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Using a three-dimensional nonlinear hydrodynamic code, we examine thedynamical stability of more than twenty self-gravitating, compressible,ellipsoidal fluid configurations that initially have the same velocitystructure as Riemann S-type ellipsoids. Our focus is on ``adjoint''configurations, in which internal fluid motions dominate over the collectivespin of the ellipsoidal figure; Dedekind-like configurations are among thisgroup. We find that, although some models are stable and some are moderatelyunstable, the majority are violently unstable toward the development of $m=1$,$m=3$, and higher-order azimuthal distortions that destroy the coherent, $m=2$bar-like structure of the initial ellipsoidal configuration on a dynamical timescale.  The parameter regime over which our models are found to be unstable generallycorresponds with the regime over which incompressible Riemann S-type ellipsoidshave been found to be susceptible to an elliptical strain instability\citep{LL96}. We therefore suspect that an elliptical instability isresponsible for the destruction of our compressible analogs of Riemannellipsoids. The existence of the elliptical instability raises concernsregarding the final fate of neutron stars that encounter the secular bar-modeinstability and regarding the spectrum of gravitational waves that will beradiated from such systems.

Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars