From stable dipolar towards reversing numerical dynamos

We are using a three-dimensional convection-driven numerical dynamo model without hyperdiffusivity to study the characteristic structure and time variability of the magnetic field in dependence of the Rayleigh number (Ra) for values up to 40 times supercritical. We also compare a variety of ways to drive the convection and basically find two dynamo regimes. At low Ra, the magnetic field at the surface of the model is dominated by the non-reversing axial dipole component. At high Ra, the dipole part becomes small in comparison to higher multipole components. At transitional values of Ra, the dynamo vacillates between the dipole-dominated and the multipolar regime, which includes excursions and reversals of the dipole axis. We discuss, in particular, one model of chemically driven convection, where for a suitable value of Ra, the mean dipole moment and the temporal evolution of the magnetic field resemble the known properties of the Earth’s field from paleomagnetic data.     

A theoretical analysis of the observed variability of the geomagnetic dipole field

We present a detailed analysis of the Sint-800 virtual axial dipole moment (VADM) data in terms of an Ω mean field model of the geodynamo that features a non-steady generation of poloidal from toroidal magnetic field. The result is a variable excitation of the dipole mode and the overtones, and there are occasional dipole reversals. The model permits a theoretical evaluation of the statistical properties of the dipole mode. We show that the model correctly predicts the distribution of the VADM and the autocorrelation function inferred from the Sint-800 data. The autocorrelation technique allows us to determine the turbulent diffusion time τ_d=R²/β of the geodynamo. We find that τ_d is about 10–15 kyr. The model is able to reproduce the observed secular variation of the dipole mode, and the mean time between successive dipole reversals. On the other hand, the duration of a reversal is a factor 2 too long. This could be due to imperfections in the model or to unknown systematics in the Sint-800 data. The use of mean field theory is shown to be selfconsistent.     

Illawarra Reversal: The fingerprint of a superplume that triggered Pangean breakup and the end-Guadalupian (Permian) mass extinction

The Permian magnetostratigraphic record demonstrates that a remarkable change in geomagnetism occurred in the Late Guadalupian (Middle Permian; ca. 265 Ma) from the long-term stable Kiaman Reverse Superchron (throughout the Late Carboniferous and Early-Middle Permian) to the Permian–Triassic Mixed Superchron with frequent polarity changes (in the Late Permian and Triassic). This unique episode called the Illawarra Reversal probably reflects a significant change in the geodynamo in the outer core of the planet after a 50 million years of stable geomagnetism. The Illawarra Reversal was likely led by the appearance of a thermal instability at the 2900 km-deep core–mantle boundary in connection with mantle superplume activity. The Illawarra Reversal and the Guadalupian–Lopingian boundary event record the significant transition processes from the Paleozoic to Mesozoic–Modern world. One of the major global environmental changes in the Phanerozoic occurred almost simultaneously in the latest Guadalupian, as recorded in 1) mass extinction, 2) ocean redox change, 3) sharp isotopic excursions (C and Sr), 4) sea-level drop, and 5) plume-related volcanism. In addition to the claimed possible links between the above-listed environmental changes and mantle superplume activity, I propose here an extra explanation that a change in the core's geodynamo may have played an important role in determining the course of the Earth's surface climate and biotic extinction/evolution. When a superplume is launched from the core–mantle boundary, the resultant thermal instability makes the geodynamo's dipole of the outer core unstable, and lowers the geomagnetic intensity. Being modulated by the geo- and heliomagnetism, the galactic cosmic ray flux into the Earth's atmosphere changes with time. The more cosmic rays penetrate through the atmosphere, the more clouds develop to increase the albedo, thus enhancing cooling of the Earth's surface. The Illawarra Reversal, the Kamura cooling event, and other unique geologic phenomena in the Late Guadalupian are all concordantly explained as consequences of the superplume activity that initially triggered the breakup of Pangea. The secular change in cosmic radiation may explain not only the extinction-related global climatic changes in the end-Guadalupian but also the long-term global warming/cooling trend in Earth's history in terms of cloud coverage over the planet.     

The instability of barotropic circular vortices

Abstract

The linear, normal mode instability of barotropic circular vortices with zero circulation is examined in the f-plane quasigeostrophic equations. Equivalents of Rayleigh's and Fjortoft's criteria and the semicircle theorem for parallel shear flow are given, and the energy equation shows the instability to be barotropic. A new result is that the fastest growing perturbation is often an internal instability, having a finite vertical scale, but may also be an external instability, having no vertical structure. For parallel shear flow the fastest growing perturbation is always an external instability; this is Squire's theorem. Whether the fastest growing perturbation is internal or external depends upon the profile: for mean flow streamfunction profiles which monotonically decrease with radius, the instability is internal for less steep profiles with a broad velocity extremum and external for steep profiles with a narrow velocity extremum. Finite amplitude, numerical model calculations show that this linear instability analysis is not valid very far into the finite amplitude range, and that a barotropic vortex, whose fastest growing perturbation is internal, is vertically fragmented by the instability.     

Secular variation in numerical geodynamo models with lateral variations of boundary heat flow

We study magnetic field variations in numerical models of the geodynamo, with convection driven by nonuniform heat flow imposed at the outer boundary. We concentrate on cases with a boundary heat flow pattern derived from seismic anomalies in the lower mantle. At a Rayleigh number of about 100 times critical with respect to the onset of convection, the magnetic field is dominated by the axial dipole component and has a similar spectral distribution as Earth’s historical magnetic field on the core-mantle boundary (CMB). The time scales of variation of the low-order Gauss coefficients in the model agree within a factor of two with observed values. We have determined the averaging time interval needed to delineate deviations from the axial dipole field caused by the boundary heterogeneity. An average over 2000 years (the archeomagnetic time scale) is barely sufficient to reveal the long-term nondipole field. The model shows reduced scatter in virtual geomagnetic pole positions (VGPs) in the central Pacific, consistent with the weak secular variation observed in the historical field. Longitudinal drift of magnetic field structures is episodic and differs between regions. Westward magnetic drift is most pronounced beneath the Atlantic in our model. Although frozen flux advection by the large-scale flow is generally insufficient to explain the magnetic drift rates, there are some exceptions. In particular, equatorial flux spot pairs produced by expulsion of toroidal magnetic field are rapidly advected westward in localized equatorial jets which we interpret as thermal winds.     

Inner-core conductivity in numerical dynamo simulations

Speculation about its possible super-rotation has drawn the attention of many geophysical researchers to the Earth’s inner core. An issue of special interest for geodynamo modelling is the influence of the inner-core conductivity. It has been suggested that the finite magnetic diffusivity of the inner core prevents more frequent reversals of the Earth’s magnetic field. We explore the possible influence of the inner-core conductivity by comparing convection-driven 3D dynamo simulations with insulating or conducting inner cores (CIC) at various parameters. The influence on the field structure in the outer core is only marginal. The time behaviour of dipole-dominated non-reversing dynamos is also little affected. Concerning reversing dynamos, the inner-core conductivity reduces the number of short dipole-polarity intervals with a typical length of a few thousand years. Reversals are always correlated with low dipole strength and these short intervals are found in periods where the dipole moment stays low. Polarity intervals longer than about 10,000 years, where the dipole moment has time recover in strength, are equally likely in insulating and CIC models. Since these latter intervals are of more geophysical relevance, we conclude that the influence of the inner-core conductivity on Earth-like reversal sequences is insignificant for the dynamo model employed here.     

Detecting thermal boundary control in surface flows from numerical dynamos

The geomagnetic field and secular variation exhibit asymmetrical spatial features which are possibly originating from an heterogeneous thermal control of the Earth's lower mantle on the core. The identification of this control in magnetic data is subject to several difficulties, some of which can be alleviated by the use of core surface flow models. Using numerical dynamos driven by heterogeneous boundary heat flux, we confirm that within the parameter space accessible to simulations, time average surface flows obey a simple thermal wind equilibrium between the Coriolis and buoyancy forces, the Lorentz, inertial and viscous forces playing only a secondary role, even for Elsasser numbers significantly larger than 1. Furthermore, we average the models over the duration of three vortex turnovers, and correlate them with a longer time average which fully reveals the signature of boundary heterogeneity. This allows us to quantify the possibility of observing mantle control in core surface flows averaged over a short time period. A scaling analysis is performed in order to apply the results to the Earth's core. We find that three vortex turnovers could represent between 100 and 360 years of Earth time, and that the heat flux heterogeneity at the core-mantle boundary could be large enough to yield an observable signature of thermal mantle control in a time average core surface flow within reach of the available geomagnetic data.     

F-layer formation in the outer core with asymmetric inner core growth

Numerical calculations of thermochemical convection in a rotating, electrically conducting fluid sphere with heterogeneous boundary conditions are used to model effects of asymmetric inner core growth. With heterogeneous inner core growth but no melting, outer core flow consists of intense convection where inner core buoyancy release is high, weak convection where inner core buoyancy release is low, and large scale, mostly westward flow in the form of spiraling gyres. With localized inner core melting, outer core flow includes a gravity current of dense fluid that spreads over the inner core boundary, analogous to the seismic F-layer. An analytical model for gravity currents on a sphere connects the structure of the dense layer to the distribution of inner core melting and solidification. Predictions for F-layer formation by asymmetric inner core growth include large-scale asymmetric gyres below the core-mantle boundary and eccentricity of the geomagnetic field.