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

Axisymmetric pipeline transportation of oil and water is simulated numerica lly as an initial value problem. The simulations succeed in predicting the spatially periodic Stokes-like waves called bamboo waves, which have been d ocumented in experiments of Bai, Chen & Joseph (1992) for up-flow. The nume rical scheme is validated against linearized stability theory for perfect c ore-annular flow, and weakly nonlinear saturation to travelling waves. Far from onset conditions, the fully nonlinear saturation to steady bamboo wave s is achieved. As the speed is increased, the bamboo waves shorten, and pea ks become more pointed. A new time-dependent bamboo wave is discovered, in which the interfacial waveform is steady, but the accompanying velocity and pressure fields are time-dependent. The appearance of vortices and the loc ations of the extremal values of pressure are investigated for both up and down-flows.