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==Motivation== These discussions began in late 2021, when [https://www.nist.gov/people/howard-cohl Howard Cohl] asked if I would be interested in working with him on establishing a better understanding of the stability of Riemann S-Type Ellipsoids. This discussion relates directly to our study of the work by {{ LL96full }}. We are motivated to pursue this discussion, in part, because our own research group at LSU has previously carried out some nonlinear dynamical simulations that relate to this topic. See … <ul> <li> [https://www.youtube.com/watch?v=Fi8Fp26uc-g YouTube Simulation] that draws from the following ApJ publication. </li> <li> <b>Relevant Publication:</b> {{ OTM2007full }}, titled, ''Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars.'' <table border="1" align="center" cellpadding="8" width="90%"> <tr><td align="left" rowspan="2"> <div align="center"><b>Publication Abstract</b></div><br /> Using a three-dimensional nonlinear hydrodynamic code, we examine the dynamical stability of more than 20 self-gravitating, compressible, ellipsoidal fluid configurations that initially have the same velocity structure as Riemann S-type ellipsoids. Our focus is on ''adjoint'' configurations, in which internal fluid motions dominate over the collective spin of the ellipsoidal figure; Dedekind-like configurations are among this group. We find that, although some models are stable and some are moderately unstable, the majority are violently unstable toward the development of m=1, m=3, and higher-order azimuthal distortions that destroy the coherent, m=2 barlike structure of the initial ellipsoidal configuration on a dynamical timescale. The parameter regime over which our models are found to be unstable generally corresponds with the regime over which incompressible Riemann S-type ellipsoids have been found to be susceptible to an elliptical strain instability. We therefore suspect that an elliptical instability is responsible for the destruction of our compressible analogs of Riemann ellipsoids. The existence of the elliptical instability raises concerns regarding the final fate of neutron stars that encounter the secular bar-mode instability and regarding the spectrum of gravitational waves that will be radiated from such systems. </td> <td align="center">[[File:OuSimulation2007.png|300px|OTM Simulation (2007)]]<br /> Initial frame of a [https://www.youtube.com/watch?v=Fi8Fp26uc-g YouTube animation] that shows one model's evolution </td> </tr> <tr> <td align="center">[[File:OTM2007Fig14.png|250px|{{ OTM2007 }}, Fig. 14]]</td> </tr> </table> </li> </ul>
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