Wavy vortices in the flow between two long eccentric rotating cylinders I. Linear theory

Source abstract

Abstract This analysis deals with the occurrence of Coles’ wavy vortices in the flow between two eccentric cylinders when no Taylor vortex flow is present, and where the eccentricity is small and the clearance ratio is very small. This mathematical investigation can be seen as an extension of the previous papers of Di Prima (1963), Roberts (1965), Davey, Di Prima & Stuart (1968) on the concentric problem and the paper of Di Prima & Stuart (19726) which includes eccentricity. An extension to the latter paper is made by the inclusion of the time variable r in the equation for the amplitude B((/),t) of the Taylor vortices, (j) being the azimuthal variable. The results are compared with the observed critical speeds of Vohr (1967) for development of wave instability on Taylor vortices, and are qualitatively similar; they differ in magnitude from experiment, however, probably due to the absence of nonlinear effects.