is known by the paleomagnetic measurement of the geomagnetic field that, although the magnetic field of the Earth is usually dominated by a dipole component, the polarity is suddenly reversed many times so far at irregular intervals. The understanding of the mechanism for both the sustainment and the reversal of the dipole field still remains the most important problem not only in the geoscience but also in the nonlinear magnetohydrodynamics. In this study, the reversal mechanism of dipole magnetic field generated by the dynamo action in a rotating spherical shell is investigated by the three-dimensional nonlinear magnetohydrodynamic simulations as well as the linear stability analyses based on the decomposition technique with respect to the equatorial symmetry. As a result, first, we found that there is the threshold of the magnetic Prandtl number, below which the dipole field is never reversed, but above which the reversal may occur at irregular intervals like the paleomagnetic evolution of the geodynamo. Second, it is shown that the dynamo process responsible for the generation of dipole field (called " a-dynamo") consists only of the anti-mirror symmetric magnetic field and the mirror symmetric velocity field with respect to the equatorial plane. Third, it is found that the components of the opposite symmetry to the a-dynamo can survive only in the case that the reversal may occur, but they quickly decay in no reversal case. It indicates that the dipole field reversal and the loss of the equatorial symmetry are tightly connected. In fact, it is clearly demonstrated by the numerical analyses that the a-dynamo process is linearly unstable for the perturbation of the opposite symmetry when the magnetic Prandtl number exceeds the threshold for the dipole reversal. The mode coupling between the longitudinal Fourier components plays a crucial role in making the instability. Based on the results above, we propose that the symmetry-breaking instability could work as the primary cause of the dipole field reversal in the geodynamo process, although the trigger mechanism of the reversal events is still a puzzle.
GP33A-0923
Effects of thermally heterogeneous structure in the lowermost mantle on the geomagnetic field strength
We have conducted a study of numerical dynamos in a rapidly rotating spherical shell with prescribed non- uniform heat flux patterns at the outer boundary to examine effects of thermal structure at the core-mantle boundary (CMB) on the geodynamo, especially on the magnetic field strength. We found that strong heterogeneity of heat flux with quatorial symmetry enhances strength of the dipolar magnetic field for an Ekman number, E = 10-5, contrary to the case E = 10-4. Strong magnetic fields are generated in the fluid core off the equatorial plane beneath high heat flux regions, while moderate magnetic fields are maintained beneath low heat flux regions. The equatorially anti- symmetric heat flux distribution at the CMB affects the magnetic dipole axis through generation of the equatorially symmetric magnetic field. The boundary-induced thermal wind has strong influence on the flow structure and on the magnetic field intensity. These results suggest that thermally heterogeneous structure of the lowermost mantle might give rise to an anomalously strong geomagnetic field such as that during the Cretaceous Normal Superchron.
GP33A-0924
Transitions in Dynamo Modes Controlled by the Domain Aspect Ratio
Magnetic fields of internal origin are observed on many planets in the solar system. The Sun itself acts as a dynamo. While these natural objects are very different in their composition, when it comes to dynamo modeling the governing equations are remarkably similar. One of the controlling parameters to distinguish between these objects is the aspect ratio of the convecting domain. Comparing the Sun to the Earth raises the issue of the nature of reversals. A challenging issue is to determine why the geomagnetic field reverses polarity on an irregular basis, whereas the Sun --which is a much larger object, governed by stronger nonlinearities-- reverses its magnetic polarity on a quasi-periodic timescale of 11 yrs. We use a three-dimensional Boussinesq model (the Parody code) to investigate the transition between these two types of behavior. We show that the aspect ratio of the convecting domain controls the nature of the dynamo field. We report a butterfly-like diagram at large aspect ratio, with magnetic activity near 30° of latitudes, which migrates with time toward the equator. We trace the existence of the dynamo wave solution at various aspect ratio and suggest possible consequences for the geomagnetic secular variation.
GP33A-0925
Constraint on the heterogeneity of mantle conductivity structure obtained from the geomagnetic jerks
It is well-known that the occurrence time of each geomagnetic jerk in the southern hemisphere delays a few years comparing with the northern hemisphere (e.g., Alexandrescu et al [1996], Nagao et al. [2002, 2003]). Two physical mechanisms are possible for this interesting phenomenon; the distribution of the magnetic field at the core-mantle boundary (CMB) and/or the effect of the mantle conductivity on the magnetic field diffusion. Although which mechanism is significant is still controversial, it is valuable to obtain a constraint on the mantle conductivity that can explain this occurrence time lag. Backus [1983] derived theoretically, in the case of 1-D mantle, several characteristic time constants of a jerk related to the mantle conductivity, in which significant ones are delay time and smoothing time. We have been developing a tool using the Kalman filter, which enables us to determine automatically the amplitude, occurrence time, smoothing time of a jerk, and estimation error in each determined parameter. We apply this tool to the eastward component of geomagnetic monthly means obtained at worldwide geomagnetic observatories, and find that the distribution of amplitude has a spherical harmonic component of S22 and that the occurrence time in the African region delays a few years comparing with the other regions. When a jerk is assumed to occur simultaneously at the whole CMB, the mantle conductance is required to be an order of 109S in order to explain this time lag. This conductance is much larger than the upper constraint estimated from several decades variation in the length-of-day (LOD) on the basis of the electromagnetic core-mantle coupling theory. Therefore, a lateral heterogeneity is to be taken into account in order to satisfy both the jerk occurrence time lag and the LOD variation. We carry out a numerical experiment in the wave number and frequency domains using the MIDM (Koyama et al. [2002]) of how a magnetic field (especially in the case of S22) input from the CMB diffuses in the 3-D mantle, and obtain a transfer function between an input at the CMB and the corresponding output at the Earthfs surface. We can construct a synthetic but realistic time-variant magnetic field model utilizing this transfer function, and obtain the time constants of a jerk. We will discuss in the presentation a constraint on the heterogeneity of the mantle conductivity structure by comparing the time constants of the jerks estimated from the data analysis with those obtained from the numerical experiment.
GP33A-0926
Fluid Flow Near the Earth's Core Surface Derived From Geomagnetic Field Models With Constraint of Radial Dependence
Earth's core surface flow models have been estimated from geomagnetic field models to understand a realistic geodynamo mechanism, to investigate the thermal structure at the core surface, and to constrain the effect of core-mantle boundary (CMB) on the fluid flow. In most of core surface flow models, magnetic lines of force are considered to move as if they are frozen-in fluid elements when the advective time scale is much shorter than the magnetic diffusion time scale. This is called the frozen-flux hypothesis. Because of fundamental non-uniqueness, additional constraints have been imposed. It should be noted that thickness of a boundary layer at the CMB had been neglected. This suggests that flow models are estimated at the top of the free stream immediately beneath a thin boundary layer at the CMB. In the meantime, we have examined contribution to temporal variations in the magnetic field near the core surface based on numerical MHD dynamo models. We have found that the effect of magnetic diffusion is more significant than that of magnetic induction inside the boundary layer at the CMB, and that the effect of magnetic diffusion is much smaller than that of magnetic induction. This means that the frozen-flux hypothesis does not necessarily hold when a significant boundary layer appears. Hence we have presented a new approach to estimate fluid flow near the CMB from geomagnetic field models. We presume that both the magnetic diffusion and the viscous force are effective inside the boundary layer. That is, not only magnetic induction but also magnetic diffusion contribute to temporal variations in the magnetic field inside the boundary layer. Also the viscous force plays an important role there, and balance among the pressure gradient, the Coriolis force, and the viscous force is presumed. The magnetic diffusion is neglected as in the frozen-flux approximation below the boundary layer, and the flow is presumed to be in a geostrophic state there. So far we have not constrained the radial dependence of fluid motion near the core surface, although the radial component of the magnetic field has been treated in form of a truncated Taylor expansion. When the radial dependence of horizontal components of fluid flow is expressed in terms of a second-order polynomial, a linear inversion problem is to be solved in the same way as that without any constraint. When the radial dependence is given by a profile as often found in boundary layers, a non-linear inversion problem must be solved.
GP33A-0927
Application of Ensemble Techniques in Geomagnetic Data Assimilation
Geomagnetic data assimilation is a recent application of data assimilation in which an improved estimate of the state of the Earth's core is achieved by combing surface geomagnetic observations with a geodynamo model. Provided that good estimates of forecast model and observation error statistics are available, an optimal estimate can potentially be obtained. Geomagnetic field observations have well understood error characteristics. On the other hand, we have begun to develop the methods to estimate the error statistics of the MoSST core dynamics model, a geodynamo model that uses spherical harmonics and finite differences for spatial derivative approximation. Together with a limited part of the poloidal magnetic field observed at the Earth's surface, we need to apply the estimated error statistics of MoSST core dynamics model correctly into a data assimilation system. We have developed a geomagnetic data assimilation system, in which the forecast error covariances are estimated using an ensemble of model solutions. By analyzing the covariances, we know not only how deep the poloidal magnetic field inside the core should be corrected by the surface observations, but also how other state variables, i.e. the remaining poloidal field, the toroidal magnetic field, the velocity field and the density perturbation should be corrected. We use an ensemble method to estimate the forecast error covariance by perturbing an ensemble of initial states. Choosing an appropriate perturbation for the model runs is a critical part of ensemble methods. In particular, perturbations which do not satisfy all of the boundary conditions, or which do not satisfy the conservation equations for all of the variables, may introduce spurious oscillations or spikes in the solutions. In the present work we investigate a number of alternate perturbation strategies for the assimilation system, and compare their impact on the assimilation system by a series of Observing System Simulation Experiments (OSSE's).
GP33A-0928
Application of Slepian Basis Functions to Magnetic Field Analysis of Saturn
Originally developed by communication engineers in an effort to maximize a signal's energy both in the time and spectral domain, these Slepian functions were later adapted by the geodetic community (Albertella 1999, Wieczorek 2005, FJ Simons 2003, 2006) to address the problem of incomplete datasets on the sphere. More often than not, Earth-observing satellites are not in a polar orbit, leaving the polar regions unsampled. Using traditional spherical harmonics for a spectral representation of such data can yield errors as they require global support to achieve orthogonality over the whole sphere. With the new basis functions, which are orthogonal over the whole sphere as well as over the region of data coverage, and which have their energy optimally concentrated in the spatial and spectral domain, we have carried out magnetic field analysis of Saturn. For Saturn, all datasets, from Pioneer 11, Voyager 1 and 2 and Cassini, primarily have their data concentrated on a latitudinal belt centered around Saturn's equator, leaving very large data gaps over the Kronian poles. Pioneer 11 and the Voyager probes were all flyby missions which took place more or less in the equatorial plane of Saturn and while Cassini will have a high inclination orbit later in its mission, thus far its data is limited to approximately 30 degrees around Saturn's equator. We have evaluated the advantages of the Slepian basis functions with respect to the more traditional spherical harmonic functions typically used in magnetic field analysis. In doing so, we have sought to characterize Saturn's magnetic field beyond that which is currently resolved, i.e. a spin-axisymmetric field with an uncertain rate of rotation.
GP33A-0929
Equivalent source mapping of lunar magnetic field
JAXA (Japan Aerospace Exploration Agency) shall launch the SELENE (SELenological and ENgineering Explorer) spacecraft this autumn. Amongst many instruments, it has a magnetometer (LMAG: Lunar MAGnetomter) which will measure the magnetic field on the orbit around the Moon. The nominal orbit of the SELENE is about 100km in altitudes for 1 year observation. Although the extended mission is still not determined, LMAG team is requesting a low altitude (less than 50km) observation, if the remaining fuel allows. We are preparing data processing software for the mission. Here, we report an objective scheme for mapping the lunar crustal magnetic field from the orbital measurement data of unequal altitudes. In this study, the magnetic field is restored by solving a linear inverse-problem determining the sources distributed on the lunar surface to satisfy the observational data, which is known as the equivalent source method. Our scheme has three features improving the method: First, the source calculation is performed simultaneously with detrending. Second, magnetic charges (magnetic monopoles) are used as the equivalent sources. It reduces the density of the sources for the same smoothness in produced field, comparing to the dipole sauces. Third, the number of sources is taken large enough to avoid the problem of configuration of the sources, instead the damped least square assuming the strength of each charge is similar to the next one, and the smoothness factor is determined by minimizing Akaikefs Bayesian Information Criterion (ABIC). It guarantees the objectivity of the calculation, in other words, there is no adjustable parameter which may depend of the researcher dealing the data analyses. For testing the scheme, we apply this method to the Lunar Prospector magnetometer data, and provide magnetic field map in the region centered at several regions of strong crustal field including the Reiner Gamma anomaly. The stability of the method and the resolution of the anomaly map are found to be satisfactory.
GP33A-0930
Testing Numerical Dynamo Models Against Experimental Results
Significant progress has been achieved over the past few years in describing the geomagnetic field using computer models for dynamo action. Such models are so far limited to parameter regimes which are very remote from actual values relevant to the Earth core or any liquid metal (the magnetic Prandtl number is always over estimated by a factor at least 104). While existing models successfully reproduce many of the magnetic observations, it is difficult to assert their validity. The recent success of an experimental homogeneous unconstrained dynamo (VKS) provides a new way to investigate dynamo action in turbulent conducting flows, but it also offers a chance to test the validity of exisiting numerical models. We use a code originaly written for the Geodynamo (Parody) and apply it to the experimental configuration. The direct comparison of simulations and experiments is of great interest to test the predictive value of numerical simulations for dynamo action. These turbulent simulations allow us to approach issues which are very relevant for geophysical dynamos, especially the competition between different magnetic modes and the dynamics of reversals.
GP33A-0931
Wave motions in rotating, spherical, hydromagnetic experiments
The geodynamo problem---understanding how Earth's magnetic field arises---has seen great progress in recent years, from self-generation in many numerical simulations to the Bullard-von Karman dynamo achieved in an experiment by Bourgoin et al.\ (New J Phys 8 12:329, 2006). First, motivated by the geometry of the Earth, we have constructed a 60~cm differentially rotating spherical shell for experiments with liquid sodium, observing the presence of inertial modes at certain rotation rate combinations (Kelley et al., to appear in Geophys Astro Fluid 2007). The experimental inertial modes match analytically-known inertial modes of the full sphere in their wavenumbers, frequencies, and spatial structures. Second, motivated by Dudley and James's observation (Philos Tr R Soc S-A 425 1869:407-429, 1989) of dynamo action in numerical simulations, we have modified the above spherical system to allow S1T1 forcing in a rotating, full sphere. Again wave motions are present, and initial results are consistent with the dispersion relation for full-sphere Rossby waves. http://complex.umd.edu
GP33A-0932
Simulations and Measurements of Fluctuation-Driven Magnetic Fields in a Liquid Metal Experiment
The Madison Dynamo Experiment is designed to demonstrate magnetic self-excitation using flowing liquid sodium in a spherical geometry. A turbulent flow is produced in the experiment by two counter-rotating impellers. The role of turbulent velocity and magnetic field fluctuations in magnetic field generation is explored by applying an external magnetic field to the flowing sodium and measuring the induced magnetic field. The mean velocity field of the experiment is determined by measuring the velocity field in a dimensionally identical water experiment. The magnetic fields induced by both the mean flow and by the fluctuations are then calculated. The presence of a strong diamagnetic field, generated by fluctuations, is identified and its spatial structure presented. Such a fluctuation-driven magnetic field is also found in simulations of the experiment, which are used to determine the nature of the fluctuations, and how they induce the diamagnetic field.
GP33A-0933
Local and Global study of the MRI With Application to the Earth's Core
We investigate the magnetorotational instability (MRI) in a geophysical context. The MRI is known to play a crucial role in the stucture and evolution of astrophysical disks. It may also influence the radiative zone of stars, and possibly the generation of magnetic field in planetary cores. In order to study a possible connection with dynamo action in the Earth's core, we have carried out a WKB analysis of the MRI using a resistivity, magnetic field, and local rotation profile taken from standard models. Unstable modes are present with characteristic growth times of 1000 years. The calculation is compared against a global numerical model of spherical, magnetized Couette flow, and good agreement is found. The role of the MRI in the geophysical dynamo is secondary to thermal convection, though it may be important for regulating angular momentum transport.
GP33A-0934
Statistical Behavior of Reversing Gravitational Dynamos
Gravitational dynamo models powered by compositional convection show different regimes of magnetic field statistics with increasing Rayleigh number, including nearly steady fields, chaotic non-reversing dipole fields, and chaotic reversing dipole fields. The time average dipole strength and the dipolarity of the magnetic field decrease, while the dipole variability, the average dipole tilt angle, and the frequency of polarity reversals increase with Rayleigh number. Chaotic gravitational dynamos have large amplitude dipole secular variation with maximum power at frequencies of a few cycles per million years. Dipole statistics, low frequency power spectra, and polarity reversal frequency of some of these dynamos are comparable to the geomagnetic field. The low frequency variability is driven by the Lorentz force and is characterized by an inverse correlation between dynamo magnetic and kinetic energy. A constant energy dissipation model accounts most of the low frequency statistical behavior of these dynamos.