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

Journal Article · Wed Aug 02 00:00:00 EDT 2017 · Physics of Fluids

DOI:https://doi.org/10.1063/1.4996049· OSTI ID:1374329

Ghorbani, Zohreh ^[1]; Riaz, Amir ^[1]; Daniel, Don  ^[2]

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1. Univ. of Maryland, College Park, MD (United States). Dept. of Mechanical Engineering
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1374329
• Report Number(s): LA-UR-17-21307
• Journal Information: Physics of Fluids, Vol. 29, Issue 8; ISSN 1070-6631
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Thermodynamic processes
Porous media
Wave mechanics
Vector calculus
Perturbation methods