Earth's Fluid Core Research Articles

ESD Ideas: A 6-year oscillation in the whole Earth system?

Abstract. An oscillation of about 6 years has been reported in Earth's fluid core motions, magnetic field, rotation, and crustal deformations. Recently, a 6-year cycle has also been detected in several climatic parameters (e.g., sea level, surface temperature, precipitation, land hydrology, land ice, and atmospheric angular momentum). Here, we suggest that the 6-year oscillations detected in the Earth's deep interior, rotation, and climate are linked together and that the core processes previously proposed as drivers of the 6-year cycle in the Earth's rotation additionally cause the atmosphere to oscillate together with the mantle, inducing fluctuations in the climate system with similar periodicities.

Solitary magnetostrophic Rossby waves in spherical shells

Abstract

Wellposedness and Convergence of Solutions to a Class of Forced Non-diffusive Equations with Applications

This paper considers a family of non-diffusive active scalar equations where a viscosity type parameter enters the equations via the constitutive law that relates the drift velocity with the scalar field. The resulting operator is smooth when the viscosity is present but singular when the viscosity is zero. We obtain Gevrey-class local well-posedness results and convergence of solutions as the viscosity vanishes. We apply our results to two examples that are derived from physical systems: firstly a model for magnetostrophic turbulence in the Earth's fluid core and secondly flow in a porous media with an "effective viscosity".

Convectively driven decadal zonal accelerations in Earth’s fluid core

Azimuthal accelerations of cylindrical surfaces co-axial with the rotation axis have been inferred to exist in Earth's fluid core on the basis of magnetic field observations and changes in the length-of-day. These accelerations have a typical timescale of decades. However, the physical mechanism causing the accelerations is not well understood. Scaling arguments suggest that the leading order torque averaged over cylindrical surfaces should arise from the Lorentz force. Decadal fluctuations in the magnetic field inside the core, driven by convective flows, could then force decadal changes in the Lorentz torque and generate zonal accelerations. We test this hypothesis by constructing a quasi-geostrophic model of magnetoconvection, with thermally-driven flows perturbing a steady, imposed background magnetic field. We show that when the Alfv\'{e}n number in our model is similar to that in Earth's fluid core, temporal fluctuations in the torque balance are dominated by the Lorentz torque, with the latter generating mean zonal accelerations. Our model reproduces both fast, free Alfv\'{e}n waves and slow, forced accelerations, with ratios of relative strength and relative timescale similar to those inferred for the Earth's core. The temporal changes in the magnetic field which drive the time-varying Lorentz torque are produced by the underlying convective flows, shearing and advecting the magnetic field on a timescale associated with convective eddies. Our results support the hypothesis that temporal changes in the magnetic field deep inside Earth's fluid core drive the observed decadal zonal accelerations of cylindrical surfaces through the Lorentz torque.

Asymptotic Analysis for Randomly Forced MHD

We consider the three-dimensional magnetohydrodynamics (MHD) equations in the presence of a spatially degenerate stochastic forcing as a model for magnetostrophic turbulence in the Earth's fluid core. We examine the multiparameter singular limit of vanishing Rossby number $\varepsilon$ and magnetic Reynold's number $\delta$, and establish that (i) the formal limit (with $\varepsilon=\delta=0$), a stochastically driven active scalar equation, possesses a unique ergodic invariant measure, and (ii) any suitable sequence of statistically invariant states of the full MHD system converges weakly, as $\varepsilon,\delta \rightarrow 0$, to the unique invariant measure of the limit equation. This latter convergence result does not require any conditions on the relative rates at which $\varepsilon, \delta$ decay. Our analysis of the limit equation relies on a recently developed theory of hypoellipticity for infinite-dimensional stochastic dynamical systems. We carry out a detailed study of the interactions between ...

Free core nutation: new large disturbance and connection evidence with geomagnetic jerks

Variations in free core nutation (FCN) are connected with various processes in the Earth's fluid core and core-mantle coupling, which are also largely responsible for the geomagnetic field variations, particularly the geomagnetic jerks (GMJs). A previous study (Malkin, 2013) revealed that the epochs of the observed extremes in the FCN amplitude and phase variations are close to the GMJ epochs. In this paper, a new evidence of this connection was found. The large FCN amplitude and phase disturbance occurred at the epoch close to the newly revealed GMJ 2011. This event occurred to be the second large change in the FCN amplitude and phase after the 1999 disturbance that is also associated with the GMJ 1999. Moreover, the long-time FCN phase drift had changed suddenly in 1998--1999, immediately before the GMJ 1999, and seemed to change again at the epoch immediately preceding the GMJ 2011. The FCN amplitude showed a general long-time decrease before GMJ 1999, and it subsequently grew until GMJ 2011, and then seemed to decrease again. A smaller FCN change can be observed at the epoch around 2013, which is also suspected as the GMJ epoch. The latter confirms the suggestion that a rapid change in the FCN amplitude and/or phase can be used as an evidence of the GMJ that is not clearly detected from the geomagnetic observations.

Quasi-geostrophic modes in the Earth's fluid core with an outer stably stratified layer

Seismic waves sensitive to the outermost part of the Earth's liquid core seem to be affected by a stably stratified layer at the core–mantle boundary. Such a layer could have an observable signature in both long-term and short-term variations of the magnetic field of the Earth, which are used to probe the flow at the top of the core. Indeed, with the recent SWARM mission, it seems reasonable to be able to identify waves propagating in the core with period of several months, which may play an important role in the large-scale dynamics. In this paper, we characterize the influence of a stratified layer at the top of the core on deep quasi-geostrophic (Rossby) waves. We compute numerically the quasi-geostrophic eigenmodes of a rapidly rotating spherical shell, with a stably stratified layer near the outer boundary. Two simple models of stratification are taken into account, which are scaled with commonly adopted values of the Brunt–Väisälä frequency in the Earth's core. In the absence of magnetic field, we find that both azimuthal wavelength and frequency of the eigenmodes control their penetration into the stratified layer: the higher the phase speed, the higher the permeability of the stratified layer to the wave motion. We also show that the theory developed by Takehiro & Lister for thermal convection extends to the whole family of Rossby waves in the core. Adding a magnetic field, the penetrative behaviour of the quasi-geostrophic modes (the so-called fast branch) is insensitive to the imposed magnetic field and only weakly sensitive to the precise shape of the stratification. Based on these results, the large-scale and high-frequency modes (1–2 month periods) may be detectable in the geomagnetic data measured at the Earth's surface, especially in the equatorial area where the modes can be trapped.

Effects of density stratification on the frequencies of the inertial-gravity modes of the Earth's fluid core

Effects of density stratification on the frequencies of the inertial-gravity modes of the Earth's fluid core

Measurements of Newton's gravitational constant and the length of day

About a dozen measurements of Newton's gravitational constant, G, since 1962 have yielded values that differ by far more than their reported random plus systematic errors. We find that these values for G are oscillatory in nature, with a period of , an amplitude of , and mean-value crossings in 1994 and 1997. However, we do not suggest that G is actually varying by this much, this quickly, but instead that something in the measurement process varies. Of other recently reported results, to the best of our knowledge, the only measurement with the same period and phase is the Length of Day (LOD —defined as a frequency measurement such that a positive increase in LOD values means slower Earth rotation rates and therefore longer days). The aforementioned period is also about half of a solar activity cycle, but the correlation is far less convincing. The 5.9 year periodic signal in LOD has previously been interpreted as due to fluid core motions and inner-core coupling. We report the G/LOD correlation, whose statistical significance is 0.99764 assuming no difference in phase, without claiming to have any satisfactory explanation for it. Least unlikely, perhaps, are currents in the Earth's fluid core that change both its moment of inertia (affecting LOD) and the circumstances in which the Earth-based experiments measure G. In this case, there might be correlations with terrestrial-magnetic-field measurements.

Free core nutation and geomagnetic jerks

Variations in free core nutation (FCN) are associated with different processes in the Earth's fluid core and core–mantle coupling. The same processes are generally caused the variations in the geomagnetic field (GMF) particularly the geomagnetic jerks (GMJs), which are rapid changes in GMF secular variations. Therefore, the joint investigation of variations in FCN and GMF can elucidate the Earth's interior and dynamics. In this paper, we investigated the FCN amplitude and phase variations derived from VLBI observations. Comparison of the epochs of the changes in the FCN amplitude and phase with the epochs of the GMJs indicated that the observed extremes in the FCN amplitude and phase variations were closely related to the GMJ epochs. In particular, the FCN amplitude begins to grow one to three years after the GMJs. Thus, processes that cause GMJs are assumed as sources of FCN excitation.

High order instabilities of the Poincaré solution for precessionally driven flow

Sloudsky in 1895 and Poincaré in 1910 were the first to derive solutions for the flow driven in the Earth's fluid core by the luni-solar precession. In 1993, Kerswell investigated the stability of this so-called “Poincaré flow” by applying a method devised in 1992 by Ponomarev and Gledzer to study the instability of flows with elliptical streamlines. They represented the components of the perturbed flow by sums of polynomials. Kerswell restricted attention to the linear and quadratic cases. Here cubic, quartic, quintic, and sextic generalizations are developed. Instabilities are located in new areas of parameter space, including some that verge on the small oblateness of the Earth's core

Direct observations of the viscosity of Earth's outer core and extrapolation of measurements of the viscosity of liquid iron

Estimates vary widely as to the viscosity of Earth's outer fluid core. Directly observed viscosity is usually orders of magnitude higher than the values extrapolated from high-pressure high-temperature laboratory experiments, which are close to those for liquid iron at atmospheric pressure. It turned out that this discrepancy can be removed by extrapolating via the widely known Arrhenius activation model modified by lifting the commonly used assumption of pressure-independent activation volume (which is possible due to the discovery that at high pressures the activation volume increases strongly with pressure, resulting in 102 Pa s at the top of the fluid core, and in 1011 Pa s at its bottom). There are of course many uncertainties affecting this extrapolation process. This paper reviews two viscosity determination methods, one for the top and the other for the bottom of the outer core, the former of which relies on the decay of free core nutations and yields 2371 ± 1530 Pa s, while the other relies on the reduction in the rotational splitting of the two equatorial translational modes of the solid inner core oscillations and yields an average of 1.247 ± 0.035 Pa s. Encouraged by the good performance of the Arrhenius extrapolation, a differential form of the Arrhenius activation model is used to interpolate along the melting temperature curve and to find the viscosity profile across the entire outer core. The viscosity variation is found to be nearly log-linear between the measured boundary values.

Stability of mantle control over dynamo flux since the mid-Cenozoic

Studies of paleomagnetic fields during polarity transitions recorded over the past few million years frequently suggest a configurational persistence consistent with long-lived mantle control over the pattern of flux emanating from Earth's fluid core. Fundamental to an understanding of the core–mantle dynamics involved is the question of the spatial-temporal nature of the physical conditions at the base of the mantle that may be responsible. Our analysis of the field during a mid-Cenozoic, reverse-to-normal (R–N) polarity change, recorded in a continuous sequence of lava flows in southeastern Queensland, Australia, provides strong evidence that the time span over which local mantle features retain such an influence is far longer than had thus far been observed. Specifically, the reversal is dominated by two sequential groupings of transitional magnetic vector directions, each associated with a clustering of virtual geomagnetic poles (VGPs) at locations common to several more youthful reversal datasets from about the globe. Our 40Ar/ 39Ar age determinations indicate that these Australian lavas erupted 25.56 ± 0.48 Ma, strongly suggesting that the characteristic time for invariant control by the mantle over flux emerging from the outer core is at least on order of a few tens of Myr. The availability of transitional paleomagnetic data from still earlier times within the Cenozoic may further delineate this duration and, perhaps, provide a means to track changes in the pattern of long-standing concentrations of magnetic flux at the core–mantle boundary.

Inertial modes of a compressible fluid core model

Computational methods are used to investigate the effects of fluid compressibility on the frequencies of the inertial modes of the Earth's fluid core. The 3PD (the three potential description) is applied to two models of compressible fluid spheres, for one of which the dilatation vanishes, in order to study these modes. We show that compressibility may have a significant effect on some of the modal frequencies. Using the shape of the displacement eigenfunctions of a fluid sphere we also infer which modes of a sphere may have counterparts in a spherical shell. We then give a few examples of the inertial modes of a compressible fluid shell proportional to the Earth's fluid core.

Turbulent structure in Earth's fluid core inferred from time series of geomagnetic dipole moment

The physical grounds are discussed for assessing turbulent structures hidden inside the Earth's liquid core by using a time series of the geomagnetic dipole moment obtained from historical and paleomagnetic data. We propose the idea that the time‐averaged wavenumber spectra of electric current density at the core‐mantle boundary (CMB) and also velocity near the CMB have relation to the frequency spectrum of the dipole moment. We performed computer simulations of a magnetohydrodynamic spherical dynamo to verify this idea. We show that the frequency spectrum of the dipole moment in the simulation is similar to that inferred by paleomagnetic observations. The simulation results indicate that the underlying kinetic energy spectrum is proportional to m−5/3 in a high wavenumber range, where m is the azimuthal wavenumber. We speculate that a similar turbulent energy spectrum may exist in the Earth's core with a peak near m = 5.

Viscosity of the Earth's fluid core and torsional oscillations

Viscous effects on the temporal behavior and spatial structure of torsional oscillation normal modes of the Earth's fluid core are examined. If the viscosity of the fluid core is equal to that inferred from theoretical and experimental studies of liquid metals, then viscous effects on torsional oscillations are unlikely to be important; however, if the viscosity is as high as allowed from observational constraints, then Ekman layers at the fluid core boundaries may play an important role in damping torsional oscillations. The observationally inferred decay time of decadal torsional oscillations leads to an upper bound on the viscosity of the fluid core at the core‐mantle boundary of the order of 10−2 m2/s. A sufficiently large viscosity would result in torsional oscillation normal modes that undergo pure decay, as opposed to damped oscillatory motion. The viscosity value at which the temporal behavior switches between these regimes depends on the period of the normal mode. Numerical geodynamo models must reach an Ekman number of the order of 10−7 for free‐slip boundaries or 10−10 for no‐slip boundaries to accurately model the temporal behavior of decadal period torsional oscillations.

Computation of geomagnetic elements for Nigeria for the year 2000 and 2010

The Earth's magnetic field may be considered to be the sum of two parts, the main geomagnetic field which originates from the earth's fluid core, and the anomaly field that has its sources in the earth crust. The analysis of the geomagnetic field residual or anomaly, obtained from the difference between these two sources are used for many applications. In the present study, the values of the geomagnetic elements were calculated for Nigeria for the year 2000 and 2010. The values of latitudes were plotted for each element land the contours were drawn from the vertical component and the total intensity. Also the changes in the values of each element for Nigeria was computed and plotted against the latitudes. Nigerian Journal of Physics Vol. 16(2) 2004: 142-161

A multi-layered kinematic dynamo model: implications of a stratified upper layer in the Earth's core

It has been suggested that there exists a stably stratified electrically conducting layer at the top of the Earth's outer fluid core and that lateral temperature gradients in the lower mantle is capable of a driving thermal-wind-type flow near the core–mantle boundary. We investigate how such a flow in a stable layer could influence the geomagnetic field and the geodynamo using a very simple two-dimensional kinematic dynamo model in Cartesian geometry. The dynamo has four layers representing the inner core, convecting lower outer core, stable upper core, and insulating mantle. An α2 dynamo operates in the convecting outer core and a horizontal shear flow is imposed in the stable layer. Exact dynamo solutions are obtained for a range of parameters, including different conductivities for the stable layer and inner core. This allows us to connect our solutions with known, simpler solutions of a single-layer α2 dynamo, and thereby assess the effects of the extra layers. We confirm earlier results that a stable, static layer can enhance dynamo action. We find that shear flows produce dynamo wave solutions with a different spatial structure from the steady α2 dynamos solutions. The stable layer controls the behavior of the dynamo system through the interface conditions, providing a new means whereby lateral variations on the boundary can influence the geomagnetic field.

Variations in the Earth's gravity field caused by torsional oscillations in the core

SUMMARY We investigate whether a component of the flow in the Earth's fluid core, namely torsional oscillations, could be detected in gravity field data at the surface and whether it could explain some of the observed time variations in the elliptical part of the gravity field (J2). Torsional oscillations are azimuthal oscillations of rigid coaxial cylindrical surfaces and have typical periods of decades. This type of fluid motion supports geostrophic pressure gradients, which produce deformations of the core–mantle boundary. Because of the density discontinuity between the core and the mantle, such deformations produce changes in the gravity field that, because of the flow geometry, are both axisymmetric and symmetric about the equator. Torsional oscillations are thus expected to produce time variations in the zonal harmonics of even degree in the gravity field. Similarly, the changes in the rotation rates of the mantle and inner core that occur to balance the change in angular momentum carried by the torsional oscillations also produce zonal variations in gravity. We have built a model to calculate the changes in the gravity field and in the rotation rates of the mantle and inner core produced by torsional oscillations. We show that the changes in the rotation rate of the inner core produce changes in J2 that are a few orders of magnitude too small to be observed. The amplitudes of the changes in J2 from torsional oscillations are 10 times smaller than the temporal changes that are observed to occur about a linear secular trend. However, provided the mechanism responsible for these changes in J2 is identified and that this contribution is removed from the data, it may be possible in the future to detect the lowest harmonic degrees of the torsional oscillations in the gravity field data. We also show that torsional oscillations have contributed to the linear secular change in J2 by about −0.75 × 10−12 per year in the last 20 years. Finally, the associated change in the vertical ground motion at the surface of the Earth that is predicted by our mechanism is of the order of 0.2 mm, which is too small to be detected with the current precision in measurements.

A comparison of the anelastic and subseismic approximations for low-frequency gravity modes in stars

A comparative study of the properties of the anelastic and subseismic approximations is presented. The anelastic approximation is commonly used in astrophysics in compressible convection studies, whereas the subseismic approximation comes from geophysics where it is used to describe long-period seismic oscillations propagating in the Earth's outer fluid core. Both approximations aim to filter out the acoustic waves while retaining the density variations of the equilibrium configuration. However, they disagree on the form of the equation of mass conservation. We show here that the anelastic approximation is in fact the only consistent approximation as far as stellar low-frequency oscillations are concerned. We also show that this approximation implies Cowling's approximation which neglects perturbations of the gravity field. Examples are given to demonstrate the efficiency of the anelastic approximation.