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

Journal Article · Fri May 01 00:00:00 EDT 2015 · Physics of Fluids

DOI:https://doi.org/10.1063/1.4921648· OSTI ID:1735910

Terrones, Guillermo  ^[1]; Carrara, Mark D.  ^[1]

---

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

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 local radial acceleration at the interface, and the density and viscosity of the denser overlying fluid, respectively). While the mathematical formulation here is general, this paper focuses on instability that arises at a spherical viscous fluid/vacuum interface as there is a great deal to be learned from the effects of one-fluid viscosity and sphericity alone. To quantify and understand the effect that curvature and radial accelerationhave on the Rayleigh-Taylor instability, a comparison of the growth rates, under homologous driving conditions, between the planar and spherical interfaces is performed. The derived dispersion relation for the planar interface accounts for an underlying finite fluid region of thickness L and normal acceleration α_R. Under certain conditions, the development of the most-unstable modes at a spherical interface can take place via the superposition of two adjacent spherical harmonics Y_n and Y_n+1. This bimodality in the evolution of disturbances in the linear regime does not have a counterpart in the planar configuration where the most-unstable modes are associated with a unique wave number.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Office of Science (SC). Basic Energy Sciences (BES); USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001; AC52-06NA25396
• OSTI ID: 1735910
• Alternate ID(s): OSTI ID: 1238594
• Report Number(s): LA-UR-20-24207; LA-UR-13-20570; TRN: US2205267
• Journal Information: Physics of Fluids, Vol. 27, Issue 5; ISSN 1070-6631
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
viscosity
perturbation theory
real analysis
flow instabilities
dispersion function
covariance and correlation
fluid mechanics
viscous liquid
Newtonian fluids
linear stability analysis