Effect of mantle and ocean tides on the Earth's rotation rate

International audienceAims: We aim to compute the rate of increase of the length of day (LOD) due to the axial component of the torque produced by the tide generating potential acting on the tidal redistribution of matter in the oceans and the solid Earth. Methods: We use an extension of the formalism applied to precession-nutation in a previous work to the problem of length of day variations of an inelastic Earth with a fluid core and oceans. Expressions for the second order axial torque produced by the tesseral and sectorial tide-generating potentials on the tidal increments to the Earth's inertia tensor are derived and used in the axial component of the Euler-Liouville equations to arrive at the rate of increase of the LOD. Results: The increase in the LOD, produced by the same dissipative mechanisms as in the theoretical work on which the IAU 2000 nutation model is based and in our recent computation of second order effects, is found to be at a rate of 2.35 ms/cy due to the ocean tides, and 0.15 ms/cy due to solid Earth tides, in reasonable agreement with estimates made by other methods