Chandrasekhar, S.
(1955)
*The character of the equilibrium of an incompressible fluid sphere of variable density and viscosity subject to radial acceleration*
The Quarterly Journal of Mechanics and Applied Mathematics, 8
(1).
pp. 1-21.
ISSN 0033-5614

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Official URL: http://qjmam.oxfordjournals.org/content/8/1/1.shor...

Related URL: http://dx.doi.org/10.1093/qjmam/8.1.1

## Abstract

This paper is devoted to a consideration of the following problem: An incompressible fluid sphere, in which the density and the viscosity are functions of the distance r from the centre only, is subject to a radial acceleration -γr, where γ is a function of r: to determine the manner of initial development of an infinitesimal disturbance. By analysing the disturbance in spherical harmonics, the mathematical problem is reduced to one in characteristic values in a fourth-order differential equation and a variational principle characterizing the solution is enunciated. The particular case of a sphere of radius R and density p_{1} embedded in a medium of a different density p_{2} (but of the same kinematic viscosity v) is considered in some detail; and it is shown that the character of the equilibrium depends on the sign of γR(p_{2}-p_{1}) and the magnitude of = γ_{R}R^{4}/v^{2}. If γ^{R}(p_{2}-p_{1}) > 0, the situation is unstable and the mode of maximum instability is l = 1 for all < 230; for larger values of it shifts progressively to higher harmonics. In the case γ_{R}(p_{2}-p_{1}) > 0 the results of both an exact calculation and an approximate calculation (based on the variational principle) are given and contrasted. In the case γ_{R}(p_{2}-p_{1}) < 0 when the situation is stable, the manner of decay of the disturbance is briefly discussed in terms of an approximate theory only.

Item Type: | Article |
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Source: | Copyright of this article belongs to Oxford University Press. |

ID Code: | 70559 |

Deposited On: | 17 Nov 2011 14:05 |

Last Modified: | 17 Nov 2011 14:05 |

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