Stability analysis for cylindrical Couette flow of compressible fluids
Abstract
A new analysis of basic Couette flow, is based on an Action Principle for compressible fluids, with a Hamiltonian as well as a kinetic potential. An effective criterion for stability recognizes the tensile strength of water. This interpretation relates the problem to capillary action and to metastable configurations (Berthelot's negative pressure experiment of 1850). We calculate the pressure and density profiles and find that the first instability of basic Couette flow is localized near the bubble point. This theoretical prediction has been confirmed by recent experiments. The theory is the result of merging the two versions of classical hydrodynamics, as advocated by Landau for superfluid Helium II, but here applied to fluids in general, in accord with a widely held opinion concerning superfluidity. In this paper twoflow dynamics is created by merging two actions, not by choosing between them, nor by combining the two vector fields as in the NavierStokes equation . At rest, as contributions to the mass flow they cancel, but a nonzero kinetic energy and kinetic potential as well as nonzero angular momentum remain, manifest as liquid tension, as is well known to exist by observation of the meniscus and configurations with negative pressure. (Fronsdal 2020b in preparation). This theory gives a very satisfactory characterization of the limit of stability of the most basic Couette flow. The inclusion of a vector field that is not a gradient has the additional affect of introducing spin, which explains a most perplexing experimental discovery: the ability of frozen Helium to remember its angular momentum.
 Publication:

arXiv eprints
 Pub Date:
 December 2016
 arXiv:
 arXiv:1701.00457
 Bibcode:
 2017arXiv170100457F
 Keywords:

 Physics  General Physics
 EPrint:
 27 pages, 11 figures.Replacement for 1701.00457, with very substantial improvements. arXiv admin note: text overlap with arXiv:1803.10599