Molecular mixing in response to stirring by turbulence is an important process in many practical applications. When the microscopic densities of the fluids are not the same, mixing itself becomes qualitatively different; these flows have been referred to as variable density (VD) flows. Many VD flows are driven by acceleration which, because the density is not uniform, leads to large differential forces. In the unstable configuration, small perturbations of the initial interface between the two fluids grow, interact nonlinearly, and lead to turbulence. This instability is known as the Rayleigh-Taylor instability (RTI) and is of fundamental importance in a multitude of applications, from fluidized beds, oceans and atmosphere, to inertial, magnetic, or gravitational confinement fusion, and to astrophysics.
Although RTI has been subjected to intense research over the last 50 years, until recently, numerical studies have been restricted to coarse mesh calculations of the Euler equations. On the other hand, it is notoriously difficult, in laboratory experiments, to accurately characterize the initial conditions and provide the detailed measurements needed for turbulence model development and validation. Thus, a large number of open questions remain unanswered about this instability and even first order global quantities, such as the layer growth, are not completely understood and still give rise to intense debate. Nevertheless, today's petascale computers allow fully resolved simulations of RTI at parameter ranges comparable to those attained in laboratory experiments, but providing, in carefully controlled initial and boundary conditions studies, much more information than physical experiments.
In this talk, I will give an overview of recent results on Rayleigh-Taylor instability, including self-similarity, turbulence and mixing asymmetries, spectral behavior, and structure of the layer. In particular, I will show results from an extensive set of Direct Numerical Simulations on up to 40962 x 4032 meshes, the largest fully resolved instability simulations to date.