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Title: Viscous effects on the Rayleigh-Taylor instability with background temperature gradient

Abstract

Here we studied the growth rate of the compressible Rayleigh-Taylor instability in the presence of a background temperature gradient, Θ, using a normal mode analysis. The effect of Θ variation is examined for three interface types corresponding to the combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous, and viscous-inviscid) at different Atwood numbers, At, and when at least one of the fluids' viscosity is non-zero, as a function of the Grashof number. For the general case, the resulting ordinary differential equations are solved numerically; however, dispersion relations for the growth rate are presented for several limiting cases. An analytical solution is found for the inviscid-inviscid interface and the corresponding dispersion equation for the growth rate is obtained in the limit of large Θ. For the viscous-inviscid case, a dispersion relation is derived in the incompressible limit and Θ=0. Compared to Θ=0 case, the role of Θ<0 (hotter light fluid) is destabilizing and becomes stabilizing when Θ>0 (colder light fluid). The most pronounced effect of Θ ≠ 0 is found at low At and/or at large perturbation wavelengths relative to the domain size for all interface types. On the other hand, at small perturbation wavelengths relative to the domainmore » size, the growth rate for the Θ<0 case exceeds the infinite domain incompressible constant density result. The results are applied to two practical examples, using sets of parameters relevant to Inertial Confinement Fusion coasting stage and solar corona plumes. The role of viscosity on the growth rate reduction is discussed together with highlighting the range of wavenumbers most affected by viscosity. The viscous effects further increase in the presence of background temperature gradient, when the viscosity is temperature dependent.« less

Authors:
 [1];  [1]
  1. 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); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1304724
Alternate Identifier(s):
OSTI ID: 1421260
Report Number(s):
LA-UR-16-22586
Journal ID: ISSN 1070-664X; 1089-7674 (Electronic)
Grant/Contract Number:  
AC52-06NA25396; 20150568ER; LANL/20150568ER
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 7; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Gerashchenko, Sergiy, and Livescu, Daniel. Viscous effects on the Rayleigh-Taylor instability with background temperature gradient. United States: N. p., 2016. Web. doi:10.1063/1.4959810.
Gerashchenko, Sergiy, & Livescu, Daniel. Viscous effects on the Rayleigh-Taylor instability with background temperature gradient. United States. doi:10.1063/1.4959810.
Gerashchenko, Sergiy, and Livescu, Daniel. Thu . "Viscous effects on the Rayleigh-Taylor instability with background temperature gradient". United States. doi:10.1063/1.4959810. https://www.osti.gov/servlets/purl/1304724.
@article{osti_1304724,
title = {Viscous effects on the Rayleigh-Taylor instability with background temperature gradient},
author = {Gerashchenko, Sergiy and Livescu, Daniel},
abstractNote = {Here we studied the growth rate of the compressible Rayleigh-Taylor instability in the presence of a background temperature gradient, Θ, using a normal mode analysis. The effect of Θ variation is examined for three interface types corresponding to the combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous, and viscous-inviscid) at different Atwood numbers, At, and when at least one of the fluids' viscosity is non-zero, as a function of the Grashof number. For the general case, the resulting ordinary differential equations are solved numerically; however, dispersion relations for the growth rate are presented for several limiting cases. An analytical solution is found for the inviscid-inviscid interface and the corresponding dispersion equation for the growth rate is obtained in the limit of large Θ. For the viscous-inviscid case, a dispersion relation is derived in the incompressible limit and Θ=0. Compared to Θ=0 case, the role of Θ<0 (hotter light fluid) is destabilizing and becomes stabilizing when Θ>0 (colder light fluid). The most pronounced effect of Θ ≠ 0 is found at low At and/or at large perturbation wavelengths relative to the domain size for all interface types. On the other hand, at small perturbation wavelengths relative to the domain size, the growth rate for the Θ<0 case exceeds the infinite domain incompressible constant density result. The results are applied to two practical examples, using sets of parameters relevant to Inertial Confinement Fusion coasting stage and solar corona plumes. The role of viscosity on the growth rate reduction is discussed together with highlighting the range of wavenumbers most affected by viscosity. The viscous effects further increase in the presence of background temperature gradient, when the viscosity is temperature dependent.},
doi = {10.1063/1.4959810},
journal = {Physics of Plasmas},
number = 7,
volume = 23,
place = {United States},
year = {2016},
month = {7}
}

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