On the stability of viscous Riemann ellipsoids
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908817315332096 |
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| author | Labarbe, Joris |
| author_facet | Labarbe, Joris |
| contents | The present study investigates the linear stability of Riemann ellipsoids in both the inviscid limit and in the presence of weak viscosity. In the inviscid regime, we derive a generalised Poincare equation governing small fluid oscillations and construct a family of polynomial solutions that extends the classical results of Cartan to flows with a uniform strain field. This formulation provides an analytic dispersion relation for three-dimensional ellipsoidal disturbances and remains computationally efficient at arbitrary harmonic degree, in contrast to the virial tensor method or to short-wavelength (WKB) approximations. The viscous effects are incorporated through a boundary-layer analysis based on Prandtls theory, leading to first-order viscous corrections to the inviscid spectrum and allowing a systematic investigation of viscosity-driven instabilities. Stability diagrams are presented over the space of admissible Riemann ellipsoids, illustrating the roles of rotation, internal strain, and diffusion, with implications for rotating shear flows in geophysical and astrophysical contexts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05658 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the stability of viscous Riemann ellipsoids Labarbe, Joris Fluid Dynamics Earth and Planetary Astrophysics Solar and Stellar Astrophysics The present study investigates the linear stability of Riemann ellipsoids in both the inviscid limit and in the presence of weak viscosity. In the inviscid regime, we derive a generalised Poincare equation governing small fluid oscillations and construct a family of polynomial solutions that extends the classical results of Cartan to flows with a uniform strain field. This formulation provides an analytic dispersion relation for three-dimensional ellipsoidal disturbances and remains computationally efficient at arbitrary harmonic degree, in contrast to the virial tensor method or to short-wavelength (WKB) approximations. The viscous effects are incorporated through a boundary-layer analysis based on Prandtls theory, leading to first-order viscous corrections to the inviscid spectrum and allowing a systematic investigation of viscosity-driven instabilities. Stability diagrams are presented over the space of admissible Riemann ellipsoids, illustrating the roles of rotation, internal strain, and diffusion, with implications for rotating shear flows in geophysical and astrophysical contexts. |
| title | On the stability of viscous Riemann ellipsoids |
| topic | Fluid Dynamics Earth and Planetary Astrophysics Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2602.05658 |