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

Gerashchenko, Sergiy; Livescu, Daniel

doi:10.1063/1.4959810

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

Journal Article · Thu Jul 28 00:00:00 EDT 2016 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4959810· OSTI ID:1304724

Gerashchenko, Sergiy ^[1]; Livescu, Daniel ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: LDRD; USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1304724

Alternate ID(s):: OSTI ID: 1421260
OSTI ID: 22599963

Report Number(s):: LA-UR--16-22586

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 7 Vol. 23; ISSN 1070-664X; ISSN 1089-7674

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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