Jeremy Bloxham

An Earth-like numerical dynamo model

The mechanism by which the Earth and other planets maintain their magnetic fields against ohmic decay is among the longest standing problems in planetary science. Although it is widely acknowledged that these fields are maintained by dynamo action, the mechanism by which the dynamo operates is in large part not understood. Numerical simulations of the dynamo process in the Earths core have produced magnetic fields that resemble the Earths field, but it is unclear whether these models accurately represent the extremely low values of viscosity believed to be appropriate to the core. Here we describe the results of a numerical investigation of the dynamo process that adopts an alternative approach to this problem in which, through the judicious choice of boundary conditions, the effects of viscosity are rendered unimportant. We thereby obtain a solution that at leading order operates in an Earth-like dynamical regime. The morphology and evolution of the magnetic field and the fluid flow at the core–mantle boundary are similar to those of the Earth, and the field within the core is qualitatively similar to that proposed on theoretical grounds.

Time‐dependent mapping of the magnetic field at the core‐mantle boundary

We consider the problem of constructing a time-dependent map of the magnetic field at the core-mantle boundary. We use almost all the available data from the last 300 years to produce two maps, one for the period 1690–1840 and the other for 1840–1990. We represent the spatial dependency of the field using spherical harmonics, the time dependency using a cubic B-spline basis, and seek the smoothest solutions compatible with the observations. Particular attention must be paid to the effects of the crustal field in the data. We argue that for observations from permanent magnetic observatories the most efficient strategy is to use first-differences of annual means; for satellite data the most efficient strategy is simply to limit the number of data used so as to minimize any tendency to map the crustal field into the core field. The resulting model fits the observatory data better than any previous model yet has less power in the secular variation than previous models, demonstrating that very simple models fit the data. The resulting time-dependent field map exhibits much of the same structure in the field and its secular variation identified in earlier studies.

Fluid flow near the surface of Earth's outer core

Maps of the fluid flow at the core surface are important for a number of reasons: foremost they may provide some insight into the workings of the geodynamo and may place useful constraints on geodynamo models; from the flow, the force balance at the top of the core can, at least in part, be deduced; the flow can provide short-term predictions of the secular variation; the flow is important in understanding changes in the length of day; and constraints on lateral temperature variations and topography at the core-mantle boundary may be derived. Unlike the case of mantle convection, only very small lateral variations in core density are required to drive the flow; these density variations are too small (by several orders of magnitude) to be imaged seismically, so instead we use the geomagnetic secular variation to infer the flow. Despite considerable recent progress in mapping the core flow, substantial differences exist between maps produced by different researchers. Here we examine the possible underlying reasons for these differences, paying particular attention to the inherent problems of nonuniqueness. We focus on the aspects of the flow which do seem to be well determined and discuss their geophysical implications.

The origin of geomagnetic jerks

Geomagnetic jerks, which in the second half of the twentieth century occurred in 1969 (refs 1, 2), 1978 (refs 3, 4), 1991 (ref. 5) and 1999 (ref. 6), are abrupt changes in the second time-derivative (secular acceleration) of the Earths magnetic field. Jerks separate periods of almost steady secular acceleration, so that the first time-derivative (secular variation) appears as a series of straight-line segments separated by geomagnetic jerks. The fact that they represent a reorganization of the secular variation implies that they are of internal origin (as has been established through spherical harmonic analysis), and their short timescale implies that they are due to a change in the fluid flow at the surface of the Earths core (as has also been established through mapping the time-varying flow at the core surface). However, little is understood of their physical origin. Here we show that geomagnetic jerks can be explained by the combination of a steady flow and a simple time-varying, axisymmetric, equatorially symmetric, toroidal zonal flow. Such a flow is consistent with torsional oscillations in the Earths core, which are simple oscillatory flows in the core that are expected on theoretical grounds, and observed in both core flow models and numerical dynamo models.

Ørsted Initial Field Model

Magnetic measurements taken by the Orsted satellite during geomagnetic quiet conditions around Jan-uary 1, 2000 have been used to derive a spherical harmonic model of the Earths magnetic field for epoch 2000.0. The maximum degree and order of the model is 19 for internal, and 2 for external, source fields; however, coefficients above degree 14 may not be robust. Such a detailed model exists for only one previous epoch, 1980. Achieved rms misfit is < 2 nT for the scalar intensity and < 3 nT for one of the vector components perpendicular to the magnetic field. For scientific purposes related to the Orsted mission, this model supercedes IGRF 2000.

Torsional oscillations and the magnetic field within the Earth's core

An estimate of the magnitude and geometry of the magnetic field within the Earths core would be valuable for understanding the dynamics of the liquid outer core and for constraining numerical models of the geodynamo. The magnetic field down to the core–mantle boundary can be estimated from surface observations by assuming that the mantle is an insulator, but such estimates cannot be further extrapolated into the conducting core itself. The magnetic field within the core has therefore remained largely unconstrained. Here we construct a simple picture of part of the magnetic field within the core by first showing that the fluid flow at the surface of the core is consistent with the presence of two large waves—‘torsional oscillations’ of the type that have been proposed to explain the temporal variation of the magnetic field at the core–mantle boundary. We then use the structure of these waves to calculate a one-dimensional map of the part of the magnetic field that points away from the rotation axis. These results may help distinguish between the different dynamic states proposed for outer-core flow and provide a test for recent numerical models of the geodynamo.

Jupiter’s interior and deep atmosphere: The initial pole-to-pole passes with the Juno spacecraft

Juno swoops around giant Jupiter Jupiter is the largest and most massive planet in our solar system. NASAs Juno spacecraft arrived at Jupiter on 4 July 2016 and made its first close pass on 27 August 2016. Bolton et al. present results from Junos flight just above the cloud tops, including images of weather in the polar regions and measurements of the magnetic and gravitational fields. Juno also used microwaves to peer below the visible surface, spotting gas welling up from the deep interior. Connerney et al. measured Jupiters aurorae and plasma environment, both as Juno approached the planet and during its first close orbit. Science, this issue p. 821, p. 826 Juno’s first close pass over Jupiter provides answers and fresh questions about the giant planet. On 27 August 2016, the Juno spacecraft acquired science observations of Jupiter, passing less than 5000 kilometers above the equatorial cloud tops. Images of Jupiter’s poles show a chaotic scene, unlike Saturn’s poles. Microwave sounding reveals weather features at pressures deeper than 100 bars, dominated by an ammonia-rich, narrow low-latitude plume resembling a deeper, wider version of Earth’s Hadley cell. Near-infrared mapping reveals the relative humidity within prominent downwelling regions. Juno’s measured gravity field differs substantially from the last available estimate and is one order of magnitude more precise. This has implications for the distribution of heavy elements in the interior, including the existence and mass of Jupiter’s core. The observed magnetic field exhibits smaller spatial variations than expected, indicative of a rich harmonic content.

Sensitivity of the geomagnetic axial dipole to thermal core-mantle interactions

Since the work of William Gilbert in 1600 (ref. 1), it has been widely believed that the Earths magnetic field, when suitably time-averaged, is that of a magnetic dipole positioned at the Earths centre and aligned with the rotational axis. This ‘geocentric axial dipole’ (GAD) hypothesis has been the central model for the study of the Earths magnetic field—it underpins almost all interpretations of palaeomagnetic data, whether for studies of palaeomagnetic secular variation, for plate tectonic reconstructions, or for studies of palaeoclimate. Although the GAD hypothesis appears to provide a good description of the Earths magnetic field over at least the past 100 Myr (ref. 2), it is difficult to test the hypothesis for earlier periods, and there is some evidence that a more complicated model is required for the period before 250 Myr ago. Kent and Smethurst suggested that this additional complexity might be because the inner core would have been smaller at that time. Here I use a numerical geodynamo model and find that reducing the size of the inner core does not significantly change the character of the magnetic field. I also consider an alternative process that could lead to the breakdown of the GAD hypothesis on this timescale, the evolution of heat-flux variations at the core–mantle boundary, induced by mantle convection. I find that a simple pattern of heat-flux variations at the core–mantle boundary, which is plausible for times before the Mesozoic era, results in a strong octupolar contribution to the field, consistent with previous findings.

The steady part of the secular variation of the Earth's magnetic field

The secular variation of the Earths magnetic field results from the effects of magnetic induction in the fluid outer core and from the effects of magnetic diffusion in the core and the mantle. Adequate observations to map the magnetic field at the core-mantle boundary extend back over three centuries, providing a model of the secular variation at the core-mantle boundary. Here we consider how best to analyze this time-dependent part of the field. We propose that the first step should be to seek the steady core flow that best fits the field maps, isolating what we call the steady secular variation, the part of the secular variation explained by steady core flow. To calculate steady core flow over long time periods, we introduce an adaptation of our earlier method of calculating the flow in order to achieve greater numerical stability. We perform this procedure for the periods 1840–1990 and 1690–1840 and find that well over 90% of the variance of the time-depedent field can be explained by simple steady core flow. The core flows obtained for the two intervals are broadly similar to each other and to flows determined over much shorter recent intervals. Although we can explain a large part of the signal with these flows, none of them provides an adequate explanation of the secular variation. In particular, the fit to the original observations from which the field models were derived is inadequate. We examine the residual secular variation, the part of the signal that remains. We argue that it is dominated by the effects of nonsteady flow and magnetic diffusion. We do not find any compelling evidence for torsional oscillations as the dominant ingredient of this nonsteady part of the secular variation.

The treatment of attitude errors in satellite geomagnetic data

Abstract Vector magnetic field measurements from magnetic field satellites are contaminated by errors from multiple sources. Previously, the effect of these errors has been treated as isotropic, in other words as affecting the components of the vector field independently. This is incorrect. Here we develop a more complete formalism for dealing with attitude uncertainty, the main source of non-isotropic data errors, both for the case where the orientation is equally well known in all directions, and also for when the attitude determination is itself anisotropic. We demonstrate that the new method can be implemented at essentially no computational cost, and produces a small improvement in field models for Magsat-like data. Preliminary estimates of the error budget for the Orsted satellite indicate that in this case correct treatment of attitude errors could be extremely important, particularly in studies of short-wavelength lithospheric fields, and of field-aligned currents.