Journal of Fluid Mechanics

Snakes and corkscrews in core–annular down-flow of two fluids

a1 Department of Mathematics and Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA


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.

(Received May 20 1996)
(Revised January 21 1997)