A numerical study of three-dimensional bubble merger in the Rayleigh-Taylor instability

The Rayleigh-Taylor instability arises when a heavy fluid adjacent to a light fluid is accelerated in a direction against the density gradient. Under this unstable configuration, a perturbation mode of small amplitude grows into bubbles of the light fluid and spikes of the heavy fluid. Taylor discovered the steady state motion with constant velocity for a single bubble or periodic bubbles in the Rayleigh-Taylor instability. Read and Youngs studied the motion of a randomly perturbed fluid interface in the Rayleigh-Taylor instability. They reported constant acceleration for the overall bubble envelope. Bubble merger is believed to cause the transition from constant velocity to constant acceleration. In this paper, we present a numerical study of this important physical phenomenon. It analyzes the physical process of bubble merger and the relationship between the horizontal bubble expansion and the vertical interface acceleration. A dynamic bubble velocity, beyond Taylor's steady state value, is observed during the merger process. It is believed that this velocity is due to the superposition of the bubble velocity with a secondary subharmonic unstable mode. The numerical results are compared with experiments.