# Simple Model for Linear and Nonlinear Mixing at Unstable Fluid Interfaces with Variable Acceleration

## Published In

Physical Review E

## Document Type

Article

## Publication Date

11-1-1998

## Subjects

Turbulence -- Mathematical models, Fluid dynamics, Change of state (Physics)

## Abstract

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 model reproduces the known linear growth rates of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities, as well as the nonlinear RT growth law h=αAat^{2} for constant a (where A is the Atwood number) and the nonlinear RM growth law h~t^{θ} for impulsive a, where α and θ depend on the rate of kinetic energy dissipation. In the case of zero dissipation, θ=2/3 in agreement with elementary scaling arguments. A conservative numerical scheme is proposed to solve the model equations, and is used to perform calculations that agree well with published experimental mixing data for four different acceleration histories.

## DOI

10.1103/PhysRevE.58.5834

## Persistent Identifier

http://archives.pdx.edu/ds/psu/7703

## Citation Details

J.D. Ramshaw, "Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration," Phys. Rev. E 58, 5834 (1998).

## Description

This is the publisher's final pdf. Article appears in Physical Review E (http://pre.aps.org/) and is copyrighted by APS Journals (http://publish.aps.org/)

*At the time of publication John Ramshaw was affiliated with the Lawrence Livermore National Laboratory, University of California