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Onset of natural convection in layered aquifers

Published online by Cambridge University Press:  23 February 2015

Don Daniel
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
Amir Riaz*
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
Hamdi A. Tchelepi
Affiliation:
Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA
*
Email address for correspondence: ariaz@umd.edu

Abstract

The stability of gravitationally unstable, transient boundary layers in heterogeneous saline aquifers is examined with respect to the onset of natural convection. Permeability is assumed to vary periodically across the thickness of the aquifer. We study the interaction between permeability variation and concentration perturbations within the boundary layer. We observe that the instability decreases with an increase in the permeability variance if the boundary layer thickness is large compared with the permeability wavelength. On the other hand, when the boundary layer thickness is smaller than the permeability wavelength, the behaviour of instability as a function of variance depends on the phase of permeability variation. Such behaviours are shown to result from the interaction of two modes of vorticity production related to the coupling of concentration and velocity perturbations with the magnitude and gradient of permeability variation, respectively. We show that these two modes of vorticity production, when coupled with the transient nature of the boundary layer, determine the evolutionary paths followed by the most amplified perturbations that trigger the onset of convection. When the permeability variance is large, we find that small changes in the permeability field can lead to large changes in the onset times for convection.

Type
Papers
Copyright
© 2015 Cambridge University Press 

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