Viscous Rayleigh-Taylor instability in spherical geometry

Mikaelian, Karnig O.

doi:10.1103/PhysRevE.93.023104

Title: Viscous Rayleigh-Taylor instability in spherical geometry

Abstract

We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J. Mech. Appl. Math. 8, 1 (1955)] analyzed this unstable configuration providing the equations needed to find, numerically, the exact growth rates for the ensuing Rayleigh-Taylor instability. He also derived an analytic but approximate solution. We point out a weakness in his approximate dispersion relation (DR) and offer one that is to some extent improved.

Authors:

Mikaelian, Karnig O. ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: Mon Feb 08 00:00:00 EST 2016

Research Org.:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1240972

Alternate Identifier(s):: OSTI ID: 1237397

Report Number(s):: LLNL-JRNL-677099
Journal ID: ISSN 2470-0045; PLEEE8

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review E

Additional Journal Information:: Journal Volume: 93; Journal Issue: 2; Journal ID: ISSN 2470-0045

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

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                    Mikaelian, Karnig O. Viscous Rayleigh-Taylor instability in spherical geometry.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevE.93.023104.

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                    Mikaelian, Karnig O. Viscous Rayleigh-Taylor instability in spherical geometry.  United States.  https://doi.org/10.1103/PhysRevE.93.023104

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                    Mikaelian, Karnig O. Mon .  
"Viscous Rayleigh-Taylor instability in spherical geometry".  United States.  https://doi.org/10.1103/PhysRevE.93.023104.  https://www.osti.gov/servlets/purl/1240972.

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@article{osti_1240972,

  title        = {Viscous Rayleigh-Taylor instability in spherical geometry},

  author       = {Mikaelian, Karnig O.},

  abstractNote = {We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J. Mech. Appl. Math. 8, 1 (1955)] analyzed this unstable configuration providing the equations needed to find, numerically, the exact growth rates for the ensuing Rayleigh-Taylor instability. He also derived an analytic but approximate solution. We point out a weakness in his approximate dispersion relation (DR) and offer one that is to some extent improved.},

  doi          = {10.1103/PhysRevE.93.023104},

  journal      = {Physical Review E},

  number       = 2,

  volume       = 93,

  place        = {United States},

  year         = {Mon Feb 08 00:00:00 EST 2016},

  month        = {Mon Feb 08 00:00:00 EST 2016}

}

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Works referenced in this record:

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Bellman, Richard; Pennington, Ralph H.
Quarterly of Applied Mathematics, Vol. 12, Issue 2
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Rayleigh-Taylor instability in finite-thickness fluids with viscosity and surface tension
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Mikaelian, Karnig O.
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Effect of viscosity on Rayleigh-Taylor and Richtmyer-Meshkov instabilities
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Nuckolls, John; Wood, Lowell; Thiessen, Albert
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Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 51, Issue 1
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On the Bell–Plesset effects: The effects of uniform compression and geometrical convergence on the classical Rayleigh–Taylor instability
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Epstein, R.
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Chandrasekhar, S.
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Rayleigh-Taylor instability at spherical interfaces between viscous fluids: Fluid/vacuum interface
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Mode 1 drive asymmetry in inertial confinement fusion implosions on the National Ignition Facility
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Instability of the interface of two gases accelerated by a shock wave
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journal, July 1987

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Taylor instability in shock acceleration of compressible fluids
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Works referencing / citing this record:

The stability of the contact interface of cylindrical and spherical shock tubes
journal, June 2018

Crittenden, Paul E.; Balachandar, S.
Physics of Fluids, Vol. 30, Issue 6
DOI: 10.1063/1.5026583

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Similar Records

Title: Viscous Rayleigh-Taylor instability in spherical geometry

Abstract

Citation Formats

Effects of surface tension and viscosity on Taylor instability journal, January 1954

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

Inhibition of turbulence in inertial-confinement-fusion hot spots by viscous dissipation journal, May 2014

The stability of the surface of a cavitation bubble journal, January 1953

On the stability of two superposed fluids journal, April 1965

Rayleigh-Taylor instability in finite-thickness fluids with viscosity and surface tension journal, October 1996

Effect of viscosity on Rayleigh-Taylor and Richtmyer-Meshkov instabilities journal, January 1993

Unstable normal mode for Rayleigh–Taylor instability in viscous fluids journal, January 1977

On the Stability of Fluid Flows with Spherical Symmetry journal, January 1954

Approximate treatment of density gradients in Rayleigh-Taylor instabilities journal, February 1986

The effects of surface tension and viscosity on the stability of two superposed fluids journal, April 1961

Laser Compression of Matter to Super-High Densities: Thermonuclear (CTR) Applications journal, September 1972

The character of the equilibrium of an incompressible heavy viscous fluid of variable density: an approximate theory journal, January 1955

On the Bell–Plesset effects: The effects of uniform compression and geometrical convergence on the classical Rayleigh–Taylor instability journal, November 2004

The character of the equilibrium of an incompressible heavy viscous fluid of variable density journal, January 1955

Motion of two superposed viscous fluids journal, January 1981

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

Mode 1 drive asymmetry in inertial confinement fusion implosions on the National Ignition Facility journal, April 2014

Instability of the interface of two gases accelerated by a shock wave journal, January 1972

The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I journal, March 1950

Comment on ‘‘Rayleigh-Taylor instability in spherical geometry’’ journal, July 1987

Taylor instability in shock acceleration of compressible fluids journal, May 1960

Rayleigh-Taylor instability in spherical geometry journal, April 1986

Radiation hydrodynamics modeling of the highest compression inertial confinement fusion ignition experiment from the National Ignition Campaign journal, February 2015

Viscous effects on perturbed spherical flows journal, January 1977

The stability of the contact interface of cylindrical and spherical shock tubes journal, June 2018

Effects of surface tension and viscosity on Taylor instability
journal, January 1954

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

Inhibition of turbulence in inertial-confinement-fusion hot spots by viscous dissipation
journal, May 2014

The stability of the surface of a cavitation bubble
journal, January 1953

On the stability of two superposed fluids
journal, April 1965

Rayleigh-Taylor instability in finite-thickness fluids with viscosity and surface tension
journal, October 1996

Effect of viscosity on Rayleigh-Taylor and Richtmyer-Meshkov instabilities
journal, January 1993

Unstable normal mode for Rayleigh–Taylor instability in viscous fluids
journal, January 1977

On the Stability of Fluid Flows with Spherical Symmetry
journal, January 1954

Approximate treatment of density gradients in Rayleigh-Taylor instabilities
journal, February 1986

The effects of surface tension and viscosity on the stability of two superposed fluids
journal, April 1961

Laser Compression of Matter to Super-High Densities: Thermonuclear (CTR) Applications
journal, September 1972

The character of the equilibrium of an incompressible heavy viscous fluid of variable density: an approximate theory
journal, January 1955

On the Bell–Plesset effects: The effects of uniform compression and geometrical convergence on the classical Rayleigh–Taylor instability
journal, November 2004

The character of the equilibrium of an incompressible heavy viscous fluid of variable density
journal, January 1955

Motion of two superposed viscous fluids
journal, January 1981

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

Mode 1 drive asymmetry in inertial confinement fusion implosions on the National Ignition Facility
journal, April 2014

Instability of the interface of two gases accelerated by a shock wave
journal, January 1972

The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I
journal, March 1950

Comment on ‘‘Rayleigh-Taylor instability in spherical geometry’’
journal, July 1987

Taylor instability in shock acceleration of compressible fluids
journal, May 1960

Rayleigh-Taylor instability in spherical geometry
journal, April 1986

Radiation hydrodynamics modeling of the highest compression inertial confinement fusion ignition experiment from the National Ignition Campaign
journal, February 2015

Viscous effects on perturbed spherical flows
journal, January 1977

The stability of the contact interface of cylindrical and spherical shock tubes
journal, June 2018