TY - JOUR
T1 - Oscillations of a gravitating and rotating uniform liquid sphere
JF - Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
JO - Proc R Soc Lond A Math Phys Sci
SP - 143
LP - 154
M3 - 10.1098/rspa.1979.0044
VL - 366
IS - 1724
AU -
AU -
Y1 - 1979/05/25
UR - http://rspa.royalsocietypublishing.org/content/366/1724/143.abstract
N2 - An analytic solution is derived for the bodily tide in a rotating and gravitating uniform liquid sphere. This simple model chooses to respond to the tidal forces as if it were incompressible. Dilatationless oscillations are restricted by a selection rule limiting the values of m in Pmn (Cos θ) to m = ±n, and m ═ ± (n—1). In the case of m = n—1 there exists, in addition, a free oscillation of inertial type, with a period close to ½n days. The inertial wave travels in a direction opposed to the direction of rotation, and the displacements are mainly in the longitudinal direction. Apart from the appearance of the inertial wave, the effect of rotation on the Love numbers is slight for models in which the centrifugal acceleration is small compared to the acceleration of gravity at the surface. There exist also sono-gravitational free oscillations in which the dilatation does not vanish. Their periods are less than one hour and are of the type familiar in terrestrial spectroscopy.
ER -