On the dynamical effects of an inhomogeneous liquid core in the theory of nutation

Molodensky, S. M.; Groten, E.

doi:10.1007/s001900050178

Cited by 12 publications

(5 citation statements)

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“…The differences between the solutions to Eqs. (58), (61), and (62) at N = 2 and N = 1 lead to differences between the amplitudes of the forced nutation far in excess of the errors of contemporary VLBRI observations; at the same time, the differences between the solutions at N = 3, 4, 5 and N = 2 prove to be very small (Molodensky and Groten, 1998a). This testifies to the fairly fast convergence of the expansions in powers of κ.…”

Section: Molodenskymentioning

confidence: 78%

“…In doing so, to avoid the above-mentioned instability of the solutions, we will use the technique of numerical integration of the equations for the bulk of the liquid core based on expansions in powers of the small parameter κ that is equal to the ratio of the period of diurnal rotation of the Earth to the period of forced nutation in space. An important advantage of this technique is the fast convergence of successive iterations for all principal nutational components-see Molodensky and Groten, 1998a. We present below the basic relationships determining the tides and nutation of an Earth that has a compositionally inhomogeneous, viscous liquid core with a frozen-in magnetic field and a solid inner core. We will show that the conditions of stability and self-consistency of the dynamical equations are satisfied to a very high accuracy for all principal tidal components except the fortnightly components (for which the parameter κ = ± 1/13.7 is not sufficiently small); it is this fact that warrants the use of the method described below.…”

Section: S M Molodenskymentioning

confidence: 99%

“…An exposition of the two above-described approaches is given in the papers cited above, and we will not consider them in detail. Instead, we will dwell on the technique of solving the problem based on the representation of oscillations in the rotating inhomogeneous, gravitating fluid as a superposition of solutions to the generalized Laplace tidal equations, which describe the oscillations of a thin spherical fluid shell with movable boundaries Sasao, 1995a, 1995b;Molodensky and Groten, 1996, 1998a, 1998b.…”

Section: Solutions To the Tidal Dynamical Equations For A Compositionmentioning

confidence: 99%

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Tides and nutation of the Earth: II. Realistic models of the liquid core

Molodensky

2005

Sol Syst Res

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In the first part of this study (Molodensky, 2004; hereinafter, paper I), a survey of the theory of tides and nutation of the Earth was given with the inclusion of the dynamical effects of the elastic mantle and liquid core in the framework of a very simple model of a homogeneous, incompressible core. Here, effects of the inhomogeneity, compressibility, and viscosity of the liquid core are considered, along with those of electromagnetic coupling of the liquid core with the mantle and solid inner core. Errors in the present-day measurements of the amplitudes of forced nutation (of the order of 20 arc µ s) are well below not only the dynamical effects of the Earth's liquid core but also the effects of the inelasticity of the mantle, the dynamical effects of the solid inner core, and the possible effects of electromagnetic coupling between the liquid core, solid inner core, and mantle. This opens up new avenues for astrometric studies of the mechanical properties and electrical conductivity of the mantle and solid inner core at very low frequencies. The modern data on the amplitudes and phases of the Earth's forced nutation cannot be interpreted entirely unambiguously, since the following factors remain unknown: (i) the role of the core-mantle electromagnetic coupling compared to the coupling due to core viscosity near the core-mantle boundary and (ii) the frequency dependence of the creep function of the mantle at low frequencies. In large measure, the effects of electromagnetic and viscous coupling can be separated if highprecision data on the tidal variations in the gravitational force at periods of about a day are invoked and allowances are made for the differences between the effects of viscous and electromagnetic coupling on the amplitudes and phases of forced nutation and on the tidal variations in the gravitational force. Here, ranges of possible values of the creep function are constructed for periods from one hour to one day; for these calculations, values consistent with the entire set of data on the forced nutation of the Earth are assumed for the effective dynamical flattening of the liquid core-mantle and liquid core-solid inner core boundaries (these values describe the ellipticity of the boundaries of the inner core, outer core, and mantle, as well as the electromagnetic coupling between the liquid core, mantle, and solid inner core).

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Section: Molodenskymentioning

confidence: 78%

Section: S M Molodenskymentioning

confidence: 99%

Section: Solutions To the Tidal Dynamical Equations For A Compositionmentioning

confidence: 99%

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Tides and nutation of the Earth: II. Realistic models of the liquid core

Molodensky

2005

Sol Syst Res

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“…The physical meaning of eqs (9a) and (12) is analogous to the meaning of eq. (71) of Molodensky & Groten (1998), who provide a detailed discussion on this subject. At the same time, there is a significant difference between the case of nutational motion [when | κ | = |( σ + ω )/ ω | ≪ 1] and the case of Chandler wobble (when σ/ω ≪ 1): in the first case, eq.…”

Section: Relations Between General 3‐d Hydrodynamical Equations Andmentioning

confidence: 99%

“…At the same time, there is a significant difference between the case of nutational motion [when | κ | = |( σ + ω )/ ω | ≪ 1] and the case of Chandler wobble (when σ/ω ≪ 1): in the first case, eq. (71) of the Molodensky & Groten (1998) contains a small parameter κ; this is why its numerical integration may be presented as an expansion of powers of this paramater. Eqs (9a) and (12) do not contain any small parameters; at the same time, they also belong to the class of ill‐posed (in the sense of Hadamard) boundary problems [because they are of hyperbolic type with one boundary condition (13) on the closed surface s; for a discussion see Melchior (1986, pp.…”

Section: Relations Between General 3‐d Hydrodynamical Equations Andmentioning

confidence: 99%

On the dynamical effects of a heterogeneous and compressible liquid core in the theory of Chandler wobble

Molodensky¹,

Groten²

1998

Geophysical Journal International

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The general 3‐D scalar equations of motion of the liquid core (with respect to the radial components of displacements and cubic dilatation) are constructed as a superposition of the solutions of ordinary differential equations describing the dynamics of a stably stratified, heterogeneous, compressible and inviscid rotating fluid inside thin spherical layers (Molodensky & Sasao 1995). The estimation of dynamical effects of a homogeneous and incompressible liquid core on the Chandler period (Groten, Lenhardt & Molodensky 1991) is generalized for the case of a heterogeneous, compressible, inviscid and neutrally stratified liquid core.

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On Some Physical Aspects of the Earth’s Rotation

Molodensky

1999

Acta Geod. Geoph. Hung

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On the dynamical effects of an inhomogeneous liquid core in the theory of nutation

Cited by 12 publications

References 0 publications

Tides and nutation of the Earth: II. Realistic models of the liquid core

Tides and nutation of the Earth: II. Realistic models of the liquid core

On the dynamical effects of a heterogeneous and compressible liquid core in the theory of Chandler wobble

On Some Physical Aspects of the Earth’s Rotation

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