### Abstract

In this work, we present an algorithm that enables computation of inertial modes and their corresponding frequencies in a rotating triaxial ellipsoid. The method consists of projecting the inertial mode equation onto finite-dimensional bases of polynomial vector fields. It is shown that this leads to a well-posed eigenvalue problem, and hence, that eigenmodes are of polynomial form. Furthermore, these results shed new light onto the question whether the eigenmodes form a complete basis, i.e. whether any arbitrary velocity field can be expanded in a sum of inertial modes. Finally, we prove that two intriguing integral properties of inertial modes in rotating spheres and spheroids also extend to triaxial ellipsoids.

Original language | English |
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Article number | 20140093 |

Number of pages | 22 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 470 |

Issue number | 2168 |

Early online date | 4 Jun 2014 |

DOIs | |

Publication status | Published - 8 Aug 2014 |

Externally published | Yes |

### Keywords

- Inertial modes
- Rotating flows
- Triaxial ellipsoid

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

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## Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*470*(2168), [20140093]. https://doi.org/10.1098/rspa.2014.0093