Title: Stability of laminar Couette flow of compressible fluids,
Abstract: Cylindrical Couette flow is a subject where the main focus has long been on
the onset of turbulence or, more precisely, the limit of stability of the
simplest laminar flow. The theoretical framework of this paper is a recently
developed action principle for hydrodynamics. It incorporates Euler-Lagrange
equations that are in essential agreement with the Navier-Stokes equation, but
applicable to the general case of a compressible fluid. The variational
principle incorporates the equation of continuity, a canonical structure and a
conserved Hamiltonian. The density is compressible, characterized by a general
(non-polar) equation of state, and homogeneous. The onset of instability is
often accompanied by bubble formation. It is proposed that the limit of
stability of laminar Couette flow may some times be related to cavitation. In
contrast to traditional stability theory we are not looking for mathematical
instabilities of a system of differential equations, but instead for the
possibility that the system is driven to a metastable or unstable
configuration. The application of this idea to cylindrical Couette flow
reported here turns out to account rather well for the observations. The
failure of a famous criterion due to Rayleigh is well known. It is here shown
that it may be due to the use of methods that are appropriate only in the case
that the equations of motion are derived from an action principle.