RayleighTaylor stability for a shock wavedensity discontinuity interaction
Abstract
The analytic solution for perturbation growth of a shock wave striking a density discontinuity in an inviscid fluid is investigated. The Laplace transform of the solution results in a functional equation, which has a simple solution for weak shock waves. The solution for strong shock waves may be given by a power series. The four independent parameters of the solution are the gamma values on each side of the material interface, the density ratio at the interface, and the shock strength. The asymptotic behavior (for large distances and times) of the perturbation velocity is given. The asymptotic value is given by a constant term and a number of slowly decaying discreet frequencies. The asymptotic velocity at the interface is tabulated for representative values of the independent parameters. For weak shocks the solution is compared with results for an incompressible fluid. The range of density ratios with possible zero asymptotic velocities is given.
 Publication:

Presented at the Topical Conf. on Symmetry Aspects of Inertial Fusion Implosions
 Pub Date:
 1981
 Bibcode:
 1981saif.conf.....F
 Keywords:

 Discontinuity;
 Fluid Dynamics;
 Perturbation;
 Shock Wave Interaction;
 Shock Wave Profiles;
 Shock Waves;
 Taylor Instability;
 Velocity Distribution;
 Asymptotic Series;
 Density (Mass/Volume);
 Equations Of State;
 Gamma Function;
 Incompressible Flow;
 Inertial Fusion (Reactor);
 Inviscid Flow;
 Laplace Transformation;
 Nuclear Fuels;
 Particle Accelerator Targets;
 Power Series;
 Viscosity;
 Fluid Mechanics and Heat Transfer