Scaling Laws Between Fingers at Richtmeyer-Meshkov Unstable Interfaces in Different Dimensions

Project: Research

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Description

Interfacial fluid mixing between two fluids of different densities is a very complicated but extremely important topic in science. The phenomenon of unstable interfacial mixing appears in many natural phenomena and industrial applications, such as supernovas, inertial confinement fusion, enhanced oil recovery process, ground water contamination, etc. To understand the dynamics of unstable mixing interfaces and to provide theoretical predictions of their behavior is an important and extremely difficult task.Small disturbances at the initial interface grow in size and develop into complicated nonlinear structures at unstable interfaces. These nonlinear structures cause great difficulties in experimental design, in numerical simulation and in theoretical analysis. A well-known unstable interfacial mixing problem is the Richtmyer-Meshkov (RM) instability. This instability occurs when a shock hits a perturbed material interface between two fluids of different densities. Unstable fingers develop at the material interface. Understanding the behavior of fingers at the RM interfaces is a classical and very difficult task in mathematics and engineering. Numerical simulations and experiments have been performed in various settings and in different dimensions. These simulations are quite time-consuming. The sophistication and difficulties in numerical algorithms increase dra- matically when we consider an unstable interface in three-dimensional space. Relative to two-dimensional simulations, it takes orders of magnitude longer in time to perform simulations in three dimensions. The purpose of this study is to establish scaling laws between the dominant behavior of RM instability in two-dimensional systems and that in three-dimensional systems. Once achieved, it will allow us to use data from RM unstable fingers in two dimensions to predict the dominant behavior of fingers in three dimensions. RM unstable system involves many physical quantities, such as fluid density, compressibility, incident shock strength, etc. The scaling laws between two-dimensional and three-dimensional systems that we are searching for are valid not only between two- dimensional and three-dimensional systems with the same physical parameters, but also between two-dimensional and three-dimensional systems with different parameters. At the completion of this project, it will provide an extremely useful theoretical tool for predicting the dominant behavior of the RM instability in three dimensions from the results in two-dimensional systems.

Detail(s)

Project number9042535
Grant typeGRF
StatusFinished
Effective start/end date1/07/178/10/20