On the Stability of a Maclaurin Spheroid of Small Viscosity.
摘要：
The stability of a viscous MacLaurin spheroid is solved asymptotically for small kinematic viscosity, nu. 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 n=n sub o + (5 nu (n sub 0)sq)/(phi(e)) + O(nu). In the foregoing formula n sub 0 denotes the frequency in the absence of viscosity, a the radius of the equational section and phi(e) a certain function of e which changes sign at e= 0.8127 and is positive for smaller values of e . From this equation it follows that the Maclaurin spheroid is indeed unstable beyond the point of bifurcation when viscosity is present.
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DOI：
10.1086/147555
被引量：
年份：
1963
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