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Refinements on precession, Nutation, and Wobble of the Earth
VИronique Dehant, Royal Observatory of Belgium

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rigid Earth nutation

Forced Nutations
oceanic/atmospheric corrections

Non-rigid Earth nutation model Earth response comparison with observation

Earth interior model
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Earth rotation changes due to the core; core-mantle coupling
coupling mechanisms: topographic torque gravitational torque viscous torque electromagnetic torque

classically

this talk
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· Outer core electrical conductivity: known from laboratory experiments: 5 105 S m-1 (Stacey & Anderson 2001). · Lowermost mantle electrical conductivity (200 m layer at the base of the mantle): unknown but has to be lower than that of the core. sm= 10 S m-1, 5 104 S m-1, 5 105 S m-1 · RMS of the radial magnetic field at the CMB: from surface magnetic field measurements: > 0.3 mT. · Viscosity of the outer core fluid close to the CMB:
­ molecular viscosity: 10-6 m2 s-1 (laboratory experiments and ab initio computations). ­ eddy viscosity: < 10-4 m2 s-1 (Buffett & Christensen 2007).
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Electromagnetic torque + viscous torque: dissipative


Constraints on the physical properties of the CMB
Coupling model used: Buffet et al. 2002 for EM and Mathews & Guo 2005 for viscomagnetic From Koot et al. 2010

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Earth rotation changes due to the core; core-mantle coupling
coupling mechanisms: topographic torque gravitational torque viscous torque electromagnetic torque

How to explain high adopted negligible magnetic field? model
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Core Angular Momentum exchange due to topographic torque at CMB
pressure at CMB core-mantle boundary topography (<2km) Difficult, challenging but cannot be ruled out
mantle

core

e.g. Hide 1977

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Topographic torque computation
· Aim at obtaining torque and associated effects on nutation · Strategy: ­ Establish the motion equations and boundary conditions in the fluid; ­ Compute analytically the solutions; ­ Obtain the dynamic pressure as a function of the physical parameters; ­ Determine the topographic torque. · Assessment: Comparison with Wu and Wahr (1997) who used a numerical technique

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· Linearized Navier-Stokes equation:
velocity pressure

Differential equations and boundary conditions

Rotation gravitational force (equilibrium+mass redistribution+tides)

· Boundary conditions:
. = 0 . = 0

= +

=

forcing

Coriolis

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Nutation
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Earth rotation changes due to the core; core-mantle coupling
coupling mechanisms: topographic torque gravitational torque viscous torque electromagnetic torque

+ Core stratification

adopted model
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Topography, stratification, and magnetism
· chemical interactions between the core and the mantle
Mg-rich minerals FeSi FeO silicate mantle CMB

Buffett EPSL (2011)

iron core layer of excess light elements

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Stratification and magnetism
silicate mantle iron core motion almost parallel to constant density surfaces CMB

Buffett EPSL (2011)

little change in density and the resulting buoyancy forces are weak

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Topography, stratification, and magnetism
silicate mantle iron core motion almost parallel to constant density surfaces silicate mantle CMB

Buffett EPSL (2011)

little change in density and the resulting buoyancy forces are weak

CMB iron core vertical component of motion stratification Required strength Further from the boundary the stratified of the radial fluid is swept past the magnetic field can mantle with the underlying tidal flow be lowered.
density field in a stratified fluid is disturbed and a buoyancy force arises

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Observation Observation data
Celestial mechanics

Models Laboratory experiments

Nutation model Predictions

Residuals

Better understanding of the Earth interior!

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Precession, nutation, and wobble of the Earth
V. Dehant
Royal Observatory of Belgium

P. M. Mathews
University of Madras, India


THANK YOU FOR YOUR ATTENTION