Library

Notes: Abstract We examine the dynamics of the angular momentum balance of the Earth's core. Not only is this balance of great importance to theories of the geodynamo process that is responsible for the generation of the Earth's magnetic field, but recent work has shown that angular momentum variations in the core have broad geophysical implications, ranging from studies of the travel times of seismic waves through the inner core to attempts to account for a possible phase discrepancy between atmospheric and oceanic angular momentum. In this review, we present a simple account of the underlying dynamics and review the relevant observations and their interpretation.

Notes: We examine the problem of determining the fluid flow and the shear (the radial derivative of the flow) at the core surface given a model of the temporal variation of the magnetic field. Whereas most previous work has focused on determining only the flow, which requires only the use of the radial component of the magnetic field, here, in addition, we determine the shear for which we must use the horizontal component of the magnetic field. Estimates of the jump in the value of the horizontal magnetic field Bh across the boundary layer between the top of the free stream and the base of the mantle are small, and suggest that to a high level of accuracy the mantle values of Bh can be used at the top of the core. Except in the special case of an insulating mantle, only the horizontal poloidal field is known at the core-mantle boundary and supplies one extra equation for the determination of velocity and shear. We show how the matrix elements relating the coefficients of the spectral expansion of the flow and shear are related to the geomagnetic secular variation coefficients in closed form. We examine the uniqueness of the resulting inverse problem, and show that one part of the non-uniqueness from which the shear suffers is particularly easy to describe: it takes the same form as that which affects the flow, namely a toroidal ambiguity in the field u′Br. However, certain uniqueness theorems can be derived: we extend the steady motions theorem of Voorhies & Backus (1985) and the geostrophic motions theorem of Hills (1979) and Backus & LeMouël (1986) to the determination of the flow and shear, and derive closely analogous results. Uniqueness in the steady case depends on the value of the same discriminant as the velocity, and in the geostrophic case the shear can be determined uniquely in the same areas as can the velocity (i.e. outside certain ambiguous patches). For the geostrophic regime, the lateral density (or temperature) variations at the top of the core can be found in a self-consistent manner. We apply our method to the temporal evolution of the field over the period 1960–1980, and produce solutions for each of the assumptions of unconstrained steady motions, geostrophic motions, and purely toroidal motions. We find that the form of the flow changes very little from solutions based only on the radial induction equation, and that the shear is weak and aligned with the flow, with a sense such that the strength of the flow decreases with depth with a length-scale for linear decay of half the core radius. This suggests that the flow near the core surface is indicative of whole core flow, rather than a flow confined to a layer near the core surface.

Notes: Owing to exchanges of angular momentum between the Earth's fluid outer core and the overlying solid mantle, the Earth's rotational rate fluctuates on periods of a few years to a few decades. However, the mechanism which allows the exchange of angular momentum is not understood. Here we examine the possibility that core-mantle coupling is predominantly electromagnetic and thus responsible for the decadal length of day variations. the electromagnetic couple on the mantle can be divided into poloidal and toroidal parts, and, by requiring continuity of the horizontal component of the electric field at the core-mantle boundary, the toroidal couple can be divided into separate advective and leakage parts. the poloidal couple results entirely from the interaction of the poloidal field with currents induced by its time variation; the advective couple results from the dragging of poloidal field lines through a conducting mantle; and the leakage couple results from the diffusion of toroidal magnetic field from the core's interior into the mantle. the poloidal and advective couples can be estimated by using models of the downward continued poloidal field and models of the core velocity. We find that neither the poloidal couple nor the advective couple exhibit sufficient variability to account for the decadal length of day variations. If this is true, and if core-mantle coupling is indeed predominantly electromagnetic, then most of the variability in the length of day must result from the leakage couple, which, unfortunately, cannot be calculated directly from surface observations.We assume that the horizontal component of the magnetic field is continuous across the core-mantle boundary, that the frozen-flux approximation adequately describes the time dependence of the horizontal component of the magnetic field at the core surface, and that most of this time dependence results from steady core motion. Then by treating the determination of the toroidal field at the core-mantle boundary as an inverse problem, we find that only very strong and spatially complex toroidal field models are consistent with both advection in the core and the decadal length of day variations. We argue that strong toroidal fields are necessary to account for the length-of-day variations since there is significant cancellation when the magnetic stress is integrated over the core-mantle boundary (CMB), the necessary time-dependent torque resulting from the slight and temporary non-cancellation of magnetic stress established by a slowly varying and spatially complex toroidal field. But, since our toroidal field models are too strong according to dynamo theory, produce electric fields at the Earth's surface which are stronger than measured values, and produce ohmic heating which either exceeds or contributes an unacceptably large fraction of the Earth's surface heat flow, we deem the toroidal-field models consistent with our analysis of electromagnetic coupling to be physically unreasonable. Thus, we argue that core-mantle coupling is not predominantly electromagnetic. However, this conclusion may not hold if, for example, core motion is highly time dependent, or if a strong diffusive boundary layer is present beneath the core-mantle boundary, the presence of which may allow for a significant discontinuity in the horizontal component of the magnetic field and the breakdown of the frozen-flux approximation.

Notes: We examine the problem of determining the fluid flow at the core surface given a model of the temporal variation of the magnetic field, seeking to fit the field over a finite time interval. The flow is assumed steady over the time interval, and we adopt the frozen-flux approximation. We produce a range of solutions of varying complexity and subject to different constraints, estimate the errors on the solutions, and assess their consistency with the underlying assumptions. We find both direct evidence for ageostrophic flow in the form of flow across the geographical equator, and indirect evidence in the form of poorer fits to the field when the flow is contained to be geostrophic. On account of this evidence we do not adopt the geostrophic approximation. However, we find that unconstrained flows are poorly determined, and consider the various alternatives for producing better determined solutions. We choose to restrict our attention to determining the large-scale toroidal part of the flow, and find a simple pattern of flow which is nearly symmetric about the equator. From a sequence of maps of the flow over 5-year time intervals back to 1915 we are still able to identify many of the basic aspects of this simple pattern, but changes in the flow pattern are discernible. Although our models of the flow explain a large proportion of the signal (typically 95 per cent of the variance), the fits which we obtain are not as good as might be expected. Failure of the underlying assumptions, together with our decision to map only the large-scale toroidal part of the flow, explains the poorer than expected fit.

Notes: [Auszug] In an earlier paper1 we presented models of the magnetic field at the core-mantle boundary (CMB) at approximately 60 yr intervals from 1715 to 1980. We showed that the secular variation (SV) is confined mainly to the hemisphere 90° E to 90° W, where its character has remained unaltered ...

Notes: [Auszug] Fig. 1 Map of the radial component of the magnetic field at the core-mantle boundary for 1980 (ref. 3). Contour interval is 100 |xT; solid contours represent flux into the core, broken contours flux out of the core; bold contours represent zero radial field. The two main pairs of lobes (1,3) and ...

Notes: [Auszug] Models of the magnetic field at the core–mantle boundary at selected epochs from 1715.0 to 1980.0 reveal novel features in the field at the core. These suggest that the flow of core fluid is coupled to the mantle, and that magnetic diffusion is ...

Notes: [Auszug] FIELD reversals, occurring roughly every million years, are the most dramatic of the wide range of phenomena exhibited by Earth's magnetic field. And the next reversal on Earth may not be so far away: if the current rate of decay of Earth's dipole component is maintained it will vanish in less than ...

Notes: [Auszug] An estimate of the magnitude and geometry of the magnetic field within the Earth's 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 ...

Notes: [Auszug] 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 ...