We examine small deviations from axial symmetry in a solid-propellant rocket motor,
and describe a ‘bath-tub-vortex’ effect, in which substantial axial vorticity is generated
in a neighbourhood of the chamber centreline. The unperturbed flow field is essentially
inviscid at modest Reynolds numbers, even at the chamber walls, as has long been
known, but the inviscid perturbed flow is singular at the centreline, and viscous terms
are required to regularize it. We examine perturbations sufficiently small that a linear
analysis is valid everywhere (εRe small, where ε is a measure of the perturbation
amplitude and Re is a Reynolds number), and larger perturbations in which a
nonlinear patch is created near the centreline of radius O(√ε). Our results provide
an explanation of swirl experimentally observed by others, and a cautionary note
for those concerned with numerical simulations of these flows, whether laminar or
turbulent.