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 Influence of the Solid Inner Core and Compressibility of the Fluid Core on the Earth Nutation

1991 ◽  
Vol 127 ◽  
pp. 250-253
Author(s):  
Sergei Diakonov
Keyword(s):  
Infinite System ◽  
Inner Core ◽  
Equations Of Motion ◽  
Liquid Core ◽  
Low Frequency ◽  
Approximate Solutions ◽  
Low Frequency Oscillations ◽  
The Earth ◽  
Fluid Core ◽  
Harmonic Representation

While calculating low frequency oscillations of the Earth liquid core spherical harmonic representation of the deformation field is usually used [1-3]:Substitution of (1) into the equations of motion gives an infinite system of differential equations for scalar functions Sɭm and Tɭm . Approximate solutions of such a system are obtained by truncating of the system. But results of [4] show that sometimes such method divergences.

scholarly journals Solved and unsolved questions in the non-rigid Earth nutation study

2007 ◽  
Vol 3 (S248) ◽  
pp. 374-378
Author(s):  
C. L. Huang
Keyword(s):  
Inner Core ◽  
Outer Core ◽  
Earth Model ◽  
Future Studies ◽  
Atmospheric Loading ◽  
The Earth ◽  
Core Boundary ◽  
Oceanic Tides ◽  
Rigid Earth ◽  
Electro Magnetic

AbstractAt the IAU 26th GA held in Prague in 2006, a new precession model (P03) was recommended and adopted to replace the old one, IAU1976 precession model. This new P03 model is to match the IAU2000 nutation model that is for anelastic Earth model and was adopted in 2003 to replace the previous IAU1980 model. However, this IAU2000 nutation model is also not a perfect one for our complex Earth, as stated in the resolution of IAU nutation working group. The Earth models in the current nutation theories are idealized and too simple, far from the real one. They suffer from several geophysical factors: the an-elasticity of the mantle, the atmospheric loading and wind, the oceanic loading and current, the atmospheric and oceanic tides, the (lateral) heterogeneity of the mantle, the differential rotation between the inner core and the mantle, and various couplings between the fluid outer core and its neighboring solids (mantle and inner core). In this paper, first we give a very brief review of the current theoretical studies of non-rigid Earth nutation, and then focus on the couplings near the core-mantle boundary and the inner core-outer core boundary, including the electro-magnetic, viscous, topographic, and gravitational couplings. Finally, we outline some interesting future studies.

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.

scholarly journals Torsional waves driven by convection and jets in Earth’s liquid core

2018 ◽  
Vol 216 (1) ◽  
pp. 123-129 ◽  
Author(s):  
R J Teed ◽  
C A Jones ◽  
S M Tobias
Keyword(s):  
Magnetic Field ◽  
Density Gradient ◽  
Inner Core ◽  
Liquid Core ◽  
Outer Core ◽  
Dynamo Action ◽  
Radial Magnetic Field ◽  
Torsional Waves ◽  
Plausible Mechanism ◽  
Rich Liquid

SUMMARY Turbulence and waves in Earth’s iron-rich liquid outer core are believed to be responsible for the generation of the geomagnetic field via dynamo action. When waves break upon the mantle they cause a shift in the rotation rate of Earth’s solid exterior and contribute to variations in the length-of-day on a ∼6-yr timescale. Though the outer core cannot be probed by direct observation, such torsional waves are believed to propagate along Earth’s radial magnetic field, but as yet no self-consistent mechanism for their generation has been determined. Here we provide evidence of a realistic physical excitation mechanism for torsional waves observed in numerical simulations. We find that inefficient convection above and below the solid inner core traps buoyant fluid forming a density gradient between pole and equator, similar to that observed in Earth’s atmosphere. Consequently, a shearing jet stream—a ‘thermal wind’—is formed near the inner core; evidence of such a jet has recently been found. Owing to the sharp density gradient and influence of magnetic field, convection at this location is able to operate with the turnover frequency required to generate waves. Amplified by the jet it then triggers a train of oscillations. Our results demonstrate a plausible mechanism for generating torsional waves under Earth-like conditions and thus further cement their importance for Earth’s core dynamics.

Constraints on core composition from shock-waves data

1982 ◽  
Vol 306 (1492) ◽  
pp. 37-47 ◽  
Keyword(s):  
Equations Of State ◽  
Liquid Core ◽  
Light Element ◽  
Outer Core ◽  
Atomic Ratio ◽  
Core Material ◽  
Solar Photosphere ◽  
The Core ◽  
The Earth ◽  
Core Composition

Seismic data demonstrate that the density of the liquid core is some 8-10 % less than pure iron. Equations of state of Fe-Si, C, FeS 2 , FeS, KFeS 2 and FeO, over the pressure interval 133-364 GPa and a range of possible core temperatures (3500- 5000 K), can be used to place constraints on the cosmochemically plausible light element constituents of the core (Si, C, S, K and O ). The seismically derived density profile allows from 14 to 20 % Si (by mass) in the outer core. The inclusion of Si, or possibly G (up to 11 %), in the core is possible if the Earth accreted inhomogeneously within a region of the solar nebulae in which a C :0 (atomic) ratio of about 1 existed, compared with a G : O ratio of 0.6 for the present solar photosphere. In contrast, homogeneous accretion permits Si, but not C, to enter the core by means of reduction of silicates to metallic Fe-Si core material during the late stages of the accumulation of the Earth. The data from the equation of state for the iron sulphides allow up to 9-13 % S in the core. This composition would provide the entire Earth with a S:Si ratio in the range 0.14-0.3, comparable with meteoritic and cosmic abundances. Shock-wave data for KFeS 2 give little evidence for an electronic phase change from 4s to 3d orbitals, which has been suggested to occur in K, and allow the Earth to store a cosmic abundance of K in the metallic core.

3. Minerals and the interior of the Earth

2014 ◽  
Author(s):  
David Vaughan
Keyword(s):  
Upper Mantle ◽  
Lower Mantle ◽  
Plate Tectonics ◽  
Inner Core ◽  
Indirect Evidence ◽  
Outer Core ◽  
The Earth ◽  
Granite Formation ◽  
Temperature And Pressure

‘Minerals and the interior of the Earth’ looks at the role of minerals in plate tectonics during the processes of crystallization and melting. The size and range of minerals formed are dependent on the temperature and pressure of the magma during its movement through the crust. The evolution of the continental crust also involves granite formation and processes of metamorphism. Our understanding of the interior of the Earth is based on indirect evidence, mainly the study of earthquake waves. The Earth consists of concentric shells: a solid inner core; liquid outer core; a solid mantle divided into a lower mantle, a transition zone, and an upper mantle; and then the outer rigid lithosphere.

scholarly journals New measurements of long-period radial modes using large earthquakes

2020 ◽  
Vol 224 (2) ◽  
pp. 1211-1224
Author(s):  
S Talavera-Soza ◽  
A Deuss
Keyword(s):  
Inner Core ◽  
Cross Coupling ◽  
Earth Model ◽  
Cylindrical Anisotropy ◽  
Long Period ◽  
Centre Frequency ◽  
The Earth ◽  
Radial Anisotropy ◽  
Crucial Information ◽  
Quality Factor Q

SUMMARY Radial modes, nS0, are long-period oscillations that describe the radial expansion and contraction of the whole Earth. They are characterized only by their centre frequency and quality factor Q, and provide crucial information about the 1-D structure of the Earth. Radial modes were last measured more than a decade ago using only one or two earthquakes. Here, we measure radial modes using 16 of the strongest and deepest earthquakes of the last two decades. By introducing more earthquake data into our measurements, we improve our knowledge of 1-D attenuation, as we remove potential earthquake bias from our results. For mode 0S0, which is dominated by compressional energy, we measure a Q value of 5982, much higher than previously measured, and requiring less bulk attenuation in the Earth than previously thought. We also show that radial modes cross-couple (resonate) strongly to their nearest spheroidal mode due to ellipticity and inner core cylindrical anisotropy. Cross-coupling improves the fit between data and synthetics, and gives better estimates of the centre frequency and attenuation value of the radial modes. Including cross-coupling in our measurements results in a systematic shift of the centre frequencies of radial modes towards the Preliminary Reference Earth Model. This shift in centre frequencies, has implications for the strength of the radial anisotropy present in the uppermost inner core, with our cross-coupling results agreeing with lower values of anisotropy than the ones inferred from just measuring the modes in self-coupling (isolation). Furthermore, cross-coupling between radial modes and angular-order two modes provides constraints on cylindrical inner core anisotropy, that will help us improve our knowledge of the 3-D structure of the inner core.

Flow in a Viscous Trailing Vortex

1959 ◽  
Vol 10 (2) ◽  
pp. 149-162 ◽  
Author(s):  
B. G. Newman
Keyword(s):  
Experimental Observation ◽  
Rotational Motion ◽  
Free Stream ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Longitudinal Velocity ◽  
Reynolds Numbers ◽  
Longitudinal Motion ◽  
Turbulent Vortex

SummaryThe equations of motion for an isolated laminar viscous vortex at moderate to large Reynolds numbers are linearised, by assuming that both the rotational velocity and the deficit of longitudinal velocity are small compared with that in the free stream. The rotational motion and the longitudinal motion may then be superimposed and solutions are readily obtained for each. If the vortex is generated by a body with profile drag it is predicted that the deficit of longitudinal velocity will be positive, which is in agreement with experimental observation. Further details of the solution and its relation to the flow in real vortices are discussed; and the theory is compared with some measurements in a turbulent vortex.

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