scholarly journals The effect of the differential rotation of the earth inner core on the free core nutation

2019 ◽  
Vol 10 (2) ◽  
pp. 146-149 ◽  
Author(s):  
Mian Zhang ◽  
Chengli Huang
Keyword(s):  
Differential Rotation ◽  
Inner Core ◽  
Free Core Nutation ◽  
The Earth ◽  
Rotation Of The Earth

scholarly journals Spin rotation, Chandler wobble and free core nutation of isolated multi-layer pulsars

2012 ◽  
Vol 8 (S291) ◽  
pp. 392-392
Author(s):  
Alexander Gusev ◽  
Irina Kitiashvili
Keyword(s):  
Neutron Star ◽  
Differential Rotation ◽  
Heat Dissipation ◽  
Inner Core ◽  
Outer Core ◽  
Chandler Wobble ◽  
Time Of Arrival ◽  
Layer Model ◽  
Free Core Nutation ◽  
Rotation Pole

AbstractAt present time there are investigations of precession and nutation for very different celestial multi-layer bodies: the Earth (Getino 1995), Moon (Gusev 2010), planets of Solar system (Gusev 2010) and pulsars (Link et al. 2007). The long-periodic precession phenomenon was detected for few pulsars: PSR B1828-11, PSR B1557-50, PSR 2217+47, PSR 0531+21, PSR B0833-45, and PSR B1642-03. Stairs, Lyne & Shemar (2000) have found that the arrival-time residuals from PSR B1828-11 vary periodically with a different periods. According to our model, the neutron star has the rigid crust (RC), the fluid outer core (FOC) and the solid inner core (SIC). The model explains generation of four modes in the rotation of the pulsar: two modes of Chandler wobble (CW, ICW) and two modes connecting with free core nutation (FCN, FICN) (Gusev & Kitiashvili 2008). We are propose the explanation for all harmonics of Time of Arrival (TOA) pulses variations as precession of a neutron star owing to differential rotation of RC, FOC and crystal SIC of the pulsar PSR B1828-11: 250, 500, 1000 days. We used canonical method for interpretation TOA variations by Chandler Wobble (CW) and Free Core Nutation (FCN) of pulsar.The two - layer model can explain occurrence twin additional fashions in rotation pole motion of a NS: CW and FCN. In the frame of the three-layer model we investigate the free rotation of dynamically-symmetrical PSR by Hamilton methods. Correctly extending theory of SIC-FOC-RC differential rotation for neutron star, we investigated dependence CW, ICW, FCN and FICN periods from flatness of different layers of pulsar.Our investigation showed that interaction between rigid crust, RIC and LOC can be characterized by four modes of periodic variations of rotation pole: CW, retrograde Free Core Nutation (FCN), prograde Free Inner Core Nutation (FICN) and Inner Core Wobble (ICW). In the frame of the three-layer model we proposed the explanation for all pulse fluctuations by differential rotation crust, outer core and inner core of the neutron star and received estimations of dynamical flattening of the pulsar inner and outer cores, including the heat dissipation. We have offered the realistic model of the dynamical pulsar structure and two explanations of the feature of flattened of the crust, the outer core and the inner core of the pulsar.

Nutation terms adjustment to VLBI and implication for the Earth rotation resonance parameters

2019 ◽  
Vol 220 (2) ◽  
pp. 759-767 ◽  
Author(s):  
I Nurul Huda ◽  
S Lambert ◽  
C Bizouard ◽  
Y Ziegler
Keyword(s):  
Polar Motion ◽  
Inner Core ◽  
Resonance Parameters ◽  
Free Core Nutation ◽  
Long Baseline ◽  
The Earth ◽  
Significant Difference ◽  
Tidal Correction ◽  
Global Parameters

SUMMARY The nutation harmonic terms are commonly determined from celestial pole offset series produced from very long baseline interferometry (VLBI) time delay analysis. This approach is called an indirect approach. As VLBI observations are treated independently for every session, this approach has some deficiencies such as a lack of consistency in the geometry of the session. To tackle this problem, we propose to directly estimate nutation terms from the whole set of VLBI time delays, hereafter referred as a direct approach, in which the nutation amplitudes are taken as global parameters. This approach allows us to reduce the correlations and the formal errors and gives significant discrepancies for the amplitude of some nutation terms. This paper is also dedicated to the determination of the Earth resonance parameters, named polar motion, free core nutation, and free inner core nutation. No statistically significant difference has been found between the estimates of resonance parameters based upon ‘direct’ and ‘indirect’ nutation terms. The inclusion of a complete atmospheric-oceanic non-tidal correction to the nutation amplitudes significantly affected the estimates of the free core nutation and the free inner core nutation resonant frequencies. Finally, we analyzed the frequency sensitivity of polar motion resonance and found that this resonance is mostly determined by the prograde nutation terms of period smaller than 386 d.

Viscous drag and the differential rotation of the Earth's core

1997 ◽  
Vol 57 (1) ◽  
pp. 231-233
Author(s):  
DAVID L. BOOK ◽  
J. A. VALDIVIA
Keyword(s):  
Simple Model ◽  
Differential Rotation ◽  
Dynamic Viscosity ◽  
Inner Core ◽  
Outer Core ◽  
Viscous Drag ◽  
Earth’S Rotation ◽  
The Core ◽  
The Earth ◽  
Earth’S Inner Core

It is proposed that the differential rotation of the Earth's inner core deduced by Song and Richards is due to a combination of the deceleration of the Earth's rotation and the viscous drag between the Earth's inner and outer cores. If this model is correct then the dynamic viscosity in the outer core of the Earth can be estimated to be μ≈104 poise. Besides providing a novel way of determining the viscosity of the core, this simple model suggests some new tests and shows how astronomical effects can influence geological phenomena.

scholarly journals Rotational Velocity of an Earth Model with a Liquid Core

1979 ◽  
Vol 82 ◽  
pp. 313-314
Author(s):  
S. Takagi
Keyword(s):  
Rotational Motion ◽  
Velocity Vector ◽  
Inner Core ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Liquid Core ◽  
Outer Core ◽  
Earth Model ◽  
The Earth ◽  
Rotation Of The Earth

There have been many papers discussing the rotation of the Earth (Jeffreys and Vicente, 1957; Molodenskij, 1961; Rochester, 1973; Smith, 1974; Shen and Mansinha, 1976). This report summarizes the application of the perturbation method of celestial mechanics to calculate the rotation of the Earth (Takagi, 1978). In this solution the Earth is assumed to consist of three components: a mantle, liquid outer core, and a solid inner core, each having a separate rotational velocity vector. Hamiltonian equations of motion were constructed to solve the rotational motion of the Earth.

scholarly journals Methods for computing internal flattening, with applications to the Earth's structure and geodynamics

1998 ◽  
Vol 132 (3) ◽  
pp. 603-642 ◽  
Author(s):  
C. Denis ◽  
M. Amalvict ◽  
Y. Rogister ◽  
S. Tomecka-Suchoń
Keyword(s):  
Field Theory ◽  
Differential Rotation ◽  
Inner Core ◽  
Static Solution ◽  
Internal Field ◽  
Earth Model ◽  
Earth Structure ◽  
First Order ◽  
The Earth ◽  
Earth Models

SUMMARY After general comments (Section 1) on using variational procedures to compute the oblateness of internal strata in the Earth and slowly rotating planets, we recall briefly some basic concepts about barotropic equilibrium figures (Section 2), and then proceed to discuss several accurate methods to derive the internal flattening. The algorithms given in Section 3 are based on the internal gravity field theory of Clairaut, Laplace and Lyapunov. They make explicit use of the concept of a level surface. The general formulation given here leads to a number of formulae which are of both theoretical and practical use in studying the Earth's structure, dynamics and rotational evolution. We provide exact solutions for the figure functions of three Earth models, and apply the formalism to yield curves for the internal flattening as a function of the spin frequency. Two more methods, which use the general deformation equations, are discussed in Section 4. The latter do not rely explicitly on the existence of level surfaces. They offer an alternative to the classical first-order internal field theory, and can actually be used to compute changes of the flattening on short timescales produced by variations in the LOD. For short durations, the Earth behaves elastically rather than hydrostatically. We discuss in some detail static deformations and Longman's static core paradox (Section 5), and demonstrate that in general no static solution exists for a realistic Earth model. In Section 6 we deal briefly with differential rotation occurring in cylindrical shells, and show why differential rotation of the inner core such as has been advocated recently is incompatible with the concept of level surfaces. In Section 7 we discuss first-order hydrostatic theory in relation to Earth structure, and show how to derive a consistent reference Earth model which is more suitable for geodynamical modelling than are modern Earth models such as 1066-A, PREM or CORE11. An important result is that a consistent application of hydrostatic theory leads to an inertia factor of about 0.332 instead of the value 0.3308 used until now. This change automatically brings ‘hydrostatic’ values of the flattening, the dynamic shape factor and the precessional constant into much better agreement with their observed counterparts than has been assumed hitherto. Of course, we do not imply that non-hydrostatic effects are unimportant in modelling geodynamic processes. Finally, we discuss (Sections 7–8) some implications of our way of looking at things for Earth structure and some current problems of geodynamics. We suggest very significant changes for the structure of the core, in particular a strong reduction of the density jump at the inner core boundary. The theoretical value of the free core nutation period, which may be computed by means of our hydrostatic Earth models CGGM or PREMM, is in somewhat better agreement with the observed value than that based on PREM or 1066-A, although a significant residue remains. We attribute the latter to inadequate modelling of the deformation, and hence of the change in the inertia tensor, because the static deformation equations were used. We argue that non-hydrostatic effects, though present, cannot explain the large observed discrepancy of about 30 days.

scholarly journals Gravitational, Inertial and Toroidal Oscillations of the Outer Core and Their Related Free Wobbles

1980 ◽  
Vol 78 ◽  
pp. 185-186
Author(s):  
Po-Yu Shen
Keyword(s):  
Inner Core ◽  
Numerical Solutions ◽  
Outer Core ◽  
Angular Frequency ◽  
Inertial Oscillations ◽  
The Earth ◽  
Core Boundary ◽  
Restoring Forces ◽  
Rotation Of The Earth ◽  
Core Modes

According to the respective restoring forces of self-gravitation, Coriolis force, and inertial coupling at the boundaries, the free oscillations of a contained fluid can be classified into gravitational, inertial, and toroidal oscillations. For the outer core of the Earth, however, due to the interplay of rotation, elasticity, and self-gravitation, the gravitational undertones and inertial oscillations are not distinguishable. Both have eigenfunctions consisting of spheroidal and toroidal parts of about equal amplitude, and exist in alternating allowed and forbidden zones depending on the gravitational stability of the outer core. The forbidden zones for a stable core correspond to the allowed zones for an unstable core, while for a neutrally stratified core there appear to be no forbidden zones. The eigenfunction of a toroidal mode consists essentially of a primary toroidal field and a secondary spheroidal component of the order of ellipticity, coupled at the outer core-mantle or outer core-inner core boundary. Therefore, in general, toroidal core modes appear in doublets Sn+1m Tnm and Sn−1m Tn−1m with degenerate frequency equal to 2m/n(n+1) times the angular frequency of rotation of the Earth. The ellipticities of the outer core boundaries are responsible for the removal of the degeneracy. It is shown that the primary toroidal and secondary spheroidal fields constitute the “generalized Poincare motion” which, for the fundamental mode S21T11, reduces to the “simple motion” defined by Poincare in 1910. Numerical solutions have been obtained for all three types of free core modes. While those for gravitational undertones and inertial oscillations are obtained by arbitrarily truncating the hydrodynamic equations, it is shown that the eigensolutions for toroidal modes are correct to first order in ellipticity due to the particular geometry of the outer core of the Earth.

On the dynamical theory of the rotation of the earth

1948 ◽  
Vol 44 (3) ◽  
pp. 345-359 ◽  
Author(s):  
H. Bondi ◽  
R. A. Lyttleton
Keyword(s):  
Rigid Body ◽  
Inner Core ◽  
Deformable Body ◽  
A Priori ◽  
Dynamical Theory ◽  
Outer Shell ◽  
Angular Velocity Vector ◽  
The Core ◽  
The Earth ◽  
Rotation Of The Earth

In the dynamical theory of the motion of the Earth relative to its centre of mass, the planet is usually regarded as a rigid or at most only slightly deformable body, and moments of inertia are adopted that are taken to refer to the Earth as a whole, while the motion itself at any instant is assumed capable of representation by a single angular velocity vector. This procedure, however, appears to involve unwarranted assumptions the recognition and removal of which may lead to conclusions of considerable importance. For it is well known from the theory of earthquake waves that the material of the central core of the Earth behaves like a liquid in that it transmits only longitudinal wave vibrations, while there is also other evidence suggesting that the material of the core is a true liquid (1). There is accordingly no a priori reason for supposing that the core will behave like a rigid body firmly attached to the surrounding shell if more or less permanent shearing forces are applied to it. In particular, in respect of any couple known to act on the outer shell, it is not permissible to assume, without examination of the assumption, that its effect will be transferred immediately to the inner core in a way preserving rigid-body rotation of the whole. If the material of the core behaves like a liquid where wave-motion is concerned, this suggests that it will probably also behave like a liquid whatever shearing forces act on it, and the extent to which changes in the rotatory motion of the outer shell can be communicated to the core, and what effects direct gravitational forces acting on the core may have, must in the first instance be questions of hydrodynamics and not rigid dynamics.

Ups and Downs

2018 ◽  
Author(s):  
Roy Livermore
Keyword(s):  
Mantle Convection ◽  
Laboratory Experiments ◽  
Inner Core ◽  
Computer Modelling ◽  
Great Depth ◽  
New Horizons ◽  
The Core ◽  
The Earth ◽  
The World ◽  
The 1960S

Despite the dumbing-down of education in recent years, it would be unusual to find a ten-year-old who could not name the major continents on a map of the world. Yet how many adults have the faintest idea of the structures that exist within the Earth? Understandably, knowledge is limited by the fact that the Earth’s interior is less accessible than the surface of Pluto, mapped in 2016 by the NASA New Horizons spacecraft. Indeed, Pluto, 7.5 billion kilometres from Earth, was discovered six years earlier than the similar-sized inner core of our planet. Fortunately, modern seismic techniques enable us to image the mantle right down to the core, while laboratory experiments simulating the pressures and temperatures at great depth, combined with computer modelling of mantle convection, help identify its mineral and chemical composition. The results are providing the most rapid advances in our understanding of how this planet works since the great revolution of the 1960s.

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