skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability

Abstract

We report nonlinear solutions for a system of conservation laws describing the dynamics of the large-scale coherent structure of bubbles and spikes in the Rayleigh-Taylor instability (RTI) for fluids with a finite density ratio. Three-dimensional flows are considered with general type of symmetry in the plane normal to the direction of gravity. The nonlocal properties of the interface evolution are accounted for on the basis of group theory. It is shown that isotropic coherent structures are stable. For anisotropic structures, secondary instabilities develop with the growth rate determined by the density ratio. For stable structures, the curvature and velocity of the nonlinear bubble have nontrivial dependencies on the density ratio, yet their mutual dependence on one another has an invariant form independent of the density ratio. The process of bubble merge is not considered. Based on the obtained results we argue that the large-scale coherent dynamics in RTI has a multiscale character and is governed by two length scales: the period of the coherent structure and the bubble (spike) position.

Authors:
 [1];  [2];  [3];  [1]
  1. FLASH, University of Chicago, Chicago, Illinois (United States)
  2. (United States)
  3. Institute for Laser Engineering, Osaka University, Osaka (Japan)
Publication Date:
OSTI Identifier:
20778872
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevE.73.036310; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; BUBBLES; CONSERVATION LAWS; EVOLUTION; GRAVITATION; GROUP THEORY; INTERFACES; MATHEMATICAL SOLUTIONS; MULTIPHASE FLOW; NONLINEAR PROBLEMS; RAYLEIGH-TAYLOR INSTABILITY; SYMMETRY; THREE-DIMENSIONAL CALCULATIONS; VELOCITY

Citation Formats

Abarzhi, S.I., Center for Turbulence Research, Stanford University, Stanford, California, Nishihara, K., and Rosner, R. Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability. United States: N. p., 2006. Web. doi:10.1103/PHYSREVE.73.0.
Abarzhi, S.I., Center for Turbulence Research, Stanford University, Stanford, California, Nishihara, K., & Rosner, R. Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability. United States. doi:10.1103/PHYSREVE.73.0.
Abarzhi, S.I., Center for Turbulence Research, Stanford University, Stanford, California, Nishihara, K., and Rosner, R. Wed . "Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability". United States. doi:10.1103/PHYSREVE.73.0.
@article{osti_20778872,
title = {Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability},
author = {Abarzhi, S.I. and Center for Turbulence Research, Stanford University, Stanford, California and Nishihara, K. and Rosner, R.},
abstractNote = {We report nonlinear solutions for a system of conservation laws describing the dynamics of the large-scale coherent structure of bubbles and spikes in the Rayleigh-Taylor instability (RTI) for fluids with a finite density ratio. Three-dimensional flows are considered with general type of symmetry in the plane normal to the direction of gravity. The nonlocal properties of the interface evolution are accounted for on the basis of group theory. It is shown that isotropic coherent structures are stable. For anisotropic structures, secondary instabilities develop with the growth rate determined by the density ratio. For stable structures, the curvature and velocity of the nonlinear bubble have nontrivial dependencies on the density ratio, yet their mutual dependence on one another has an invariant form independent of the density ratio. The process of bubble merge is not considered. Based on the obtained results we argue that the large-scale coherent dynamics in RTI has a multiscale character and is governed by two length scales: the period of the coherent structure and the bubble (spike) position.},
doi = {10.1103/PHYSREVE.73.0},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 3,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}
  • It is shown that the Rayleigh--Taylor instability of magnetized plasma is nonlinearly stabilized by the external imposition of transverse velocity shear with zero spatial second derivative. The critical velocity shear required for stabilization is of order {gamma}{sub {ital g}}(ln Ra){sup 1/2}, where {gamma}{sub {ital g}} is the linear growth rate and Ra is the Rayleigh number.
  • Using Lagrangian transformation, the nonlinear evolution of Rayleigh-Taylorinstability is investigated in magnetic fluids. We show that the formation ofbubbles on the interface can be inhibited by using magnetic fluids of higherpermeabilities or increasing the strength of the applied magnetic field. Themodel developed here successfully explains qualitatively the trend observedexperimentally by Rosensweig.
  • A numerical simulation scheme is developed to examine the nonlinear evolution of the Rayleigh--Taylor instability of a thin sheet in three dimensions. It is shown that the erosion of mass at the top of the bubble is approximately as described by two-dimensional simulations. However, mass is lost into spikes more slowly in three-dimensional than in two-dimensional simulations.
  • A simple model is derived heuristically for the nonlinear evolution of the Rayleigh-Taylor instability. Ordinary differential equations for time evolution of the spike and bubble amplitudes are found by constructing terms that smoothly connect the regimes of small and large amplitude behavior. The results apply to arbitrarily varying acceleration fields, including shock-induced instabilities. The model predicts amplitudes accurate to better than 20% (velocity predictions are more accurate), in comparisons with published experimental data and two-dimensional numerical simulations with hydrocodes. A limitation in the present model is that the density ratio of the two fluids should not be close to onemore » for accurate modeling.« less
  • The nonlinear evolution of the Rayleigh-Taylor instability of a thin sheet in three dimensions is studied numerically. Results show that erosion of mass at the top of the bubble is similar to that found in two-dimensional simulations, but mass flow into spikes is slower in three dimensions.