Fluid mixing
Mixing under Rayleigh-Taylor instability
This project continues the line of research initiated in [1], where the authors derived an asymptotic model for the motion of multiphase incompressible Euler flows in two dimensions, subject to Rayleigh–Taylor (RT) instability and capable of describing turn-over phenomena.
The Matlab simulations in [2] visualize the mixing process driven by RT instability — even in immiscible fluids where no diffusion is present. For a detailed discussion on how to quantify the degree of mixing without diffusion, see [3].
In the movie, the top panel simulates the “rocket rig” experiment (mixing of an NaI solution and pentane accelerated by rocket motors). It performs ensemble averaging over multiple runs. The second panel shows the occupied density within the zoom-in window, averaged across all realizations. The third panel tracks the evolution of mixedness in terms of $\dot{H}^{-1}$ norm. The fourth panel illustrates the influence of artificial viscosity on the dynamics.
Please refer to [4] for the recent refinement and development.