1204.3957 (Sylvio Ferraz-Mello)
Sylvio Ferraz-Mello
New theory of the dynamical tides of celestial bodies founded on a Newtonian creep instead of the classical delaying approach of the standard viscoelastic theories. The results of the theory derive mainly from the solution of a non-homogeneous ordinary differential equation. Lags appear in the solution, but as quantities determined from the solution of the equation and are not arbitrary external quantities plugged on an elastic model. The resulting lag of each tide component is an increasing function of its frequency (as in Darwin's theory), and are not small quantities. The amplitudes of the tide components depend on the viscosity of the body and on their frequencies; they are not constants. The resulting stationary rotations (often called pseudo-synchronous) have an excess velocity roughly proportional to 6ne^2/(\chi^2+1/\chi^2) (\chi\ is the mean-motion in units of one relaxation factor inversely proportional to the viscosity) instead of the exact 6ne^2 of standard theories. The dissipation in the pseudo-synchronous solution is inversely proportional to (\chi+1/\chi); thus, in the inviscid limit it is roughly proportional to the frequency (as in standard theories), but that behavior is inverted when the viscosity is high and the relaxation factor much smaller than the tide frequency. For free rotating bodies, the dissipation is given by the same law, but now \chi\ is the frequency of the semidiurnal tide in units of the relaxation factor. This approach fails, however, to reproduce the actual tidal lags on Earth and on natural satellites. To reconcile theory and observations, in this case, we had to assume the coexistence of a small elastic tide superposed to the creeping tide. The theory is applied to several Solar System and extrasolar bodies and values of the relaxation factor \gamma\ are derived for these bodies on the basis of currently available data.
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http://arxiv.org/abs/1204.3957
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