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## Full-Text Articles in Physics

Similarity-Based Constitutive Relations For Local Mass Fluxes In Incompressible Mixing Layers, John D. Ramshaw

#### Similarity-Based Constitutive Relations For Local Mass Fluxes In Incompressible Mixing Layers, John D. Ramshaw

*Physics Faculty Publications and Presentations*

The local concentrations of the two fluids within a mixing layer produced by an interfacial instability are determined by their individual continuity equations. Solution of these equations requires constitutive relations for the local mass fluxes of the two fluids. We derive explicit analytical expressions for these fluxes in planar incompressible mixing layers characterized by a single integral length scale h(t), which is presumed to be provided by a suitable mix or turbulence model. Elementary scaling arguments imply that in mixing layers of this type, the mean volume fraction profile α(x,t) depends on x and t only through ...

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

#### 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 ...

Simple Model For Linear And Nonlinear Mixing At Unstable Fluid Interfaces In Spherical Geometry, John D. Ramshaw

#### Simple Model For Linear And Nonlinear Mixing At Unstable Fluid Interfaces In Spherical Geometry, John D. Ramshaw

*Physics Faculty Publications and Presentations*

A simple model was recently described for predicting linear and nonlinear mixing at an unstable planar fluid interface subjected to an arbitrary time-dependent variable acceleration history [J. D. Ramshaw, Phys. Rev. E 58, 5834 (1998)]. Here we present an analogous model for describing the mixing of two adjacent spherical fluid shells of different density resulting from an arbitrary time-dependent mean interface radius R(t). As in the planar case, the model is based on a heuristic expression for the kinetic energy of the system. This expression is based on that for the kinetic energy of a linearly perturbed interface, but ...

Simple Model For Linear And Nonlinear Mixing At Unstable Fluid Interfaces With Variable Acceleration, John D. Ramshaw

#### Simple Model For Linear And Nonlinear Mixing At Unstable Fluid Interfaces With Variable Acceleration, John D. Ramshaw

*Physics Faculty Publications and Presentations*

A simple model is described for predicting the time evolution of the half-width h of a mixing layer between two initially separated immiscible fluids of different density subjected to an arbitrary time-dependent variable acceleration history a(t). The model is based on a heuristic expression for the kinetic energy per unit area of the mixing layer. This expression is based on that for the kinetic energy of a linearly perturbed interface, but with a dynamically renormalized wavelength which becomes proportional to h in the nonlinear regime. An equation of motion for h is then derived from Lagrange's equations. This ...