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

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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 <i>a(l)</i>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 ... continued below

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Ramshaw, J. D. & Rathkopf, J. December 23, 1998.

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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 <i>a(l)</i>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 are briefly discussed.

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167 Kilobytes

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  • 1998 Nuclear Explosives Development Conference, Las Vegas, NV, October 25-30, 1998

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  • Other: DE00003402
  • Report No.: UCRL-JC-132872
  • Grant Number: W-7405-Eng-48
  • Office of Scientific & Technical Information Report Number: 3402
  • Archival Resource Key: ark:/67531/metadc684985

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  • December 23, 1998

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  • July 25, 2015, 2:20 a.m.

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  • May 6, 2016, 11:31 p.m.

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Ramshaw, J. D. & Rathkopf, J. Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration, article, December 23, 1998; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc684985/: accessed September 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.