A classic Mistake and what it tells us
A classic Mistake and what it tells us
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听听 the reason is that it fails. I shall identify the mistake as one that is endemic in the literature.
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Briefly, the argument depends on the Navier-Stokes equation and the mistake is the assumption that a certain expression听 called听 "energy density"听or "kinetic potential"听can be interpreted and used听 as听 such. No energy density compatible with the Navier-Stokes equation exists.
An alternative analysis of basic Couette flow, based听 on an听 action principle for compressible fluids, provides a Hamiltonian density as well as a kinetic potential.
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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.