Helical instability of a rotating viscous liquid jet

Abstract

Vertical rotating viscous liquid jet experiments show a clear preference for helical instabilities that evolve from initially planar disturbances at large rotation rates for fixed fluid properties. The laboratory setup for the experiments described herein was chosen as the nearest earth-based equivalent to a uniformly rotating viscous liquid column in the absence of gravity. In the ideal situation with stress-free boundaries, the preferred modes of linear temporal instability are theoretically known over the entire physical domain spanned by the Hocking parameter L=γ∕ρa3Ω2 and the rotational Reynolds number Re=a2Ω∕ν, where a is the column radius, Ω is its uniform angular velocity, and ρ, ν, and γ are, respectively, the fluid density, kinematic viscosity, and surface tension. The theoretical results show that instability in L-Re parameter space is dominated by three mode types: The axisymmetric mode, the n≥2 planar modes, and the first n=1 spiral mode. Experiments reveal that, in the L-Re region for which the uniformly rotating liquid column is dominated by planar modes of instability, the rotating liquid jet spontaneously gives rise to planar disturbances of mode n≥2 that rapidly evolve into helical instabilities. However, these observed instabilities are not the spiral normal modes that exist for n≥1 as posited in linear stability theory. In spite of obvious fundamental differences between the rotating liquid jet and the uniformly rotating liquid column, some remarkable similarities associated with initial growth rates, angular frequencies, and mode transitions between the two systems are found.