Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010dps....42.2507h&link_type=abstract
American Astronomical Society, DPS meeting #42, #25.07; Bulletin of the American Astronomical Society, Vol. 42, p.996
Astronomy and Astrophysics
Astronomy
Scientific paper
Many studies of tidal dissipation in solar system objects make use of Love numbers (non-dimensional measures of the height of the tidal bulge and the associated induced gravitational quadrupole moment) based on Kelvin's solution for the deformation of a homogeneous incompressible body. This solution ignores (assumes negligible) the inertial terms in the equations of motion. When the oscillatory tidal time dependence is included, analytic solutions can be obtained which, surprisingly, do not asymptote to Kelvin's solution in the long-period limit. When the Coriolis terms are also included, a system of three coupled second-order partial differential equations (for the three velocity components, or suitable substitutes) results. Free surface boundary conditions must be satisfied. When the object is not homogeneous, the Poisson equation for the gravitational potential must also be solved. There appear to be no analytic solutions for this system, but numerical solutions are straightforward, and the results can be tabulated in terms of non-dimensionalized values of the rigidity, viscosity, forcing frequency, and rotation frequency. This rotating system couples modes with different latitude structures. The resulting tidal torque is more complicated than usually assumed. In addition to the global net tidal torque that exchanges rotational and orbital angular momentum (and thus leads to the traditional tidal heating and orbital evolution), local differential torques act on the body. Depending on the body's long-term viscoelastic properties, considerable additional heating (which does not affect the orbital evolution and therefore does not figure in the calculation of the body's tidal dissipation factor) may occur, particularly in a layered, inhomogeneous object.
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