Vortex breakdown phenomena in a circular pipe (4th Report, mechanism of axisymmetric bubble type breakdown).

An investigation is reported for the relation between an axisymmetric vortex breakdown and a stationary internal wave in a swirling flow field. An approximate mathematical model of the internal wave (wave disturbance) was constructed in consideration of fluid viscosity. Experiments were carried out on a swirling flow in a rotating pipe. The flow field, where internal waves occur, was observed by a visualization technique and was measured by a laser Doppler velocimeter. The effect of the upstream boundary condition on the internal wave was examined both by experiments and numerical calculations. The results are summarized as follows. A stationary internal wave occurs in a rotating pipe when the rotation is faster than a certain critical value. The characteristics of the waves were predicted fairly well by an approximate mathematical model. The bubble type breakdown is ultimately identified with the stationary internal wave of a sufficiently large amplitude.