Direct simulation of unsteady axisymmetric core-annular ow with high viscosity ratio

Axisymmetric pipeline transportation of oil and water is simulated numerically as an initial value problem. The simulations succeed in predicting the spatially periodic Stokes-like waves called bamboo waves, which have been documented in experiments of Bai, Chen and Joseph (1992) for upow. The numerical scheme is validated against linearized stability theory for perfect core-annular ow, and weakly nonlinear saturation to traveling waves. Far from onset conditions, the fully nonlinear saturation to steady bamboo waves is achieved. As the speed is increased, the bamboo waves shorten, and peaks become more pointed. A new timedependent bamboo wave is discovered, in which the interfacial waveform is steady, but the accompanying velocity and pressure elds are time-dependent. The appearance of vortices and the locations of the extremal values of pressure are investigated for both up and down ows.