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

Abstract

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 themore » 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).« less

Authors:
 [1]
  1. Lawrence Livermore National Laboratory, Livermore, CA (USA)
Publication Date:
OSTI Identifier:
6366825
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Journal Name:
Physical Review, A (General Physics); (USA)
Additional Journal Information:
Journal Volume: 42:6; Journal ID: ISSN 0556-2791
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; FLUIDS; RAYLEIGH-TAYLOR INSTABILITY; EXPLOSIVE INSTABILITY; GRAVITATIONAL COLLAPSE; IMPLOSIONS; INERTIAL CONFINEMENT; INTERFACES; MATHEMATICAL MODELS; PELLETS; STARS; THERMONUCLEAR REACTIONS; CONFINEMENT; INSTABILITY; NUCLEAR REACTIONS; NUCLEOSYNTHESIS; PLASMA CONFINEMENT; PLASMA INSTABILITY; SYNTHESIS; 640410* - Fluid Physics- General Fluid Dynamics; 700101 - Fusion Energy- Plasma Research- Confinement, Heating, & Production

Citation Formats

Mikaelian, K O. Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells. United States: N. p., 1990. Web. doi:10.1103/PhysRevA.42.3400.
Mikaelian, K O. Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells. United States. https://doi.org/10.1103/PhysRevA.42.3400
Mikaelian, K O. Sat . "Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells". United States. https://doi.org/10.1103/PhysRevA.42.3400.
@article{osti_6366825,
title = {Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells},
author = {Mikaelian, K O},
abstractNote = {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).},
doi = {10.1103/PhysRevA.42.3400},
url = {https://www.osti.gov/biblio/6366825}, journal = {Physical Review, A (General Physics); (USA)},
issn = {0556-2791},
number = ,
volume = 42:6,
place = {United States},
year = {1990},
month = {9}
}