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Title: Convective mixing in vertically-layered porous media: The linear regime and the onset of convection

Abstract

In this paper, we study the effect of permeability heterogeneity on the stability of gravitationally unstable, transient, diffusive boundary layers in porous media. Permeability is taken to vary periodically in the horizontal plane normal to the direction of gravity. In contrast to the situation for vertical permeability variation, the horizontal perturbation structures are multimodal. We therefore use a two-dimensional quasi-steady eigenvalue analysis as well as a complementary initial value problem to investigate the stability behavior in the linear regime, until the onset of convection. We find that thick permeability layers enhance instability compared with thin layers when heterogeneity is increased. On the contrary, for thin layers the instability is weakened progressively with increasing heterogeneity to the extent that the corresponding homogeneous case is more unstable. For high levels of heterogeneity, we find that a small change in the permeability field results in large variations in the onset time of convection, similar to the instability event in the linear regime. However, this trend does not persist unconditionally because of the reorientation of vorticity pairs due to the interaction of evolving perturbation structures with heterogeneity. Consequently, an earlier onset of instability does not necessarily imply an earlier onset of convection. A resonantmore » amplification of instability is observed within the linear regime when the dominant perturbation mode is equal to half the wavenumber of permeability variation. On the other hand, a substantial damping occurs when the perturbation mode is equal to the harmonic and sub-harmonic components of the permeability wavenumber. Finally, the phenomenon of such harmonic interactions influences both the onset of instability as well as the onset of convection.« less

Authors:
 [1];  [1]; ORCiD logo [2]
  1. Univ. of Maryland, College Park, MD (United States). Dept. of Mechanical Engineering
  2. 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
OSTI Identifier:
1374329
Report Number(s):
LA-UR-17-21307
Journal ID: ISSN 1070-6631
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 29; Journal Issue: 8; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Thermodynamic processes; Porous media; Wave mechanics; Vector calculus; Perturbation methods

Citation Formats

Ghorbani, Zohreh, Riaz, Amir, and Daniel, Don. Convective mixing in vertically-layered porous media: The linear regime and the onset of convection. United States: N. p., 2017. Web. doi:10.1063/1.4996049.
Ghorbani, Zohreh, Riaz, Amir, & Daniel, Don. Convective mixing in vertically-layered porous media: The linear regime and the onset of convection. United States. doi:10.1063/1.4996049.
Ghorbani, Zohreh, Riaz, Amir, and Daniel, Don. Wed . "Convective mixing in vertically-layered porous media: The linear regime and the onset of convection". United States. doi:10.1063/1.4996049. https://www.osti.gov/servlets/purl/1374329.
@article{osti_1374329,
title = {Convective mixing in vertically-layered porous media: The linear regime and the onset of convection},
author = {Ghorbani, Zohreh and Riaz, Amir and Daniel, Don},
abstractNote = {In this paper, we study the effect of permeability heterogeneity on the stability of gravitationally unstable, transient, diffusive boundary layers in porous media. Permeability is taken to vary periodically in the horizontal plane normal to the direction of gravity. In contrast to the situation for vertical permeability variation, the horizontal perturbation structures are multimodal. We therefore use a two-dimensional quasi-steady eigenvalue analysis as well as a complementary initial value problem to investigate the stability behavior in the linear regime, until the onset of convection. We find that thick permeability layers enhance instability compared with thin layers when heterogeneity is increased. On the contrary, for thin layers the instability is weakened progressively with increasing heterogeneity to the extent that the corresponding homogeneous case is more unstable. For high levels of heterogeneity, we find that a small change in the permeability field results in large variations in the onset time of convection, similar to the instability event in the linear regime. However, this trend does not persist unconditionally because of the reorientation of vorticity pairs due to the interaction of evolving perturbation structures with heterogeneity. Consequently, an earlier onset of instability does not necessarily imply an earlier onset of convection. A resonant amplification of instability is observed within the linear regime when the dominant perturbation mode is equal to half the wavenumber of permeability variation. On the other hand, a substantial damping occurs when the perturbation mode is equal to the harmonic and sub-harmonic components of the permeability wavenumber. Finally, the phenomenon of such harmonic interactions influences both the onset of instability as well as the onset of convection.},
doi = {10.1063/1.4996049},
journal = {Physics of Fluids},
number = 8,
volume = 29,
place = {United States},
year = {2017},
month = {8}
}

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