On the Stability of a Maclaurin Spheroid of Small Viscosity.
Abstract
The stability of a viscous Maclaurin spheroid is solved asymptotically for small kinematic viscosity, It is shown that, in this limit, the frequency of oscillation, n, with respect to the mode which becomes neutrally stable in the absence of viscosity at the point of bifurcation (where the eccentricity, e, of the meridional section is approximately 0.8127), is 5pn2o n=n0+i +o(p) (1) a2Q(e) In the foregoing formula n0 denotes the frequency in the absence of viscosity, a is the radius of the equatorial section, and Q(e) is a certain function of e which changes sign at e = 0.8127 and is positive for smaller values of e. From equation (1) it follows that the Maclaurin spheroid is indeed unstable beyond the point of bifurcation when viscosity is present.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 1963
 DOI:
 10.1086/147555
 Bibcode:
 1963ApJ...137..777R