Compressibility effects on the Rayleigh-Taylor instability growth between immiscible fluids

The linearized Navier-Stokes equations for a system of superposed immiscible compressible ideal fluids are analyzed. The results of the analysis reconcile the stabilizing and destabilizing effects of compressibility reported in the literature. It is shown that the growth rate $n$ obtained for an inviscid, compressible flow in an infinite domain is bounded by the growth rates obtained for the corresponding incompressible flows with uniform and exponentially varying density. As the equilibrium pressure at the interface $p_\infty$ increases (less compressible flow), $n$ increases towards the uniform density result, while as the ratio of specific heats $\gamma$ increases (less compressible fluid), $n$ decreases towards the exponentially varying density incompressible flow result. This remains valid in the presence of surface tension or for viscous fluids and the validity of the results is also discussed for finite size domains. The critical wavenumber imposed by the presence of surface tension is unaffected by compressibility. However, the results show that the surface tension modifies the sensitivity of the growth rate to a differential change in $\gamma$ for the lower and upper fluids. For the viscous case, the linearized equations are solved numerically for different values of $p_\infty$ and $\gamma$. It is found that the largest differences compared with the incompressible cases are obtained at small Atwood numbers. The most unstable mode for the compressible case is also bounded by the most unstable modes corresponding to the two limiting incompressible cases.Comment: To appear in Physics of Fluid

Non-premixed Flame-Turbulence Interaction in Compressible Turbulent Flow

Nonpremixed turbulent reacting flows are intrinsically difficult to model due to the strong coupling between turbulent motions and reaction. The large amount of heat released by a typical hydrocarbon flame leads to significant modifications of the thermodynamic variables and the molecular transport coefficients and thus alters the fluid dynamics. Additionally, in nonpremixed combustion, the flame has a complex spatial structure. Localized expansions and contractions occur, enhancing the dilatational motions. Therefore, the compressibility of the flow and the heat release are intimately related. However, fundamental studies of the role of compressibility on the scalar mixing and reaction are scarce. In this paper we present results concerning the fundamental aspects of the interaction between non-premixed flame and compressible turbulence.Comment: 4 pages, 4 figures; to appear in Proceedings ETC9, Eds: I.P. Castro and P.E. Hancock, CIMNE, Barcelona, 200

Learning to Embed Words in Context for Syntactic Tasks

We present models for embedding words in the context of surrounding words. Such models, which we refer to as token embeddings, represent the characteristics of a word that are specific to a given context, such as word sense, syntactic category, and semantic role. We explore simple, efficient token embedding models based on standard neural network architectures. We learn token embeddings on a large amount of unannotated text and evaluate them as features for part-of-speech taggers and dependency parsers trained on much smaller amounts of annotated data. We find that predictors endowed with token embeddings consistently outperform baseline predictors across a range of context window and training set sizes.Comment: Accepted by ACL 2017 Repl4NLP worksho