An interpretation of the core–mantle interaction problem
Juan Getino,
Juan Getino
National Astronomical Observatory. Celestial Mechanics Division, Mitaka-Shi, Tokyo 181, Japan
On leave from Departamento de MatemAtica Aplicada Fundamental, Facultad de Ciencias, 47005 Valladolid, Spain.
Search for more papers by this authorJuan Getino,
Juan Getino
National Astronomical Observatory. Celestial Mechanics Division, Mitaka-Shi, Tokyo 181, Japan
On leave from Departamento de MatemAtica Aplicada Fundamental, Facultad de Ciencias, 47005 Valladolid, Spain.
Search for more papers by this authorSUMMARY
This paper deals with the canonical formulation of the rotation of a non-rigid earth with a heterogeneous stratified liquid core. The treatment of Kubo (1979) for a rigid core-rigid mantle earth model is extended by considering the core as liquid instead of rigid. We show that the tensional torque introduced by Kubo to explain the core-mantle interaction is due to the hypothesis of rigidity of the core, this interaction now being included in the new expression of the kinetic energy. More precisely, this interaction is due to a kind of variation or deformation of the inertia tensor of the core, which we have named inertial deformation, in correspondence with the inertial coupling of Sasao. Okubo & Saito (1980) and Kubo (1979) among other authors. The Hamiltonian obtained is compared with that of Sevilla & Romero (1987), showing the equivalence between them.
References
-
Busse, F.H., 1970. The dynamical coupling between inner core and mantle of the Earth and the 24 year libration of the pole, in
Earthquake Displacement Fields and the Rotation of the Earth, pp. 88–98, eds
L. Mansinha,
D.E. Smylie &
A.E. Beck, Reidel,
Dordrecht
.
10.1007/978-94-010-3308-4_9 Google Scholar
- Dehant, V., Hinderer, J., Legros, H. & Lefftz, M., 1993. Analytical approach to the computation of the Earth, the outer core and the inner core: rotational motions, Phys. Earth planet. Inter., 76, 259–282.
- Getino, J., 1994a. Kinetic energy of a non-spherical elastic Earth mantle in Andoyer variables, Celest. Mech., in press.
- Getino, J., 1994b. Forced nutations of a rigid mantle-liquid core Earth model. Geophys. J. Int., submitted.
- Getino, J. & Ferrándiz, J.M., 1990. A Hamiltonian theory for an elastic Earth: canonical variables and kinetic energy, Celest. Mech., 49, 303–326.
- Getino, J. & Ferrándiz, J.M., 1991a. A Hamiltonian theory for an elastic Earth: elastic energy of deformation. Celest. Mech., 51, 17–34.
- Getino, J. & Ferrándiz, J.M., 1991b. A Hamiltonian theory for an elastic Earth: first order analytical integration, Celest. Mech., 51, 35–65.
- Getino, J. & Ferrándiz, J.M., 1994a. On the effect of the elastic mantle on the Earth rotation, Celest. Mech., in press.
- Getino, J. & Ferrándiz, J.M., 1994. A rigorous Hamiltonian approach to the rotation of elastic bodies. Celest. Mech., 58, 277–295.
- Hori, G., 1966. Theory of general perturbations with unspecified canonical variables, Publ. Astron. Soc. Jpn. 18, 287.
- Jeffreys, H., 1948. The Earth's core and the lunar nutation, Mon. Not. R. astr. Soc., 108, 206.
- Jeffreys, H. & Vicente, R.O., 1957a. The theory of nutation and the variation of latitude, Mon. Not. R. astr. Soc., 117, 142–161.
- Jeffreys, H. & Vicente, R.O., 1957b. The theory of nutation and the variation of latitude: The Roche model core, Mon. Not. R. astr. Soc., 117, 162–173.
- Kakuta, C., Okamoto, I. & Sasao, T., 1975. Is the nutation of the solid inner core responsible for the 24 year libration of the pole?, Publ. Astron. Soc. Jpn, 71, 357–365.
- Kinoshita, H., 1977. Theory of the rotation of the rigid Earth, Celest. Mech., 15, 277–326.
- Kinoshita, R. & Souchay, J., 1990. The theory of the nutation for the rigid Earth model at the second order, Celest. Mech., 48, 187–265.
- Kubo, Y., 1979. A core-mantle interaction in the rotation of the Earth, Celest. Mech., 19, 215–241.
- Markowitz, Wm., 1960. Longitude, latitude and secular motion of the pole, in Methods and Techniques in Geophysics, p. 325, ed. S.K. Runcorn, Interscience Publ., New York .
- Markowitz, Wm., 1968. Continental Drift, Secular Motion of the Pole, and Rotation of the Earth, in Proceedings of the IAU Symp. No. 32, p. 25, eds Wm. Markowitz, & B. Gunot, Reidel, Dordrecht .
- Mathews, P. M., Buffet, B.A., Herring, T.A. & Shapiro, I.I., 1991a. Forced nutations of the Earth: Influence of inner core dynamics, 1, Theory, J. geophys. Res., 96 (B5), 8219–8242.
- Mathews, P.M., Buffet, B.A., Herring, T.A. & Shapiro, I.I., 1991b. Forced nutations of the Earth: Influence of inner core dynamics, 2, Numerical results and comparisons. J. geophys. Res., 96 (B5), 8243–8257.
- Molodensky, M.S., 1961. The theory of nutation and diurnal Earth tides, Commun. Obs. R. Belg., 188, 25–56.
-
Moritz, H., 1982. A variational principle for Molodensky's liquid core problem, Bull. Geod., 56, 381–400.
10.1007/BF02525735 Google Scholar
- Moritz, H., 1984. Cursillos de Geodesia Superior, No. 1. Instituto Geofísico Nacional-Instituto de Astronomía y Geodesia, Madrid .
- Moritz, H. & Mueller, I., 1987. Earth Rotation, Ungar, New York .
- Nikitina, L.V., 1990. Angle between the axes of rotation of the Earth's core and mantle, Geomagn. Aeron., 30, 702–705.
- Poincaré, H., 1910. Sur la précession des corps deformables. Bull. Astron., 27, 321–356.
- Sasao, T., Okubo, S. & Saito, M., 1980. A simple theory on the dynamical effects of a stratified fluid core upon nutational motion of the Earth, in Proceedings of IAU Symp. No. 78, pp. 165–183.
-
Sevilla, M. &
Romero, P., 1987. Polar motion for an elastic Earth model with a homogeneous liquid core using a canonical theory.
Bull. Geod., 61, 1–20.
10.1007/BF02520412 Google Scholar
-
Shen, P. &
Mansinha, L., 1976. Oscillation, nutation and wobble of an elliptical Earth with liquid outer core, Geophys. J. R. astr. Soc., 46, 167–196.
10.1111/j.1365-246X.1976.tb04167.x Google Scholar
- Smith, M.L., 1977. Wobble and nutation of the Earth, Geophys. J. T. astr. Soc., 50, 103–140.
- Szeto, A.M.K. & Smylie, D.F., 1984. Coupled motions of the inner core and possible geomagnetic implications. Phys. Earth planet. Inter., 36, 27–42.
- Wahr, J.M., 1981a. A normal mode expansion for the forced response of a rotating Earth, Geophys. J. R. astr. Soc., 64, 651–675.
- Wahr, J.M., 1981b. Body tides of an elliptical, rotating, elastic and oceanless Earth, Geophys. J. R. astr. Soc., 64, 677–703.
- Wahr, J.M., 1981c. The forced nutations of an elliptical, rotating, elastic and oceanless Earth, Geophys. J. R. astr. Soc., 64, 705–727.
- Woolard, E.W., 1953. Theory of the rotation of the Earth around its center of mass, Astron. Pap. Am. Ephemeris, 15 (1).
