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

Research output: Contribution to journalConference articlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)213-222
Number of pages10
JournalProcedia IUTAM
Volume7
DOIs
Publication statusPublished - 2013
EventIUTAM Symposium on Topological Fluid Mechanics II - Cambridge, United Kingdom
Duration: Jul 23 2012Jul 27 2012

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

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