Limits of stability and irregular flow patterns in wavy vortex flow

Abstract

We have determined the Reynolds number versus axial wavelength stability curve for a six-wave state in the range $1.4R_c<R<\mathrm{}8\mathrm{}{R}_c$, where $R_c$ corresponds to the onset of Taylor vortex flow. At points well within the region bounded by the stability curve, the entire flow pattern has an axial periodicity and a sixfold rotational symmetry, even for fluid height-to-gap ratios as large as 290. However, when a stability boundary is approached, irregularities in the flow pattern appear; then when the stability boundary is reached, there is a change in the number of waves or the number of vortices or both.