Non-linear equations for the rotation of a viscoelastic planet taking into account the influence of a liquid core

S U M M A R YThe geological evolution of the rotational axis of the Earth is most likely controlled by internal mass redistribution within the mantle. Palaeomagnetic observations suggest that it is episodic in nature, with periods of quasi-standstill alternating with periods of faster wander. Here, we investigate two models for the influence of mantle plumes that vary at different spatial wavelengths on the time variations of the rotational axis (true polar wander; TPW). In the first model, we represent an upwelling plume as a sphere whose radius varies as a function of the flux of material in the conduit and that traverses the mantle at the Stokes velocity. Such a plume produces very little wander of the rotational axis. We then study the effects of two superswells that mimic the ones observed with seismic tomography and conclude that a doming regime within the mantle involves significant polar wander. Some of the features of this TPW that are directly linked to the periodicity of doming are reminiscent of observed phases of slow and fast TPW, with similar peak velocities.True polar wander (TPW) is the coherent motion of Earth with respect to its rotation axis. In view of the angular momentum theorem, it may be interpreted physically as the motion of the rotational axis with respect to the fixed terrestrial frame described by hotspots. On geological timescales, this motion is most likely controlled by internal mass redistribution within the mantle.Palaeomagnetic evidence from recent Earth history suggests that this motion has been small. Palaeomagnetic studies combine apparent polar wander based on palaeomagnetic data (the palaeomagnetic reference frame) with motions of hotspots with respect to lithospheric plates (the hotspot reference frame). Given the relative motions between the plates, the position of these plates with respect to the rotation axis (provided by palaeomagnetic results), and the relative motions between plates and a reference frame attached to the mantle, TPW can be defined as the motion of the mantle with respect to the rotation axis. A recent study (Besse & Courtillot 2002), hereafter referred to as BC02, confirms earlier findings that TPW appears to be episodic in nature, with periods of quasi-standstill alternating with periods of faster TPW (Fig. 1). Specifically, the path back to 200 Ma shows a standstill at 160-130 Ma, then a circular track from 130 to 70 Ma and finally a standstill at 50-10 Ma. As a result of the uncertainties in models of hotspot kinematics prior to 130 Ma, the behaviour of the TPW prior to that time is doubtful. The major event since 130 Ma is the end of the 130-60 Ma period of relatively fast polar wander (where the TPW rate averages 30 km Ma −1 ), with a standstill (i.e. no or little TPW) from 50 Ma (possibly as early as 80 Ma because of larger 95 per cent confidence circles) to 10 Ma. It seems that TPW may have been negligible for approximately 50 Ma, but accelerated a few millions years ago, with a velocity of the order of 100 km Ma −1 ; this recent acceleration ...

Section: Theo Ry O F T H E Ro Tat I O N O F T H E E a Rt H O N G E O mentioning

confidence: 99%

Section: Theory Of the Rotation Of The Earth On Geological Timescalementioning

confidence: 99%

Upwelling plumes, superswells and true polar wander

Greff-Lefftz

2004

“…C ij is equal to the time convolution of the degree 2 tidal Love number k T ( t ) with the time history of the changes in the centrifugal potential (e.g. Lefftz et al 1991; Ricard et al 1993a) where G is the gravitational constant and * denotes time convolution.…”

Section: Theory Of the Earth’s Rotation On Geological Timescalesmentioning

confidence: 99%

Length of day variations due to mantle dynamics at geological timescale

Greff-Lefftz

2011

S U M M A R YThe geological evolution of length of day (LOD) variations is mainly controlled by the frictional tidal torque responsible for the secular slowdown of the Earth's rotation and for the receding of the Moon. Superimposed on this variation, which has existed since the early history of the planet, there are, at shorter timescales (less than 1 Myr), LOD perturbations induced by the glaciation-deglaciation cycles. In this paper, we investigate the influence of mantle dynamics on LOD at the geological timescale. We use the complete non-linear equations to compute the influence of mantle density heterogeneities on the angular velocity of the rotation, that is to say on the LOD. We discuss the degree zero coefficient of the spherical harmonic expansion of the mantle mass anomaly, which is strongly dependent on the conservation of mass of the Earth.We first compute the effects induced by upwelling domes and subducted plates sinking into the mantle, which are known to induce geological variations in the orientation of the rotation axis with respect to a fixed terrestrial frame (the so-called True Polar Wander). We find that the time-variable mantle density heterogeneities associated with the large-scale pattern of plate tectonic motions since 120 Ma and with the upwelling domes can perturb LOD by about 0.4 µs per year, that is, with an order of magnitude smaller than the effects induced by the last deglaciation. Superimposed on this linear trend, we show that there are fluctuations around 0.1-0.2 s Myr −1 on a timescale of a few tens of millions of years.We then combine a spherical model of mantle circulation with solutions for the equations governing the rotation of a viscous planet, to improve the constraint of mantle mass conservation.Finally, we compare our results with other effects.

“…Although important, this problem is not the only one which pertains to the Earth's rotational evolution: some other boundary conditions at the Earth's surface or at the core-mantle interface can also play a non-negligible role. We have presented elsewhere (Lefftz, Legros & Hinderer 1991) a non-linear theory for the rotation of a viscous planet with a Maxwell rheology and having a liquid core with a quasi-rigid differential rotation with respect to the mantle. Here we wish to present a simplified model using the linear approximation, in which the equatorial rotations of the Earth and its fluid core are always small with respect to the axial rotation relative to the mantle.…”

Section: Introductionmentioning

confidence: 99%

Some remarks about the rotations of a viscous planet and its homogeneous liquid core: linear theory

Lefftz

Legros

1992

Self Cite

S U M M A R Y Linear equations governing the rotation of the Earth are developed for a model with a Maxwell homogeneous mantle and a homogeneous inviscid fluid core having a differential rotation relative to the mantle.We find four eigenfrequencies for the equatorial perturbations in rotation. Two are well known: the rotational nearly diurnal frequency and the Chandlerian frequency with a damping related to the relaxation time of the Earth. The other two frequencies, one being a heavily damped long-period oscillation and the other one zero, are related to the relaxation modes, but are nevertheless coupled with the rotational eigenfrequencies.We investigate the kinetic and deformation energy resulting from both impulsive and time-constant geophysical sources. Using a generalized notation, we derive an analytical solution for the rotations of the Earth and its fluid core due to various excitation sources at the Earth's surface and at the core-mantle boundary.We obtain some results concerning phenomena acting at the CMB which are able to produce a significant shift of the rotation axis.