Abstract:

Rayleigh's stability analysis of cylindrical Couette flow, of 1916, is in contradiction with observation, but it is still widely quoted and no one seems to know what the reason is that it fails. I shall identify the mistake as one that is endemic in the literature. Briefly, the argument depends on the Navier-Stokes equation and the mistake is the assumption that a certain expression called ``energy density" or ``kinetic potential" can be interpreted and used as such. No energy density compatible with the Navier-Stokes equation exists.

An alternative analysis of basic Couette flow, based on an action principle for compressible fluids, provides a Hamiltonian density as well as a kinetic potential. A new criterion for stability recognizes the profound effect of the surface adhesion and the tensile strength of water. It is in full agreement with observation.