Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids
Abstract
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. ρi denotes the density, μi is the viscosity, and Ri 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], density ratio [Formula: see text], spherical harmonic mode n, [Formula: see text], [Formula: see text], and the dimensionless growth rate [Formula: see text], where σ is the exponential growth rate. We show that the boundedness provided by the outer spherical shell has a strong influence on the instability behavior, which is reflected not only in the modulation of the growth rate but also in the selection of the most unstable modes that are physically possible. This outer boundary effect is quantified by the relative magnitude of the radius ratio H. We find that when H is close to unity, lower ordermore »
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Boston Univ., MA (United States)
- 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); National Science Foundation (NSF)
- OSTI Identifier:
- 1871484
- Report Number(s):
- LA-UR-22-20717
Journal ID: ISSN 2158-3226; TRN: US2306758
- Grant/Contract Number:
- 89233218CNA000001; DMS-1748883
- Resource Type:
- Accepted Manuscript
- Journal Name:
- AIP Advances
- Additional Journal Information:
- Journal Volume: 12; Journal Issue: 4; Journal ID: ISSN 2158-3226
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; linear stability analysis; fluid instabilities; viscosity; viscous liquid; flow instabilities
Citation Formats
Oren, Garrett H., and Terrones, Guillermo. Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids. United States: N. p., 2022.
Web. doi:10.1063/5.0090277.
Oren, Garrett H., & Terrones, Guillermo. Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids. United States. https://doi.org/10.1063/5.0090277
Oren, Garrett H., and Terrones, Guillermo. Fri .
"Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids". United States. https://doi.org/10.1063/5.0090277. https://www.osti.gov/servlets/purl/1871484.
@article{osti_1871484,
title = {Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids},
author = {Oren, Garrett H. and Terrones, Guillermo},
abstractNote = {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. ρi denotes the density, μi is the viscosity, and Ri 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], density ratio [Formula: see text], spherical harmonic mode n, [Formula: see text], [Formula: see text], and the dimensionless growth rate [Formula: see text], where σ is the exponential growth rate. We show that the boundedness provided by the outer spherical shell has a strong influence on the instability behavior, which is reflected not only in the modulation of the growth rate but also in the selection of the most unstable modes that are physically possible. This outer boundary effect is quantified by the relative magnitude of the radius ratio H. We find that when H is close to unity, lower order harmonics are excluded from becoming the most unstable within a vast region of the parameter space. In other words, the effect of H has precedence over the other controlling parameters d, B, and a wide range of s in establishing what the lowest most unstable mode can be. When H ~ 1, low order harmonics can become the most unstable only for s >> 1. However, in the limit when s → ∞, we show that the most unstable mode is n = 1 and derive the dispersion relation in this limit. The exclusion of most unstable low order harmonics caused by a finite outer boundary is not realized when the outer boundary extends beyond a certain threshold length-scale in which case all modes are equally possible depending on the value of B.},
doi = {10.1063/5.0090277},
journal = {AIP Advances},
number = 4,
volume = 12,
place = {United States},
year = {Fri Apr 01 00:00:00 EDT 2022},
month = {Fri Apr 01 00:00:00 EDT 2022}
}
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