On the friction of fluids between rotating cylinders

Abstract

The onset of turbulence and friction in the flow between two concentric cylinders is analysed for the case when the outer cylinder is rotating and the inner one is at rest. In this case the angular momentum distribution stabilizes the laminar motion. The classical experiments by Taylor (1936) showed that the critical Reynolds number was larger and the friction smaller than in the plane flow of Couette (1890). In this paper a criterion for stabilization similar to that of Bradshaw (1969) is derived to explain the Taylor dependence of the critical Reynolds number on the ratio of the radii. Breakdown of laminar motion occurs near the inner cylinder since the stability criterion is zero on its surface. The friction law is given a phenomenological description by using the velocity distribution in the turbulent zone, observed by Taylor and corresponding to a constant value of the criterion. Two empirical parameters are sufficient to describe the dependence of the skin friction on the Reynolds number and the radius ratio. A programme of further experiments is proposed. The relevance of the results is discussed in application to some astrophysical problems, e.g. the turbulence generation in accretion disks near compact stars which are X-ray sources.