Search for: All records

SUMMARY Recent geomagnetic observations reveal localized oscillations in the field’s secular acceleration at high latitudes, with periods of about 20 yr. Several types of waves in rotating magnetized fluids have been proposed to explain equatorial oscillations with similar high frequencies. Among these are non-axisymmetric Alfvén waves, magneto-Coriolis waves and, in the presence of fluid stratification, magnetic-Archimedes–Coriolis (MAC) waves. We explore the hypothesis that the observed high latitude patterns are the signature of MAC waves by modelling their generation in Earth’s core. We quantitatively assess several generation mechanisms using output from dynamo simulations in a theoretical framework due to Lighthill. While the spatio-temporal structure of the sources from the dynamo simulations are expected to be realistic, their amplitudes are extrapolated to reflect differences between the simulation’s parameter space and Earth-like conditions. We estimate full wave spectra spanning monthly to centennial frequencies for three plausible excitation sources: thermal fluctuations, Lorentz force and magnetic induction. When focusing on decadal frequencies, the Lorentz force appears to be most effective in generating high-latitude MAC waves with amplitude estimates falling within an order of magnitude of observed oscillations. Overall, this study puts forward MAC waves as a viable explanation, in the presence of fluid stratification at the top of Earth’s core, for observed field variations at high latitudes. 

Abstract Rapid growth of magnetic‐field observations through SWARM and other satellite missions motivate new approaches to analyze it. Dynamic mode decomposition (DMD) is a method to recover spatially coherent motion with a periodic time dependence. We use this method to simultaneously analyze the geomagnetic radial field and its secular variation from CHAOS‐7 at high latitudes. A total of five modes are permitted by noise levels in the observations. One mode represents a slowly evolving background state, whereas the other four modes describe a pair of waves; each wave is comprised of a complex DMD mode and its complex conjugate. The waves have periods ofT₁ = 19.1 andT₂ = 58.4 years and quality factors ofQ₁ = 11.0 andQ₂ = 4.6, respectively. A 60‐year wave is consistent with previous predictions for zonal waves in a stratified fluid. The 20‐year wave is also consistent with previous reports at high latitudes, although its nature is less clear. 

Ekman layers develop at the boundaries of the Earth’s fluid core in response to precession. Instabilities in these layers lead to turbulence when a local Reynolds number, Re, based on the thickness of the Ekman layer, exceeds a critical value. The transition to turbulence is often assessed using experiments for steady Ekman layers, where the interior geostrophic flow is independent of time. Precessionally driven flow varies on diurnal timescales, so the transition to turbulence may occur at a different value of Re.We use 3-D numerical calculations in a local Cartesian geometry to assess the transition to turbulence in precessional flow. Calculations retain the horizontal component of the rotation vector and account for the influence of fluid stratification. The transition to turbulence in a neutrally stratified fluid occurs near Re = 500, which is higher than the value Re = 150 usually cited for steady Ekman layers. However, it is comparable to the nominal value for precessional flow in the Earth. Complications due to fluid stratification or a magnetic field can suppress the transition to turbulence, reducing the likelihood of turbulent Ekman layers in the Earth’s core. 

We consider a stochastic differential equation model for Earth's axial magnetic dipole field. The model's parameters are estimated using diverse and independent data sources that had previously been treated separately. The result is a numerical model that is informed by the full paleomagnetic record on kyr to Myr time scales and whose outputs match data of Earth's dipole in a precisely defined feature-based sense. Specifically, we compute model parameters and associated uncertainties that lead to model outputs that match spectral data of Earth's axial magnetic dipole field but our approach also reveals difficulties with simultaneously matching spectral data and reversal rates. This could be due to model deficiencies or inaccuracies in the limited amount of data. More generally, the approach we describe can be seen as an example of an effective strategy for combining diverse data sets that is particularly useful when the amount of data is limited. 

Abstract. We consider a stochastic differential equation modelfor Earth's axial magnetic dipole field.Our goal is to estimate the model's parametersusing diverse and independent data sources that had previously been treated separately,so that the model is a valid representation of an expanded paleomagnetic recordon kyr to Myr timescales.We formulate the estimation problem within the Bayesian frameworkand define a feature-based posterior distributionthat describes probabilities of model parameters givena set of features derived from the data.Numerically, we use Markov chain Monte Carlo (MCMC)to obtain a sample-based representation of the posterior distribution.The Bayesian problem formulation and its MCMC solutionallow us to study the model's limitations and remaining posterior uncertainties.Another important aspect of our overall approach is thatit reveals inconsistencies between model and data or within the various data sets.Identifying these shortcomings is a first and necessary step towards building more sophisticated models or towards resolving inconsistencies within the data.The stochastic model we derive representsselected aspects of the long-term behavior of the geomagnetic dipole fieldwith limitations and errors that are well defined.We believe that such a model is useful (besides its limitations) for hypothesis testing and give a few examples of how the model can be used in this context. 

Abstract Models for the second time‐derivative of the geomagnetic field reveal prominent activity at high latitudes. Alternating patches of positive and negative geomagnetic acceleration propagate to the west at speeds that exceed nominal fluid velocities in the core. We show that waves are a viable interpretation of these observations. Magnetic Rossby waves produce a high‐latitude response with suitable phase velocities. However, the spatial complexity of the prediction is not compatible with the observations. Our preferred interpretation involves zonal MAC waves. These waves can account for the observed geomagnetic field when a stratified layer exists at the top of the core. The required layer has a thickness in excess of 100 km and a buoyancy frequency comparable to the rotation frequency. We anticipate a gradual reduction in the phase velocity over time, leading to a future change in the propagation direction.