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:: Journal Article: 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

Citation Formats


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

Copy to clipboard


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

Copy to clipboard


                    Mikaelian, Karnig O. 2016.  
        "Viscous Rayleigh-Taylor instability in spherical geometry".  United States.  https://doi.org/10.1103/PhysRevE.93.023104.  https://www.osti.gov/servlets/purl/1240972.

Copy to clipboard


                    
@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},

  url          = {https://www.osti.gov/biblio/1240972},
  journal      = {Physical Review E},

  issn         = {2470-0045},

  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}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1103/PhysRevE.93.023104

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 19 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

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

Bellman, Richard; Pennington, Ralph H.
Quarterly of Applied Mathematics, Vol. 12, Issue 2
https://doi.org/10.1090/qam/63198

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
https://doi.org/10.1093/qjmam/8.1.1

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

Weber, C. R.; Clark, D. S.; Cook, A. W.
Physical Review E, Vol. 89, Issue 5
https://doi.org/10.1103/PhysRevE.89.053106

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

Binnie, A. M.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 49, Issue 1
https://doi.org/10.1017/S0305004100028152

On the stability of two superposed fluids
journal, April 1965

Willson, A. J.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 61, Issue 2
https://doi.org/10.1017/S0305004100004163

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

Mikaelian, Karnig O.
Physical Review E, Vol. 54, Issue 4
https://doi.org/10.1103/PhysRevE.54.3676

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

Mikaelian, Karnig O.
Physical Review E, Vol. 47, Issue 1
https://doi.org/10.1103/PhysRevE.47.375

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

Menikoff, R.; Mjolsness, R. C.; Sharp, D. H.
Physics of Fluids, Vol. 20, Issue 12
https://doi.org/10.1063/1.861831

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

Plesset, M. S.
Journal of Applied Physics, Vol. 25, Issue 1
https://doi.org/10.1063/1.1721529

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

Mikaelian, Karnig O.
Physical Review A, Vol. 33, Issue 2
https://doi.org/10.1103/PhysRevA.33.1216

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

Reid, W. H.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 57, Issue 2
https://doi.org/10.1017/S0305004100035362

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

Nuckolls, John; Wood, Lowell; Thiessen, Albert
Nature, Vol. 239, Issue 5368, p. 139-142
https://doi.org/10.1038/239139a0

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

Hide, Raymond
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 51, Issue 1
https://doi.org/10.1017/S030500410003005X

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

Epstein, R.
Physics of Plasmas, Vol. 11, Issue 11
https://doi.org/10.1063/1.1790496

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

Chandrasekhar, S.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 51, Issue 1
https://doi.org/10.1017/S0305004100030048

Motion of two superposed viscous fluids
journal, January 1981

Prosperetti, Andrea
Physics of Fluids, Vol. 24, Issue 7
https://doi.org/10.1063/1.863522

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
https://doi.org/10.1063/1.4921648

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

Spears, Brian K.; Edwards, M. J.; Hatchett, S.
Physics of Plasmas, Vol. 21, Issue 4
https://doi.org/10.1063/1.4870390

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

Meshkov, E. E.
Fluid Dynamics, Vol. 4, Issue 5
https://doi.org/10.1007/BF01015969

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

Taylor, Geoffrey Ingram
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 201, Issue 1065, p. 192-196
https://doi.org/10.1098/rspa.1950.0052

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

Mikaelian, Karnig O.
Physical Review A, Vol. 36, Issue 1
https://doi.org/10.1103/PhysRevA.36.411

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

Richtmyer, Robert D.
Communications on Pure and Applied Mathematics, Vol. 13, Issue 2
https://doi.org/10.1002/cpa.3160130207

Rayleigh-Taylor instability in spherical geometry
journal, April 1986

Gupta, N. K.; Lawande, S. V.
Physical Review A, Vol. 33, Issue 4
https://doi.org/10.1103/PhysRevA.33.2813

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

Clark, D. S.; Marinak, M. M.; Weber, C. R.
Physics of Plasmas, Vol. 22, Issue 2
https://doi.org/10.1063/1.4906897

Viscous effects on perturbed spherical flows
journal, January 1977

Prosperetti, Andrea
Quarterly of Applied Mathematics, Vol. 34, Issue 4
https://doi.org/10.1090/qam/99652

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
https://doi.org/10.1063/1.5026583

Similar records in OSTI.GOV collections:

Rayleigh-Taylor instability at spherical interfaces between viscous fluids: Fluid/vacuum interface

Journal Article Terrones, Guillermo; Carrara, Mark - Physics of Fluids

For a spherical interface of radius R separating two different homogeneous regions of incompressible viscous fluids under the action of a radially directed acceleration, we perform a linear stability analysis in terms of spherical surface harmonics Y _n to derive the dispersion relation. The instability behavior is investigated by computing the growth rates and the most-unstable modes as a function of the spherical harmonic degree n. This general methodology is applicable to the entire parameter space spanned by the Atwood number, the viscosity ratio, and the dimensionless number B = (α_RΡ²₂/μ²_²)¹^/³ R (where α_R, Ρ₂ and μ₂ are the localmore »« less
Cited by 23
https://doi.org/10.1063/1.4921648

Full Text Available
Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids

Journal Article Oren, Garrett; Terrones, Guillermo - AIP Advances

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. ρ_i denotes the density, μ_i is the viscosity, and R_i 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], densitymore »« less
https://doi.org/10.1063/5.0090277

Full Text Available
Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

Journal Article Morgan, R.; Likhachev, O.; Jacobs, J. - Journal of Fluid Mechanics

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of themore »« less
Cited by 29
https://doi.org/10.1017/jfm.2016.46

Full Text Available
The magnetic Rayleigh-Taylor instability for inviscid and viscous fluids

Journal Article Chambers, K; Forbes, L - Physics of Plasmas

The Rayleigh-Taylor instability arises whenever two fluids with different densities are arranged such that the heavier fluid sits above the lighter fluid, with a sharp interface in between. The magnetic Rayleigh-Taylor instability has the further complication due to the presence of a magnetic field throughout both media. The two fluids in question may also have differing magnetic properties, such as the magnetic permeability. When the fluids in consideration are in fact plasmas comprised of charged particles, induced currents, magnetic fields, and Lorentz forces can all act in ways that will affect the stability of the system. Stable base flows existmore »« less
https://doi.org/10.1063/1.3574370
Ablative stabilization of the Rayleigh-Taylor instability in regimes relevant to inertial confinement fusion

Conference Kilkenny, J

As shown elsewhere an ablatively imploded shell is hydrodynamically unstable, the dominant instability being the well known Rayleigh-Taylor instability with growth rate {gamma} = {radical}Akg where k = 2{pi}/{lambda} is the wave number, g is the acceleration and A the Attwood number ({rho}{sub hi} {minus} {rho}{sub lo})/({rho}{sub hi} + {rho}{sub lo}) where {rho}{sub hi} is the density of the heavier fluid and {rho}{sub lo} is the density of the lighter fluid. A theoretical understanding of ablative stabilization has gradually evolved, confirmed over the last five years by experiments. The linear growth is very well understood with excellent agreement between experimentmore »« less
Full Text Available

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