Rayleigh-Taylor and Richtmyer-Meshkov Instabilities and Mixing in Stratified Cylindrical Shells

Journal Article · Thu Apr 15 04:00:00 EDT 2004 · Physics of Fluids

OSTI ID:859922

Mikaelian, K O

We study the linear stability of an arbitrary number N of cylindrical concentric shells undergoing a radial implosion or explosion.We derive the evolution equation for the perturbation {eta}{sub i} at interface i; it is coupled to the two adjacent interfaces via {eta}{sub i{+-}1}. For N=2, where there is only one interface, we verify Bell's conjecture as to the form of the evolution equation for arbitrary {rho}{sub 1} and {rho}{sub 2}, the fluid densities on either side of the interface. We obtain several analytic solutions for the N=2 and 3 cases. We discuss freeze-out, a phenomenon that can occur in all three geometries (planar, cylindrical, or spherical), and ''critical modes'' that are stable for any implosion or explosion history and occur only in cylindrical or spherical geometries. We present numerical simulations of possible gelatin-ring experiments illustrating perturbation feedthrough from one interface to another. We also develop a simple model for the evolution of turbulent mix in cylindrical geometry and define a geometrical factor G as the ratio h{sub cylindrical}/h{sub planar} between cylindrical and planar mixing layers. We find that G is a decreasing function of R/R{sub o}, implying that in our model h{sub cylindrical} evolves faster (slower) than h{sub planar} during an implosion (explosion).

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 859922
• Report Number(s): UCRL-JRNL-204014
• Journal Information: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 9 Vol. 17
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
EXPLOSIONS
GEOMETRY
IMPLOSIONS
STABILITY