We propose to develop numerical and theoretical methods for studying the nonlinear dynamics of the Rayleigh-Taylor (RT) driven unstable interface separating two immiscible fluids with account for the effects of molecular viscosity, surface tension, unsteady acceleration, and broad band initial perturbations. We are motivated by the intellectual challenges associated with the numerical modeling and theoretical analysis aspects of the problem, and by the necessity to build up advanced computational and mathematical tools that are needed to describe, simulate, and reliably predict the complex interfacial process, and to further apply this expertise to aerodynamic and environmental problems. The Rayleigh-Taylor instability (RTI) develops when fluids of different densities are accelerated against their density gradients. Extensive interfacial mixing of the fluids ensues with time. RT instability and mixing govern a broad variety of processes in nature and technology, from astrophysical to atomistic scales. Examples include inertial confinement and magnetic fusion in nuclear energy technology, supernovae and stellar convection in astrophysics, volcanic eruptions and oceanographic flows in geophysics, pollution transport in urban areas, and liquid breakup and atomization in aerodynamic and environmental flows. Tremendous success has been recently achieved in theoretical analysis and large-scale numerical simulations of RT dynamics, as well as in laboratory experiments and diagnostics. This success and the striking similarity in behavior of RT dynamics in vastly different physical regimes, both make this moment right for developing advanced computational and mathematical tools that are capable to describe, and reliably predict the complex interfacial processes in aerodynamic and environmental problems. The scientific goal of our project is to advance knowledge of the RT dynamics and interfacial mixing. The specific objectives of the project are: (i) develop fast and affordable computational and theoretical tools and advanced methods of analysis and diagnostics, that can accurately describe the linear and nonlinear dynamics of the unstable interface separating two immiscible fluids; (ii) on the basis of scrupulous comparison and synergy of the theoretical analysis and numerical simulations, identify a set of benchmarks and invariant measures that accurately describe the flow dynamics at small scales and the coupling of small to large scales; (iii) apply our methods, tools and benchmarks to application problems in gas and oil industry, such as the problem of atomization of liquid jets injected into the either gas or liquid, and problems of flows in horizontal pipelines, including intermittent slug flows and highly stratified flows.
