The Stability of Viscous Flow between Horizontal Concentric Cylinders

D. B. Brewster, P. Grosberg, A. H. Nissan
1959 Proceedings of the Royal Society A  
P late 3] The critical conditions for the form ation of Taylor vortices betw een horizontal concentric cylinders are considered in detail. (1) Where the flow is unidirectional round the annular space and is caused entirely b y the rotat ion of the inner cylinder. (2) Where the flow is caused entirely by pumping round the annular space. (3) Where a liquid is caused to reverse its flow at a free surface, the flow being entirely caused by the rotation o f the inner cylinder. The last case is
more » ... last case is analyzed by the m ethod of small disturbances and the conditions under which Taylor vortices will form are found. R esults for the first tw o cases are already available in the literature. From exam ination of the three criteria a dimensionless number is proposed to correlate the critical values o f the various parameters at the onset o f these Taylor vortices. The proposed number has the advantage that it is insensitive to the velocity distribution in the annulus. I t is subsequently used to predict the critical conditions for the onset o f Taylor vortices under conditions th at have not been analyzed, i.e. where flow is due to pumping and rotation of the inner cylinder. The criterion is found to predict successfully the results of various experim ents carried out. In addition experim ental verification of the theoretical work of D ean (1928) and of the additional analysis carried out in this paper is also given.
doi:10.1098/rspa.1959.0091 fatcat:entloisuyjbahhwgzbqma66o2e