Accession Number : ADP000334

Title :   On Synge's Criterion for the Stability of Plane Couette Flow,


Personal Author(s) : Lee,K. F. ; Millsaps,Knox

Report Date : JUN 1982

Pagination or Media Count : 8

Abstract : A simple proof for the conjectured hydrodynamical stability of plane Couette flows against perturbations of all frequencies and of infinitesmal amplitude is one of the classically formulated problems in theoretical fluid dynamics, and its solution has eluded everyone including many of the most powerful mathematical analysts of modern times. J. L. Synge made one of the most appealing approaches to the solution by giving a simple criterion for the lower bound of the minimally critical Reynolds Number. Synge's criterion was thought to be relatively weak although the limit of applicability has not been reported, and this investigation examines exactly the weakness by determining the extremum in terms of the maximum Reynolds Number, Rm, for stability. It is shown that Rm = 4 is the maximum using Synge's criterion which is unfortunately less than Rm = 44.3 using a much more complicated analysis due to Orr. The importance of these results is enhanced somewhat if the eventual proof, assuming the truth of the conjecture, follows von Mises' formulation in which stability for a small finite range from zero is required as a starting point in the subsequent analysis. (Author)

Descriptors :   *Hydrodynamics, *Couette flow, *Mathematical analysis, Stability, Planar structures, Perturbations, Frequency, Fluid dynamics, Theory

Distribution Statement : APPROVED FOR PUBLIC RELEASE