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Title: Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids

Abstract

For the Rayleigh–Taylor unstable arrangement of a viscous fluid sphere embedded in a finite viscous fluid spherical shell with a rigid boundary and a radially directed acceleration, a dispersion relation is developed from a linear stability analysis using the method of normal modes. [Formula: see text] is the radially directed acceleration at the interface. ρi denotes the density, μi is the viscosity, and Ri is the radius, where i = 1 is the inner sphere and i = 2 is the outer sphere. The dispersion relation is a function of the following dimensionless variables: viscosity ratio [Formula: see text], density ratio [Formula: see text], spherical harmonic mode n, [Formula: see text], [Formula: see text], and the dimensionless growth rate [Formula: see text], where σ is the exponential growth rate. We show that the boundedness provided by the outer spherical shell has a strong influence on the instability behavior, which is reflected not only in the modulation of the growth rate but also in the selection of the most unstable modes that are physically possible. This outer boundary effect is quantified by the relative magnitude of the radius ratio H. We find that when H is close to unity, lower ordermore » harmonics are excluded from becoming the most unstable within a vast region of the parameter space. In other words, the effect of H has precedence over the other controlling parameters d, B, and a wide range of s in establishing what the lowest most unstable mode can be. When H ~ 1, low order harmonics can become the most unstable only for s >> 1. However, in the limit when s → ∞, we show that the most unstable mode is n = 1 and derive the dispersion relation in this limit. The exclusion of most unstable low order harmonics caused by a finite outer boundary is not realized when the outer boundary extends beyond a certain threshold length-scale in which case all modes are equally possible depending on the value of B.« less

Authors:
 [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Boston Univ., MA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
OSTI Identifier:
1871484
Report Number(s):
LA-UR-22-20717
Journal ID: ISSN 2158-3226; TRN: US2306758
Grant/Contract Number:  
89233218CNA000001; DMS-1748883
Resource Type:
Accepted Manuscript
Journal Name:
AIP Advances
Additional Journal Information:
Journal Volume: 12; Journal Issue: 4; Journal ID: ISSN 2158-3226
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; linear stability analysis; fluid instabilities; viscosity; viscous liquid; flow instabilities

Citation Formats

Oren, Garrett H., and Terrones, Guillermo. Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids. United States: N. p., 2022. Web. doi:10.1063/5.0090277.
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Oren, Garrett H., & Terrones, Guillermo. Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids. United States. https://doi.org/10.1063/5.0090277
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Oren, Garrett H., and Terrones, Guillermo. Fri . "Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids". United States. https://doi.org/10.1063/5.0090277. https://www.osti.gov/servlets/purl/1871484.
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@article{osti_1871484,
title = {Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids},
author = {Oren, Garrett H. and Terrones, Guillermo},
abstractNote = {For the Rayleigh–Taylor unstable arrangement of a viscous fluid sphere embedded in a finite viscous fluid spherical shell with a rigid boundary and a radially directed acceleration, a dispersion relation is developed from a linear stability analysis using the method of normal modes. [Formula: see text] is the radially directed acceleration at the interface. ρi denotes the density, μi is the viscosity, and Ri is the radius, where i = 1 is the inner sphere and i = 2 is the outer sphere. The dispersion relation is a function of the following dimensionless variables: viscosity ratio [Formula: see text], density ratio [Formula: see text], spherical harmonic mode n, [Formula: see text], [Formula: see text], and the dimensionless growth rate [Formula: see text], where σ is the exponential growth rate. We show that the boundedness provided by the outer spherical shell has a strong influence on the instability behavior, which is reflected not only in the modulation of the growth rate but also in the selection of the most unstable modes that are physically possible. This outer boundary effect is quantified by the relative magnitude of the radius ratio H. We find that when H is close to unity, lower order harmonics are excluded from becoming the most unstable within a vast region of the parameter space. In other words, the effect of H has precedence over the other controlling parameters d, B, and a wide range of s in establishing what the lowest most unstable mode can be. When H ~ 1, low order harmonics can become the most unstable only for s >> 1. However, in the limit when s → ∞, we show that the most unstable mode is n = 1 and derive the dispersion relation in this limit. The exclusion of most unstable low order harmonics caused by a finite outer boundary is not realized when the outer boundary extends beyond a certain threshold length-scale in which case all modes are equally possible depending on the value of B.},
doi = {10.1063/5.0090277},
journal = {AIP Advances},
number = 4,
volume = 12,
place = {United States},
year = {Fri Apr 01 00:00:00 EDT 2022},
month = {Fri Apr 01 00:00:00 EDT 2022}
}
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Works referenced in this record:

The Character of the Equilibrium of an Incompressible Fluid Sphere of Variable Density and Viscosity Subject to Radial Acceleration
journal, January 1955

  • Chandrasekhar, S.
  • The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 8, Issue 1
  • DOI: 10.1093/qjmam/8.1.1

Supernova, nuclear synthesis, fluid instabilities, and interfacial mixing
journal, November 2018

  • Abarzhi, Snezhana I.; Bhowmick, Aklant K.; Naveh, Annie
  • Proceedings of the National Academy of Sciences, Vol. 116, Issue 37
  • DOI: 10.1073/pnas.1714502115

3D xRAGE simulation of inertial confinement fusion implosion with imposed mode 2 laser drive asymmetry
journal, August 2020

Impact of imposed mode 2 laser drive asymmetry on inertial confinement fusion implosions
journal, January 2019

  • Gatu Johnson, M.; Appelbe, B. D.; Chittenden, J. P.
  • Physics of Plasmas, Vol. 26, Issue 1
  • DOI: 10.1063/1.5066435

Elastic stability and the onset of plastic flow in accelerated solid plates
journal, August 2007

  • Terrones, Guillermo
  • Journal of Applied Physics, Vol. 102, Issue 3
  • DOI: 10.1063/1.2764208

Plasma transport simulations of Rayleigh–Taylor instability in near-ICF deceleration regimes
journal, September 2021

  • Vold, E.; Yin, L.; Albright, B. J.
  • Physics of Plasmas, Vol. 28, Issue 9
  • DOI: 10.1063/5.0059043

Rayleigh-Taylor instability in elastic solids
journal, November 2005

Evidence of Three-Dimensional Asymmetries Seeded by High-Density Carbon-Ablator Nonuniformity in Experiments at the National Ignition Facility
journal, January 2021

Observation of Hydrodynamic Flows in Imploding Fusion Plasmas on the National Ignition Facility
journal, September 2021

Analysis of mixing in high-explosive fireballs using small-scale pressurised spheres
journal, February 2018

Fastest growing linear Rayleigh-Taylor modes at solid∕fluid and solid∕solid interfaces
journal, March 2005

Mitigation of mode-one asymmetry in laser-direct-drive inertial confinement fusion implosions
journal, April 2021

  • Mannion, O. M.; Igumenshchev, I. V.; Anderson, K. S.
  • Physics of Plasmas, Vol. 28, Issue 4
  • DOI: 10.1063/5.0041554

Thin plate effects in the Rayleigh–Taylor instability of elastic solids
journal, June 2006

  • Piriz, A. R.; LÓPez Cela, J. J.; Serna Moreno, M. C.
  • Laser and Particle Beams, Vol. 24, Issue 2
  • DOI: 10.1017/s0263034606060423

Trending low mode asymmetries in NIF capsule drive using a simple viewfactor metric *
journal, August 2021

The Rayleigh–Taylor instability in a self-gravitating two-layer viscous sphere
journal, November 2017

  • Mondal, Puskar; Korenaga, Jun
  • Geophysical Journal International, Vol. 212, Issue 3
  • DOI: 10.1093/gji/ggx507

Rayleigh-Taylor instability at spherical interfaces between viscous fluids: Fluid/vacuum interface
journal, May 2015

  • Terrones, Guillermo; Carrara, Mark D.
  • Physics of Fluids, Vol. 27, Issue 5
  • DOI: 10.1063/1.4921648

Rayleigh–Taylor instabilities in high-energy density settings on the National Ignition Facility
journal, June 2018

  • Remington, Bruce A.; Park, Hye-Sook; Casey, Daniel T.
  • Proceedings of the National Academy of Sciences, Vol. 116, Issue 37
  • DOI: 10.1073/pnas.1717236115

Numerical modeling of protocore destabilization during planetary accretion: Methodology and results
journal, December 2009

An analytic asymmetric-piston model for the impact of mode-1 shell asymmetry on ICF implosions
journal, June 2020

  • Hurricane, O. A.; Casey, D. T.; Landen, O.
  • Physics of Plasmas, Vol. 27, Issue 6
  • DOI: 10.1063/5.0001335

Viscous Rayleigh-Taylor instability in spherical geometry
journal, February 2016

The Rayleigh-Taylor instability in a self-gravitating two-layer fluid sphere
journal, February 1989

  • Ida, Shigeru; Nakagawa, Yoshitsugu; akazawa, Kiyoshi
  • Earth, Moon and Planets, Vol. 44, Issue 2
  • DOI: 10.1007/bf00056314

The Earth's core formation due to the Rayleigh-Taylor instability
journal, February 1987

Elastic Rayleigh–Taylor and Richtmyer–Meshkov instabilities in spherical geometry
journal, December 2020

  • Sun, Y. B.; Zeng, R. H.; Tao, J. J.
  • Physics of Fluids, Vol. 32, Issue 12
  • DOI: 10.1063/5.0027909

Rayleigh–Taylor instability at spherical interfaces between viscous fluids: The fluid/fluid interface
journal, September 2020

  • Terrones, Guillermo; Heberling, Tamra
  • Physics of Fluids, Vol. 32, Issue 9
  • DOI: 10.1063/5.0018601

Numerical simulation of Earth's core formation
journal, February 1993

  • Honda, Rie; Mizutani, Hitoshi; Yamamoto, Tetsuo
  • Journal of Geophysical Research: Solid Earth, Vol. 98, Issue B2
  • DOI: 10.1029/92jb02699

Rayleigh–Taylor and Richtmyer–Meshkov instabilities: A journey through scales
journal, September 2021

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