Harmonic generation in Taylor vortices between rotating cylinders

Abstract

A theory of finite-amplitude secondary flow between concentric rotating cylinders has been published by Davey (1962). A necessary feature of the theory is the generation of harmonics of the spatial periodicity in the axial direction of the velocity field. A method has been devised to measure the amplitude of each harmonic separately and experimental results for the fundamental and first three harmonics are presented here for Taylor numbers up to 100 times the critical value. The agreement with Davey's theory is excellent, and the agreement extends far beyond the range where the theory is expected to be valid. It is shown that all the harmonics are in phase with the fundamental. This result requires that jets and shock-like structure must be present in the velocity field.