Open AccessTidal deformation of a viscoelastic body
Author(s) -
VanArsdale William E.
Publication year - 1982
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1982.tb05985.x
Subject(s) - viscoelasticity , physics , classical mechanics , moment of inertia , legendre polynomials , mechanics , euler's equations , compressibility , deformation (meteorology) , isotropy , gravitational field , angular velocity , inertia , rotary inertia , thermodynamics , optics , quantum mechanics , meteorology
Summary. The tidal deformation of a homogeneous viscoelastic sphere due to the gravitational attraction of an external body is calculated. The sphere is modelled as an incompressible Kelvin‐Voigt solid. An equation for the displacement field is obtained assuming that strains are small and inertia is negligible. This equation has a series solution in terms of Legendre polynomials. The resulting expression for the displacement field reduces to that for an elastic solid and a viscous fluid in the appropriate limits of the material constants. The first term in the viscoelastic solution is used to calculate the moments induced by tidal deformation assuming a circular orbit. In the absence of obliquity and precession, these moments reduced to a torque about the spin axis. This torque is compared to that predicted by a phase lag analysis. These two approaches are formally equivalent if the tidal dissipation function Q −1 depends in a specific way on the difference of the spin and orbital angular velocities.