Instability of a Planar Expansion Wave
Abstract
An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent gamma. At gamma > 3, the mass modulation amplitude delta-m in a rippled expansion wave exhibits a power-law growth with time alpha tau(beta), where beta = (gamma - 3)/(gamma - 1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme gamma - 1 much less than 1, delta-m exhibits oscillatory growth, approximately linear with time, until it reaches its peak value approximately (gamma - 1)^(- 1/2), and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac's instability of a blast wave in a gas with low gamma. Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 11, 2005
- Accession Number
- ADA483433
Entities
People
- A. L. Velikovich
- J. G. Wouchuk
- N. Metzler
- Steven T.P. Zalesak
Organizations
- United States Naval Research Laboratory