Viscous effects on the RayleighTaylor instability with background temperature gradient
Abstract
The growth rate of the compressible RayleighTaylor instability is studied 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 (inviscidinviscid, viscousviscous, and viscousinviscid) at different Atwood numbers, At, and when at least one of the fluids' viscosity is nonzero, 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 inviscidinviscid interface and the corresponding dispersion equation for the growth rate is obtained in the limit of large Θ. For the viscousinviscid 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.
 Publication:

Physics of Plasmas
 Pub Date:
 July 2016
 DOI:
 10.1063/1.4959810
 arXiv:
 arXiv:1605.00022
 Bibcode:
 2016PhPl...23g2121G
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 doi:10.1063/1.4959810