An Eulerian variational principle and a criterion for the occurrence of nonaxisymmetric neutral modes along rotating axisymmetric sequences

Details An Eulerian variational principle and a criterion for the occurrence of nonaxisymmetric neutral modes along rotating axisymmetric sequences An Eulerian variational principle and a criterion for the occurrence of nonaxisymmetric neutral modes along rotating axisymmetric sequences

May 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985apj...292..517i&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 292, May 15, 1985, p. 517-521.

Statistics

Computation

32

Computational Astrophysics, Stellar Oscillations, Stellar Rotation, Variational Principles, Branching (Mathematics), Inviscid Flow, Perturbation Theory, Points (Mathematics)

Scientific paper

In the theory of self-gravitating fluid configurations, an important development is related to the discovery that general-relativistic effects of gravitational radiation reaction induce secular instability at certain nonaxisymmetric points of bifurcation along Newtonian sequences of axisymmetric rotating equilibria. Such a point of bifurcation is a point of neutral stability. The present investigation has the objective to develop a new method for isolating nonaxisymmetric bifurcation points. The basis is a derivation of an 'Eulerian' variational principle for neutral, or zero-frequency, nonaxisymmetric modes of oscillation of axisymmetric configurations. The equations governing fluid configurations are discussed, taking into account the equations governing the unperturbed axisymmetric equilibrium configuration, and the equations governing the perturbed configuration. Attention is given to the variational principle, the method for locating Dedekind bifurcation points, and Dedekind and Jacobi bar modes of uniformly rotating configurations.

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