A New Method for Predicting the Critical Taylor Number in Rotating Cylindrical Flows

Abstract

A method for determining the boundaries of dynamic stability of a fluid system, as distinct from the prediction of the subsequent motion, is presented. The method is based on well-known approaches to the problem of instability in elastic systems. The extension of these methods to fluid systems, specifically, to the stability of flow between concentric cylinders, confirms that it may be possible in some cases to determine the boundaries of stability of fluid systems without recourse to an Orr-Sommerfeld type treatment. The results also suggest that the concept of apparent (virtual) viscosity may have implications for fluid stability outside the current realm of turbulence modelling. Finally, it is also shown that flow instability may be preceded by the onset of a critical stress condition in analogy with elastic systems.