A unified view of topological invariants of barotropic and baroclinic fluids and their application to formal stability analysis of three-dimensional ideal gas flows

Yasuhide Fukumoto, Hirofumi Sakuma

研究成果: Contribution to journalConference article査読

2 被引用数 (Scopus)

抄録

Noether's theorem associated with the particle relabeling symmetry group leads us to a unified view that all the topological invariants of a barotropic fluid are variants of the cross helicity. The same is shown to be true for a baroclinic fluid. A cross-helicity representation is given to the Casimir invariant, a class of integrals including an arbitrary function of the specific entropy and the potential vorticity. We then develop a new energy-Casimir convexity method for three-dimensional stability of equilibria of general rotating flows of an ideal baroclinic fluid, without appealing to the Boussinesq approximation. By fully exploiting the Casimir invariant, we have succeeded in ruling out a term including the gradient of a dependent variable from the energy-Casimir function and have established a sharp linear stability criterion, being an extension of the Richardson-number criterion.

本文言語英語
ページ(範囲)213-222
ページ数10
ジャーナルProcedia IUTAM
7
DOI
出版ステータス出版済み - 2013
イベントIUTAM Symposium on Topological Fluid Mechanics II - Cambridge, 英国
継続期間: 7 23 20127 27 2012

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

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