Spanwise homogeneous buoyancy-drag model for Rayleigh–Taylor mixing and experimental evaluation

Abstract

A buoyancy-drag model for Rayleigh–Taylor (RT) mixing is developed on the premise that the bubble and spike regions behave as distinct and spanwise homogeneous fluids. Then, mass conservation is applied accross the mixing zone to obtain their average mixture densities dynamically. These are used to explicitly calculate the inertia and buoyancy terms in the evolutionary equation. The only unknown parameter in the model is the Newtonian drag constant C∼2.5±0.6, which is determined from turbulent RT experiments over various Atwood numbers A and acceleration histories g(t). The bubble (i=2) and spike (i=1) amplitudes are found to obey the familiar hi=αiAgt2 for a constant g and hi∼tθi for an impulsive g. For bubbles, both α2 and θ2 are insensitive to A. For the spikes, both α1 and θ1 increase as a power law with the density ratio. However, θ1 is not universal because it depends on the initial value of h1/h2.