Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration
- Lawrence Livermore National Laboratory, University of California, P.O. Box 808, L-097, Livermore, California 94551 (United States)
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{close_quote}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={alpha}Aat{sup 2} for constant a (where A is the Atwood number) and the nonlinear RM growth law h{approximately}t{sup {theta}} for impulsive a, where {alpha} and {theta} depend on the rate of kinetic energy dissipation. In the case of zero dissipation, {theta}=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. {copyright} {ital 1998} {ital The American Physical Society}
- OSTI ID:
- 664700
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 58, Issue 5; Other Information: PBD: Nov 1998
- Country of Publication:
- United States
- Language:
- English
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