Three-dimensional solutions for the geostrophic flow in the Earth's core

In his seminal work, Taylor (1963) argued that the geophysically relevant limit for dynamo action within the outer core is one of negligibly small inertia and viscosity in the magnetohydrodynamic equations. Within this limit, he showed the existence of a necessary condition, now well known as Taylor's constraint, which requires that the cylindrically-averaged Lorentz torque must everywhere vanish; magnetic fields that satisfy this condition are termed Taylor states. Taylor further showed that the requirement of this constraint being continuously satisfied through time prescribes the evolution of the geostrophic flow, the cylindrically-averaged azimuthal flow. We show that Taylor's original prescription for the geostrophic flow, as satisfying a given second order ordinary differential equation, is only valid for a small subset of Taylor states. An incomplete treatment of the boundary conditions renders his equation generally incorrect. Here, by taking proper account of the boundaries, we describe a generalisation of Taylor's method that enables correct evaluation of the instantaneous geostrophic flow for any 3D Taylor state. We present the first full-sphere examples of geostrophic flows driven by non-axisymmetric Taylor states. Although in axisymmetry the geostrophic flow admits a mild logarithmic singularity on the rotation axis, in the fully 3D case we show that this is absent and indeed the geostrophic flow appears to be everywhere regular.Comment: 29 Pages, 8 figure

The evolution of a magnetic field subject to Taylor′s constraint using a projection operator

In the rapidly rotating, low-viscosity limit of the magnetohydrodynamic equations as relevant to the conditions in planetary cores, any generated magnetic field likely evolves while simultaneously satisfying a particular continuous family of invariants, termed Taylor′s constraint. It is known that, analytically, any magnetic field will evolve subject to these constraints through the action of a time-dependent coaxially cylindrical geostrophic flow. However, severe numerical problems limit the accuracy of this procedure, leading to rapid violation of the constraints. By judicious choice of a certain truncated Galerkin representation of the magnetic field, Taylor′s constraint reduces to a finite set of conditions of size O(N), significantly less than the O(N3) degrees of freedom, where N denotes the spectral truncation in both solid angle and radius. Each constraint is homogeneous and quadratic in the magnetic field and, taken together, the constraints define the finite-dimensional Taylor manifolδ whose tangent plane can be evaluated. The key result of this paper is a description of a stable numerical method in which the evolution of a magnetic field in a spherical geometry is constrained to the manifold by projecting its rate of change onto the local tangent hyperplane. The tangent plane is evaluated by contracting the vector of spectral coefficients with the Taylor tensor, a large but very sparse 3-D array that we define. We demonstrate by example the numerical difficulties in finding the geostrophic flow numerically and how the projection method can correct for inaccuracies. Further, we show that, in a simplified system using projection, the normalized measure of Taylorization, t, may be maintained smaller than O(10-10) (where t= 0 is an exact Taylor state) over 1/10 of a dipole decay time, eight orders of magnitude smaller than analogous measures applied to recent low Ekman-number geodynamo model

Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

The impact of geomagnetic spikes on the production rates of cosmogenic 14C and 10Be in the Earth's atmosphere

We seek corroborative evidence of the geomagnetic spikes detected in the Near East ca. 980 BC and 890 BC in the records of the past production rates of the cosmogenic nuclides 14C and 10Be. Our forward modeling strategy rests on global, time-dependent, geomagnetic spike field models feeding state-of-the-art models of cosmogenic nuclide production. We find that spike models with an energy budget in line with presently inferred large-scale flow at Earth's core surface fail to produce a visible imprint in the nuclide record. Spike models able to reproduce the intensity changes reported in the Near East require an unaccountably high-magnitude core flow, yet their computed impact on cosmogenic isotope production rates remains ambiguous. No simple and unequivocal agreement is obtained between the observed and modeled nuclide records at the epochs of interest. This indicates that cosmogenic nuclides cannot immediately be used to confirm the occurrence of these two geomagnetic spikes

Climatological predictions of the auroral zone locations driven by moderate and severe space weather events

Auroral zones are regions where, in an average sense, aurorae due to solar activity are most likely spotted. Their shape and, similarly, the geographical locations most vulnerable to extreme space weather events (which we term ‘danger zones’) are modulated by Earth’s time-dependent internal magnetic field whose structure changes on yearly to decadal timescales. Strategies for mitigating ground-based space weather impacts over the next few decades can benefit from accurate forecasts of this evolution. Existing auroral zone forecasts use simplified assumptions of geomagnetic field variations. By harnessing the capability of modern geomagnetic field forecasts based on the dynamics of Earth’s core we estimate the evolution of the auroral zones and of the danger zones over the next 50 years. Our results predict that space-weather related risk will not change significantly in Europe, Australia and New Zealand. Mid-to-high latitude cities such as Edinburgh, Copenhagen and Dunedin will remain in high-risk regions. However, northward change of the auroral and danger zones over North America will likely cause urban centres such as Edmonton and Labrador City to be exposed by 2070 to the potential impact of severe solar activity

An accelerating high-latitude jet in Earth's core

Observations of the change in Earth's magnetic field, the secular variation, provide information on the motion of liquid metal within the core that is responsible for its generation. The very latest high-resolution observations from ESA's Swarm satellite mission show intense field change at high-latitude localised in a distinctive circular daisy-chain configuration centred on the north geographic pole. Here we explain this feature with a localised, non-axisymmetric, westwards jet of 420 km width on the tangent cylinder, the cylinder of fluid within the core that is aligned with the rotation axis and tangent to the solid inner core. We find that the jet has increased in magnitude by a factor of three over the period 2000--2016 to about 40 km/yr, and is now much stronger than typical large-scale flows inferred for the core. The current accelerating phase may be a part of a longer term fluctuation of the jet causing both eastwards and westwards movement of magnetic features over historical periods, and may contribute to recent changes in torsional wave activity and the rotation direction of the inner core

Transdimensional inference of archeomagnetic intensity change

One of the main goals of archeomagnetism is to document the secular changes of Earth's magnetic field by laboratory analysis of the magnetization carried by archeological artefacts. Typical techniques for creating a time-dependent model assume a prescribed temporal discretisation which, when coupled with sparse data coverage, require strong regularisation generally applied over the entire time series in order to ensure smoothness. Such techniques make it difficult to characterise uncertainty and frequency content, and robustly detect rapid changes. Key to proper modelling (and physical understanding) is a method that places a minimum level of regularisation on any fit to the data. Here we apply a transdimensional Bayesian technique based on piecewise linear interpolation to sparse archeointensity datasets, in which the temporal complexity of the model is not set a priori, but is self-selected by the data. The method produces two key outputs: (i) a posterior distribution of intensity as a function of time, a useful tool for archeomagnetic dating, whose statistics are smooth but formally unregularised; (ii) by including the data ages in the model of unknown parameters, the method also produces posterior age statistics of each individual contributing datum. We test the technique using synthetic datasets and confirm agreement of our method with an integrated likelihood approach. We then apply the method to three archeomagnetic datasets all reduced to a single location: one temporally well-sampled within 700km from Paris (here referred to as Paris700), one that is temporally sparse centred on Hawaii, and a third (from Lübeck, Germany and Paris700) that has additional ordering constraints on age from stratification. Compared with other methods, our average posterior distributions largely agree, however our credible intervals appear to much better reflect the uncertainty during periods of sparse data coverage. Because each ensemble member of the posterior distribution is piecewise linear, we only fit oscillations when required by the data. As an example, we show that an oscillatory signal, associated with temporally-localised intensity maxima reported for a sparse Hawaiian dataset, is not required by the data. However, we do recover the previously reported oscillation of period 260 yrs for the Paris700 dataset and compute the probability distribution of the period of oscillation. We further demonstrate that such an oscillation is unresolved when accounting for age uncertainty by using a fixed age and with an artificially inflated error budget on intensity

Comparison of the Virulence Potential of Acinetobacter Strains from Clinical and Environmental Sources

Several Acinetobacter strains have utility for biotechnology applications, yet some are opportunistic pathogens. We compared strains of seven Acinetobacter species (baumannii, Ab; calcoaceticus, Ac; guillouiae, Ag; haemolyticus, Ah; lwoffii, Al; junii, Aj; and venetianus, Av-RAG-1) for their potential virulence attributes, including proliferation in mammalian cell conditions, haemolytic/cytolytic activity, ability to elicit inflammatory signals, and antibiotic susceptibility. Only Ah grew at 102 and 104 bacteria/well in mammalian cell culture medium at 37°C. However, co-culture with colonic epithelial cells (HT29) improved growth of all bacterial strains, except Av-RAG-1. Cytotoxicity of Ab and Ah toward HT29 was at least double that of other test bacteria. These effects included bacterial adherence, loss of metabolism, substrate detachment, and cytolysis. Only Ab and Ah exhibited resistance to killing by macrophage-like J774A.1 cells. Haemolytic activity of Ah and Av-RAG-1 was strong, but undetectable for other strains. When killed with an antibiotic, Ab, Ah, Aj and Av-RAG-1 induced 3 to 9-fold elevated HT29 interleukin (IL)-8 levels. However, none of the strains altered levels of J774A.1 pro-inflammatory cytokines (IL-1β, IL-6 and tumor necrosis factor-α). Antibiotic susceptibility profiling showed that Ab, Ag and Aj were viable at low concentrations of some antibiotics. All strains were positive for virulence factor genes ompA and epsA, and negative for mutations in gyrA and parC genes that convey fluoroquinolone resistance. The data demonstrate that Av-RAG-1, Ag and Al lack some potentially harmful characteristics compared to other Acinetobacter strains tested, but the biotechnology candidate Av-RAG-1 should be scrutinized further prior to widespread use