Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells

Journal Article · Sat Sep 15 04:00:00 EDT 1990 · Physical Review, A (General Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevA.42.3400· OSTI ID:6366825

Mikaelian, K O ^[1]

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1. Lawrence Livermore National Laboratory, Livermore, CA (USA)

We study the linear stability of an arbitrary number of spherical concentric shells undergoing a radial implosion or explosion. The system consists of {ital N} incompressible fluids with small amplitude perturbations at each of the {ital N}{minus}1 interfaces. We derive the evolution equation for the perturbation {eta}{sub {ital i}} at interface {ital i}; it is coupled to the two adjacent interfaces via {eta}{sub {ital i}{plus minus}1}. We show that the {ital N}{minus}1 evolution equations are symmetric under {ital n}{leftrightarrow}{minus}{ital n}{minus}1, where {ital n} is the mode number of the spherical perturbation, provided that the first and last fluids have zero density ({rho}{sub 1}={rho}{sub {ital N}}=0). In plane geometry this translates to symmetry under {ital k}{leftrightarrow}{minus}{ital k}. We obtain several analytic solutions for the {ital N}=2 and 3 cases that we consider in some detail. As an application we derive the shock timing that is required to freeze out an amplitude. We also identify critical modes'' that are stable for any implosion or explosion history. Several numerical examples are presented illustrating perturbation feedthrough from one interface to another. Finally, we develop a model for the evolution of turbulent mix in spherical geometry, and introduce a geometrical factor {ital G} relating the mixing width {ital h} in spherical and planar geometries via {ital h}{sub spherical}={ital h}{sub planar}{ital G}. We find that {ital G} is a decreasing function of {ital R}/{ital R}{sub 0}, implying that in our model {ital h}{sub spherical} evolves faster (slower) than {ital h}{sub planar} during an implosion (explosion).

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6366825
• Journal Information: Physical Review, A (General Physics); (USA), Journal Name: Physical Review, A (General Physics); (USA) Vol. 42:6; ISSN PLRAA; ISSN 0556-2791
• Country of Publication: United States
• Language: English

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75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CONFINEMENT
EXPLOSIVE INSTABILITY
FLUIDS
GRAVITATIONAL COLLAPSE
IMPLOSIONS
INERTIAL CONFINEMENT
INSTABILITY
INTERFACES
MATHEMATICAL MODELS
NUCLEAR REACTIONS
NUCLEOSYNTHESIS
PELLETS
PLASMA CONFINEMENT
PLASMA INSTABILITY
RAYLEIGH-TAYLOR INSTABILITY
STARS
SYNTHESIS
THERMONUCLEAR REACTIONS