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Non-modal growth of perturbations in density-driven convection in porous media

Published online by Cambridge University Press:  31 July 2008

SAIKIRAN RAPAKA ,
SHIYI CHEN ,
RAJESH J. PAWAR ,
PHILIP H. STAUFFER  and
DONGXIAO ZHANG
SAIKIRAN RAPAKA
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USAsaikiran@jhu.edu
SHIYI CHEN
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USAsaikiran@jhu.edu COE & CCSE, Peking University, Beijing, China
RAJESH J. PAWAR
Affiliation:
EES-6, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
PHILIP H. STAUFFER
Affiliation:
EES-6, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
DONGXIAO ZHANG
Affiliation:
Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA 90089, USA
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Abstract

In the context of geologic sequestration of carbon dioxide in saline aquifers, much interest has been focused on the process of density-driven convection resulting from dissolution of CO2 in brine in the underlying medium. Recent investigations have studied the time and length scales characteristic of the onset of convection based on the framework of linear stability theory. It is well known that the non-autonomous nature of the resulting matrix does not allow a normal mode analysis and previous researchers have either used a quasi-static approximation or solved the initial-value problem with arbitrary initial conditions. In this manuscript, we describe and use the recently developed non-modal stability theory to compute maximum amplifications possible, optimized over all possible initial perturbations. Non-modal stability theory also provides us with the structure of the most-amplified (or optimal) perturbations. We also present the details of three-dimensional spectral calculations of the governing equations. The results of the amplifications predicted by non-modal theory compare well to those obtained from the spectral calculations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 609 , 25 August 2008 , pp. 285 - 303
Copyright
Copyright © Cambridge University Press 2008

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