1204.5919 (Michael Efroimsky)

Justification of the two-bulge method in the theory of bodily tides    [PDF]

Michael Efroimsky

On various occasions, several authors suggested to model bodily tides with superposition of two symmetrical bulges. One bulge is always aimed at the secondary, and thus implements the instantaneous reaction of the primary's shape and potential to the tide-rising gravitational pull exerted on it by the secondary. This portion of the tide is called "adiabatic tide" (Zahn 1966a,b) or "elastic tide" (Ferraz Mello 2012; Krasinsky 2006). The second bulge is assumed to align orthogonally to the direction to the tide-raising secondary. So this bulge is set to implement the entire nonelastic portion of the primary's deformation. This, second bulge is called "dissipative tide" (Zahn 1966a,b; Krasinsky 2006) or "creep tide" (Ferraz Mello 2012). We demonstrate that the two-bulge method is not a separate approximation, but ensues directly from the Fourier expansion of a linear tidal theory equipped with an arbitrary rheological model involving a departure from elasticity. While less economical mathematically, the two-bulge approach has a good illustrative power, and may be employed (like, e.g., in Remus et al. 2012a,b) on a par with a more concise method of complex amplitudes.

View original: http://arxiv.org/abs/1204.5919