Turbulent diffusion in tall tubes. I. Models for Rayleigh-Taylor instability

Rayleigh-Taylor instability in high-aspect-ratio domains has been studied experimentally and a hierarchy of modelling approaches has been used to understand the dynamics of the problem. Part I examines the simplest case of initially homogenous layers above and below the Rayleigh-Taylor unstable interface. Part II examines the more complex case where one layer is stably stratified in density. Here, in Part I, we develop models for turbulent mixing induced by Rayleigh-Taylor instability based on a diffusion equation for density. By considering the force balance in the problem, and using Prandtl’s mixing length hypothesis, we compute a non-constant turbulent diffusivity, and this leads to a non-linear diffusion equation. We reiterate a h ~t^(2/5) scaling and use this to develop a new similarity solution to the nonlinear diffusion equation in an infinite domain. To match experimental boundary conditions of a finite domain, we use numerical integration, and finally, we compare with implicit large eddy simulation.