Core–annular flow of two fluids is examined at the onset
of
a non-axisymmetric
instability. This is a pattern selection problem: the bifurcating solutions
are travelling
waves and standing waves. The former travel in the azimuthal direction
as well as the
axial direction and would be observed as corkscrew waves. The standing
waves travel
in the axial direction but not in the azimuthal direction and appear
as snakes. Weakly
nonlinear interactions are studied to see whether one of these
waves will be stable to
small-amplitude perturbations. Sample situations for down-flow are discussed.
The
corkscrews tend to be preferred when the annulus is narrow, while snakes
are more
likely when the annulus is wide.