A unified view of topological invariants of barotropic & baroclinic fluids & their application to formal stability analysis of three-dimensional ideal gas flows
Seminar Room 1, Newton Institute
AbstractIntegrals of an arbitrary function of the vorticity, two-dimensional topological invariants of an ideal barotropic fluid, take different guise from the helicity. 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. Baroclinic fluid flows admit, as the Casimir invariants, a class of integrals including an arbitrary function of the entropy and the potential vorticity. A consideration is given to them from the view point of Noether's theorem. We then develop a new energy-Casimir convexity method for a baroclinic fluid, and establish a novel linear stability criterion, to three-dimensional disturbances, for equilibria of general rotating flows of an ideal gas without appealing to the Boussinesq approximation. By exploiting a larger class of the Casimir invariants, we have succeeded in ruling out a term including the gradient of a dep endent variable from the energy-Casimir function. For zonally symmetric flows, the resulting criterion is regarded as an extended Richardson number criterion for stratified rotating shear flows with compressibility taken into account.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.