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Title: Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration

A simple model is described for predicting the time evolution of the half-width h of a planar mixing layer between two immiscible incompressible fluids driven by an arbitrary time-dependent variable acceleration history a(l)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 by means of 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 quadratic RT and power-law RM growth laws in the nonlinear regime. The time exponent in the RM power law depends on the rate of kinetic energy dissipation. In the case of zero dissipation, this exponent reduces to 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 mixing data from linear electric motor experiments. Considerations involved in implementing the model in hydrodynamics codes aremore » briefly discussed.« less
Publication Date:
OSTI Identifier:
Report Number(s):
DP0101031; ON: DE00003402
DOE Contract Number:
Resource Type:
Resource Relation:
Conference: 1998 Nuclear Explosives Development Conference, Las Vegas, NV, October 25-30, 1998
Research Org:
Lawrence Livermore National Laboratory, Livermore, CA
Sponsoring Org:
USDOE Office of Defense Programs (DP)
Country of Publication:
United States
66 PHYSICS; Mixing; Instability; Rayleigh-Taylor Instability; Helmholtz Instability; Fluids; Interfaces; Acceleration