Turbulent Mixing and Beyond

Abstract

Whenever fluids of different densities are accelerated against the density gradient we observe the development of the Rayleigh-Taylor instability (RTI), which causes extensive interfacial mixing of the fluids. The turbulent mixing plays a key role in preventing the formation of "hotspot" in inertial confinement fusion, providing proper conditions for the synthesis of heavy mass elements in supernovae, in determining the drop size distribution in sprays, in premixed and non-premixed combustion, in the recovery and production of oil, etc.
The dynamics of RTI is governed by a system of conservation laws, which are nonlinear partial differential equations with initial and boundary conditions at the fluid interface. Singular aspects of the interface evolution cause significant difficulties for theoretical and numerical studies of RTI.
We suggest a new theoretical approach to the long-standing problem, based on group theory and scale separation. The dynamics of the large-scale coherent structures in RTI is studied, the invariants of the flow are identified, and the non-local and multi-scale character of the instability evolution is shown. A phenomenological model is suggested to describe the turbulent mixing under various physical conditions and to account for the stochastic properties of the process. The applications of the obtained results are discussed.