Nonlinear Taylor Instability in a Cylindrical Vessel

Abstract

A new class of Taylor-unstable waves, consisting of ring waves appearing at the interface of two fluids of differing densities within a around pipe when the interface is accelerated in the direction of the denser fluid, is considered. The analysis employs a generalized coordinate method introduced by Dienes [16]. The characteristic “bubble-spike” configuration is obtained, although the singularity corresponding to infinite spike tip velocity occurs at a later time than for the one-dimensional plane wave. In addition, it has been shown previously [19] that condensation of vapor at the interface produces negligible correction to the growth rate.