New Global Instabilities of the Riemann Ellipsoids

Details New Global Instabilities of the Riemann Ellipsoids New Global Instabilities of the Riemann Ellipsoids

Feb 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996apj...458..699l&link_type=abstract

Astrophysical Journal v.458, p.699

Astronomy and Astrophysics

Astronomy

11

Hydrodynamics, Instabilities, Methods: Analytical, Stars: Rotation

Scientific paper

The stability of the classical ellipsoids is reconsidered in view of recent developments in fluid dynamics indicating the widespread occurrence of instabilities of flows possessing, in addition to a rotational component, a strain component associated with noncircular streamlines. We find that, beyond the familiar gravitational rotational instabilities that set in for figures with high angular momentum, the ellipsoidal figures are subject also to these hydrodynamic "strain" instabilities, which occupy most of the parameter space and set in at much more modest values of the angular momentum. They typically have growth rates that are small in comparison to the rotation rate and to the growth rates of the gravitational-rotational instabilities but are nonetheless on the dynamical timescale. The highest growth rates are found among the "adjoint" figures, including the region of parameter space where the Dedekind family is found. Many of these instability domains are found in the form of tongues emanating from points of the parameter space representing axisymmetric ellipsoids (Maclaurin spheroids). These critical points among the Maclaurin spheroids are characterized by the coincidence of two oscillation frequencies of the latter family.

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