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Related Experiment Videos

Instability of a planar expansion wave.

A L Velikovich1, S T Zalesak, N Metzler

  • 1Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
Summary

A rippled expansion wave in ideal gases can lead to hydrodynamic instability. Mass modulation grows with time, depending on the adiabatic exponent, with analytical solutions derived for different conditions.

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Area of Science:

  • Fluid Dynamics
  • Plasma Physics
  • Astrophysical Hydrodynamics

Background:

  • Shock wave interaction with surfaces generates expansion waves, crucial for processes like inertial confinement fusion.
  • Rippled expansion waves in ideal gases exhibit unique behaviors based on the adiabatic exponent (gamma).
  • Previous studies often focused on decaying oscillations, overlooking specific instability mechanisms.

Purpose of the Study:

  • To analytically investigate the behavior of rippled expansion waves in ideal gases.
  • To characterize the mass modulation growth and its dependence on the adiabatic exponent.
  • To compare analytical findings with hydrodynamic simulation results.

Main Methods:

  • Derivation of exact analytical expressions for growth rates.

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  • Analysis of fluid variables under different adiabatic exponent regimes (gamma > 3 and gamma - 1 << 1).
  • Comparison of theoretical predictions with numerical simulations.

    • Main Results:

    • For gamma > 3, mass modulation amplitude exhibits power-law growth (delta(m) ~ t^((gamma-3)/(gamma-1))), driven by a Richtmyer-Meshkov-like instability.
    • For gamma - 1 << 1, mass modulation shows approximately linear oscillatory growth, driven by Vishniac's instability.
    • Analytical growth laws are derived and validated against simulation data.

    Conclusions:

    • The study provides a closed-form analytical description of hydrodynamic instability in rippled expansion waves.
    • The adiabatic exponent significantly dictates the instability's growth mechanism and rate.
    • This work offers insights into perturbation transfer in fusion targets and astrophysical phenomena.