Physical Sciences and Mathematics Commons^™

Fluid Dynamics And Energetics In Ideal Gas Mixtures, John D. Ramshaw

Physics Faculty Publications and Presentations

The generalization of fluid dynamics from pure to multicomponent fluids (fluid mixtures composed of different components or species) requires the introduction of new concepts, some of which are rather subtle and are less widely appreciated than they deserve to be. The purpose of this paper is to provide a simple didactic introduction to some of these concepts based on a detailed analysis of the equations governing the flow of ideal gas mixtures. The treatment is based entirely on a continuum description and makes no explicit use of the kinetic theory of gases. We include a straightforward and physically transparent derivation …

Effect Of Slow Compression On The Linear Stability Of An Accelerated Shear Layer, John D. Ramshaw

Physics Faculty Publications and Presentations

An analysis is given of the effect of a slow uniform anisotropic compression or expansion on the linear stability of a normally accelerated planar interface between two fluids with different densities and tangential velocities, i.e., a combined Kelvin-Helmholtz and Rayleigh-Taylor instability, but generalized to an arbitrary time-dependent acceleration history. The compression is presumed to be sufficiently slow that the density remains uniform within each fluid and hence depends only on time. The perturbation is taken to be sinusoidal with amplitude h(t). The time evolution of h is determined by requiring pressure continuity across the interface in the usual way. The …

Probability Densities And The Random Variable Transformation Theorem, John D. Ramshaw

Physics Faculty Publications and Presentations

D. T. Gillespie has recently derived and discussed a random variable transformation (RVT) theorem relating the joint probability densities of functionally dependent sets of random variables.....

It is hoped that the present discussion will help to disseminate this basic relation among a wider circle of nonspecialists.

Partial Chemical Equilibrium In Fluid Dynamics, John D. Ramshaw

Physics Faculty Publications and Presentations

An analysis is given for the flow of a multicomponent fluid in which an arbitrary number of chemical reactions may occur, some of which are in equilibrium while the others proceed kinetically. The primitive equations describing this situation are inconvenient to use because the progress rates ω [subscript s] for the equilibrium reactions are determined implicitly by the associated equilibrium constraint conditions. Two alternative equivalent equation systems that are more pleasant to deal with are derived. In the first system, the ω [subscript s] are eliminated by replacing the transport equations for the chemical species involved in the equilibrium reactions …