A three-dimensional renormalization group bubble merger model for Rayleigh-Taylor mixing

In this paper we formulate a model for the merger of bubbles at the edge of an unstable acceleration driven (Rayleigh-Taylor) mixing layer. Steady acceleration defines a self-similar mixing process, with a time-dependent inverse cascade of structures of increasing size. The time evolution is itself a renormalization group (RNG) evolution, and so the large time asymptotics define a RNG fixed point. We solve the model introduced here at this fixed point. The model predicts the growth rate of a Rayleigh-Taylor chaotic fluid mixing layer. The model has three main components: the velocity of a single bubble in this unstable flow regime, an envelope velocity, which describes collective excitations in the mixing region, and a merger process, which drives an inverse cascade, with a steady increase of bubble size. The present model differs from an earlier two-dimensional (2-D) merger model in several important ways. Beyond the extension of the model to three dimensions, the present model contains one phenomenological parameter, the variance of the bubble radii at fixed time. The model also predicts several experimental numbers: the bubble mixing rate, alpha(b)=h(b)/Agt(2)approximate to0.05-0.06, the mean bubble radius, and the bubble height separation at the time of merger. From these we also obtain the bubble height to the radius aspect ratio. Using the experimental results of Smeeton and Youngs (AWE Report No. O 35/87, 1987) to fix a value for the radius variance, we determine alpha(b) within the range of experimental uncertainty. We also obtain the experimental values for the bubble height to width aspect ratio in agreement with experimental values. (C) 2002 American Institute of Physics.