Decade Fluctuations Research Articles

Planetary gyre, time‐dependent eddies, torsional waves, and equatorial jets at the Earth's core surface

AbstractWe report a calculation of time‐dependent quasi‐geostrophic core flows for 1940–2010. Inverting recursively for an ensemble of solutions, we evaluate the main source of uncertainties, namely, the model errors arising from interactions between unresolved core surface motions and magnetic fields. Temporal correlations of these uncertainties are accounted for. The covariance matrix for the flow coefficients is also obtained recursively from the dispersion of an ensemble of solutions. Maps of the flow at the core surface show, upon a planetary‐scale gyre, time‐dependent large‐scale eddies at midlatitudes, and vigorous azimuthal jets in the equatorial belt. The stationary part of the flow predominates on all the spatial scales that we can resolve. We retrieve torsional waves that explain the length‐of‐day changes at 4 to 9.5 years periods. These waves may be triggered by the nonlinear interaction between the magnetic field and subdecadal nonzonal motions within the fluid outer core. Both the zonal and the more energetic nonzonal interannual motions were particularly intense close to the equator (below 10∘ latitude) between 1995 and 2010. We revise down the amplitude of the decade fluctuations of the planetary‐scale circulation and find that electromagnetic core‐mantle coupling is not the main mechanism for angular momentum exchanges on decadal time scales if mantle conductance is 3 × 108 S or lower.

Historical eclipses and the variability of the Earth's rotation

Ancient Babylonian clay tablets buried for centuries beneath the sands of the desert are part of an extensive historical archive which contains vital information about the rotation of the Earth. Many eclipse records are preserved from a variety of cultures, and using these seemingly crude ancient and medieval observations, variations in the Earth's rotation can be traced back over the past 2500 years. The tidal torque exerted by the Moon (and to a lesser extent, the Sun) is the predominant mechanism in reducing the Earth's rate of spin. It is known that by this mechanism, the length of the day is increasing by 2.3 ms per century. From analyses of the discordance between observations and calculations of eclipses, the average measured increase in the length of the day is 1.8 ms per century, from which it is concluded that besides the tidal contribution there is another long-term component acting to decrease the length of the day by 0.5 ms per century. This component, which is thought to result from the decrease of the Earth's oblateness following the last ice age, is consistent with recent measurements made by artificial satellites. Besides these secular trends, there is clear evidence of fluctuations of the length of the day on a timescale of centuries, with an amplitude of 4 ms which is similar to that of the decade fluctuations.

Control of inner core rotation by electromagnetic, gravitational and mechanical torques

We compute the polar rotation of the Earth's inner core in response to the combined effects of electromagnetic, gravitational and mechanical torques. We obtain electromagnetic torques between 10 18 and 10 20 Nm, compared to gravitational torques between 10 19 and 10 21 Nm estimated by Xu et al. [Xu, S., Crossley D., Szeto, A.M.K., 1999. Variations in length of day and inner core differential rotation from gravitational coupling. Phys. Earth Planet. Inter., 116, 95–110] and Buffett [Buffett, B.A., 1996b. A mechanism for decade fluctuations in the length of day. Geophys. Res. Lett., 23, 3803–3806.], respectively. We obtain mechanical torques on the order of 10 15 Nm. Gravitationally dominated cases produce inner core oscillations with periods between 1 and 10 years. In electromagnetically dominated cases, the inner core rotates close to the imposed rotation rate of the outer core fluid. Modulations in the rotation rate are produced as the inner core passes through successive gravitational wells. These modulations occur over roughly 90 year timescales for outer core flow rates of 1°/year. When the electromagnetic torques are only marginally stronger than the gravitational torques, the inner core slowly rotates prograde by 90° relative to the mantle, escaping a gravitational well in roughly 100 years, then falls into the next gravitational well, rotating through 90° in just 4 years. Finite inner core viscosity is modeled using a relaxation time for the inner core topography. With relaxation, the gravitational torque reduces but does not eliminate the anomalous inner core rotation. Because of the short timescales of many of the irregularities in inner core rotation, it may be possible to observe them in presently-available seismic data.

A mechanism for decade fluctuations in the length of day

Strong gravitational coupling between the solid inner core and the mantle provides a means of exchanging angular momentum between the fluid outer core and the mantle. The proposed mechanism involves oscillations in the fluid core which exert a large electromagnetic torque on the inner core by virtue of its high electrical conductivity. The inner core does not freely respond to this torque because it is constrained by gravitational forces to remain nearly aligned with the mantle. Angular momentum is transferred to the mantle by the gravitational torques that result from small misalignments with the inner core. A calculation of the normal modes of this coupled system predicts observable fluctuations of the mantle with periods of several decades. Damping of the oscillations due to ohmic losses produces a quality factor Q of about 20. An excitation mechanism to sustain the oscillations is proposed on the basis of recent dynamo calculations.

Climate variations and the earth's rotation

The similar temporal behaviour of climate parameters and the Earth's rotation leads to the assumption that there exists a relation between both phenomena. As is well known, the relationship between atmospheric dynamics and the Earth's rotation is proved to vary seasonally. In the area of decade fluctuations, which are more related to climate change, the 11- and 22-years periods could be proved to be generated by atmospheric dynamics. Longer periods are caused by core-mantle coupling torques which are possibly related to climate change via geomagnetic field variations.

About possible geophysical causes of the decade fluctuations in the length of day

AbstractFluctuations in the length of day (Δlod) can be caused by temporal variations of the inertia tensor described by the excitation function and by disturbances of the torque balance between core and mantle. Recent models of the atmospheric excitation of the variations of the lod certainly failed with respect to longer periods (e.g., at about 70 years), but seem to be responsible for the annual period, the 22 years period and for a part of the nearly 30 years period. So, another geophysical phenomenon is needed which is responsible for the remaining part of unexplained lod variations. Previous studies of the geomagnetic core‐mantle coupling were re‐examined using lod values from which atmospherically excited parts were removed. The remaining part of the 30 years period could be explained by core‐mantle coupling. Additionally, the torque blance was realized by assuming lower values of the electrical conductivity at the bottom of the mantle. It was concluded that the consideration of geophysical processes within atmosphere and hydrosphere will be important for future refinements of the core‐mantle coupling models of the decade fluctuations in the lod.

Fluctuations in the Earth's rotation since 1830 from high-resolution astronomical data

SUMMARY Fluctuations in the Earth's rotation since 1830, as evidenced by changes in the length of the day, are derived from astronomical data having subannual resolution. Before 1955.5, timings of linar occultations are used; after 1955.5, the data are taken from the time series TAI-UT1. Although the data in the earliest period, 1830–90, display decade fluctuations in the length of the day, they are not accurate enough to reveal interannual variations. In this regard, also, the results from 1890–1925 are somewhat dubious. The quality of the data after 1925, though, is such that the temporal behaviour of the interannual fluctuations in the length of the day can be traced with confidence. We present plots of the interannual fluctuations in the period 1890–1987 and the longer-term decade fluctuations in the period 1830–1983. The interannual fluctuations in the length of the day since 1925 are compared with an index of the El Nino/Southern Oscillation (ENSO) phenomenon in the ocean-atmosphere system and are subjected to spectral analysis. The results support the conclusions reached by other authors that these fluctuations are linked to circulation changes in the atmosphere associated with ENSO, and in part to the quasi-biennial oscillation in the equatorial stratosphere's zonal winds. A spectral analysis of our 62 yr series of length of day values since 1925 reveals two significant peaks in the interannual range 2–4 yr. One is roughly biennial and the other is about twice this period, broadly supporting results obtained previously from shorter records. Our analysis of high-resolution data, therefore, contributes to ongoing efforts to establish a close relationship between the length of the day and aspects of the global climate system in the period before modern data became available in 1955.5.

Antennacluster-Antennacluster VLBI for Study of the Core-Mantle Coupling

Search for evidences of the dissipative core-mantle coupling is probably the most interesting subject for VLBI Earth rotation observations in view of physical informations to be obtained about the core-mantle boundary region. It is shown that the VLBI detected out-of-phase component of the retrograde annual nutation term is most likely to be a manifestation of the dissipative coupling because the coupling coefficient required to explain the observed out-of-phase component is just in the same order of magnitude as the one associated with the decade fluctuations in the rotation rate of the Earth, which are commonly attributed to the dissipative core-mantle coupling. Several observational tests are proposed to clarify the mechanism and frequency characteristics of the coupling. Researches along this direction require accuracy and time resolution of the VLBI observations beyond their present-day level. It is shown that a VLBI system of new design, 'antennacluster-antennacluster VLBI system', will be able to realize the high performance required.

Decade fluctuations in the Earth's rate of rotation and long-term librations in polar motion

An investigation into long series of astronomical latitude and time observations is presented in order to analyse their long-term variations. Decade fluctuations in the Earth's rate of rotation and long-term librations in polar motion (secular drift and Markowitz wobble) are discussed. Available data show a good correlation between observed rotational acceleration of the Earth and the motion of the mean pole over periods of about thirty years.

Decade fluctuations in the rotation rate of the earth in the last 200 years

Maximum Entropy Spectral Analysis and Multiple Regression Analysis of the 200 year series (1781–1980) of the change in L.O.D. (Length of Day) revealed significant peaks atT=21, 32, 50, 63 and possibly 120 years. The periodsT=22 and 44 years seem to be stable over 200 years.

Core-mantle topographic torque: a spherical harmonic approach and implications for the excitation of the Earth's rotation by core motions

The interaction of the fluid pressure over the topography of the core mantle boundary generates a torque that leads to perturbations in the Earth's rotation. A general formulation of this topographic torque is proposed with the help of a development in spherical harmonics of the pressure and shape. Various implications of this coupling mechanism are discussed according to the symmetry properties of the dynamic pressure field at the core surface and the distribution of the topographical deviations (bumps) of the core mantle boundary inferred from seismology. Specifically, it is shown that different interaction terms contribute to the equatorial torque; although their sum cannot be precisely quantified using present knowledge, it could be sufficient to excite the Earth's wobble. The axial torque contribution seems to be too large to explain the decade fluctuations of the Earth's rotation rate, suggesting the existence of a mechanism which reduces the axial resulting torque without altering the equatorial one.

Electromagnetic core-mantle coupling: The fourier method for the solution of the induction equation

Abstract The Gauss coefficients of the geomagnetic field since 1903 are used as a time-dependent boundary condition for the poloidal field in the Earth's mantle. The coefficients are Fourier transformed, and the induction equation for the mantle field is solved in Fourier space. The phase advance of the poloidal field at the base of the mantle, and of the ensuing “poloidal” electromagnetic couple, is investigated as a function of the conductivity profile. Since, except for the phase shift, the couple behaves essentially as the one calculated by Stix and Roberts (1984) for each epoch separately, the “toroidal” part of the couple is calculated according to their instantaneous method. The phase shift is then obtained from a comparison with the couple required by the decade fluctuations in the length of the day. This permits a determination of the electrical conductivity of the mantle, which we find to be a rather flat function of radius.

The influence of the electromagnetic core‐mantle coupling torques on earth's rotation

AbstractThe electromagnetic core‐mantle coupling is one of the most likely hypotheses to explain the connections between both, the decade fluctuations of the Earth rotation and such of the magnetic field of the Earth. Within this paper, the axial and equatorial electromagnetic torques are computed at time intervals of two years from 1903.5 to 1975.5. They are compared with mechanical torques necessary for the excitation of the decade variations of the rotation of the Earth. The comparison is made with regard to the magnitude of the torques, to their time behaviour and to the periods within the time variations of both types of the torques. The computed electromagnetic torques are comparable with that necessary to excite the variations of the rotation of the Earth. But they are two or three orders less than that necessary to excite the decade variations of the polar motion. Some comparable periods were found within the spectra of the electromagnetic and the mechanical torques. This speaks in favour of the core‐mantle coupling. But there are differences between both spectra too hinting at other processes which we cannot describe by a simple model of the core‐mantle coupling.

Causes of fluctuations in the rotation of the Earth

Over the last decade considerable progress has been made in closing the gap between geophysical theory and the observed changes in the Earth's spin rate and polar motion, which are affected by the Earth’s internal structure, properties and processes. New observational techniques and data have had a marked impact on understanding the short-term variations in the length of day and pole position, but we can expect between another 5 and 30 years to pass before they permit improved explanations of longer-term phenomena (18.6 year tidal effects, the Markowitz wobble, decade fluctuations in the length of day, etc.) This review summarizes recent advances, problems newly illuminated by recent Earth rotation data (for example mantle anelasticity, core-mantle coupling) and problems still unresolved.

Time-dependent electromagnetic core-mantle coupling

The magnetic field in the Earth's mantle is computed using a depth-dependent electrical conductivity, of form σ = σ a ( r/ a) − α , and an approximation scheme in which the electromagnetic time constant of the mantle is assumed small compared with the time scales of the secular variation, and in which the induced currents and fields are obtained iteratively. We first associate the toroidal fields in the mantle with motions at the core surface ( r = a) which create the observed geomagnetic field by flux rearrangement, and compute the resulting couple, Γ, parallel to the geographical axis. Using only zonal core motions, and values σ a = 3 × 10 3 ω −1 m −1, α = 30 for the conductivity profile, we find that the toroidal induced fields create a couple, Γ T, that over most of this century has been roughly ten times greater than the poloidal part, Γ S, of Γ, and has the same sign. The total couple, Γ, has fluctuations of order 10 18 Nm as required for the observed decade fluctuations in the length of the day. Its average is ∼ −1.5 × 10 18 Nm, i.e., it is too large to remain unbalanced. We suppose that an equally important couple in the opposite sense is created by flux leakage from the core, and we estimate the necessary gradient of toroidal field in the core to be of order −0.5 Gs km −1 at the core surface. During the course of the data analysis needed for the present work, we found some evidence for a torsional wave in the Earth's core with a period of ∼ 60 y.

On electromagnetic core-mantle coupling

Abstract The induced magnetic field in the Earth's mantle is computed for an electrical conductivity of the mantle of form σ = σa(a/r)α where a is the core radius. When the inducing core motion is a uniform westward drift of −10−10s−1 relative to the mantle, the retarding couple reaches −1019 Nm. This result can be obtained with values σα and α such that the time scale of screening, μσa2/α2, is still below 10 years. The retarding couple, and in particular the contribution from the higher field harmonics, increases with increasing concentration of the conducting layer towards the core-mantle boundary. Deviations from the average torque balance of order 10% of the retarding couple can account for the “decade fluctuations” in the Earth's rate of rotation.

On the topographic coupling at the core-mantle interface

The mean tangential stresses at a corrugated interface between a solid, electrically insulating mantle and a liquid core of magnetic diffusivity λ are calculated for uniform rotation of both mantle and core at an angular velocity Ω in the presence of a corotating magnetic field B. The core and mantle are assumed to extend indefinitely in the horizontal plane. The interface has the form z = η( x, y), where z is the upward vertical distance and x, y are the zonal and latitudinal distances respectively. The function η( x, y) has a planetary horizontal length scale (i.e. of the order of the radius of the Earth) and small amplitude and vertical gradient. The liquid core flows with uniform mean zonal velocity U 0 relative to the mantle. Ω and B possess vertical and horizontal components. The vertical (poloidal) component B p is uniform and has a value of 5 G while the horizontal (toroidal) field B T = B p αz, where α is a constant. When |α| ⪡ 1, the mean horizontal stresses are found to have the same order of magnitude (10 −2 N m −2) as those inferred from variations in the decade fluctuations in the length of the day, although the exact numerical values depend on the orientation of Ω as well as on the wavenumbers in the zonal and latitudinal directions. The influence of the steepness (as measured by α) of the toroidal field on the stresses is investigated to examine whether the constraint that the mean horizontal stresses at the core-mantle interface be of the order of 10 −2 N m −2 might provide a selection mechanism for the behaviour of the toroidal field in the upper reaches of the outer core of the Earth. The results indicate that the restriction imposed on α is related to the value assigned to the toroidal field deep into the core. For example, if |α| ⪢ 1 then the tangential stresses are of the right order of magnitude only if the toroidal field is comparable with the poloidal field deep in the core.

Decade fluctuations in geomagnetic westward drift and Earth rotation

Numerous studies of the variations of the Earth's rotation have been made since 1900 (summarized in refs 1, 2). It seems well established that variations in the rotation with periods equal to or less than 2 yr are due to variations in the zonal circulation of the atmosphere2–4. However, there is no general agreement about the cause of the longer-period variations of the Earth's rotation, sometimes known as the ‘decade variations’, although the most favoured explanation is electromagnetic core–mantle coupling (see ref. 5). Several studies6–8 of the correlation between Earth rotation and magnetic field variations have obtained marginally positive results. We have been able to clarify such a correlation over the past 120 yr by studying those magnetic field indicators that are the most sensitive to variations in westward drift of the outer regions of the core. We suggest here that the correlation can be extended back ∼300 yr. Simple models of core–mantle coupling, based on Dullard's ideas, give reasonable quantitative agreement with the observations.

Effect of the fluid core on changes in the length of day due to long period tides

The long period luni-solar tidal potential is known to cause periodic changes in the Earth's rotation rate. We find that the effect of a dissipationless fluid outer core is to reduce the amplitudes of these tidal perturbations by ∼ 11 per cent. When the fluid core effect is added to Agnew & Farrell's estimate of the effect of an equilibrium ocean, the result is in accord with observation. The effects of dissipative processes within the fluid core are also examined. We find out-of-phase perturbations which could be as large as ∼ 10ms at 18.6 yr. We conclude, however, that the poorly understood decade fluctuations in the Earth's rotation rate will prohibit observation of this effect.

Re-determination of the decade fluctuations in the rotation of the Earth in the period 1861-1978

Summary The ‘decade’ fluctuations in the Earth's rate of rotation are derived from a comparison of the universal time-scale, based on the Earth's diurnal rotation, with: (a) the dynamical time-scale of the lunar ephemeris from 1861 to 1955 (using the collected times of occultations of stars), and (b) the international atomic time-scale from 1955 to 1978. It is concluded from these fluctuations that the torques which operated on the Earth's mantle varied in magnitude in a characteristic period of about 30 yr and reached a maximum of 1018Nm around 1900.