Inertial modes in a rotating triaxial ellipsoid

S. Vantieghem

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


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 languageEnglish
Article number20140093
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2168
Early online date4 Jun 2014
Publication statusPublished - 8 Aug 2014
Externally publishedYes


  • Inertial modes
  • Rotating flows
  • Triaxial ellipsoid

ASJC Scopus subject areas

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


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