Journal of Fluid Mechanics

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

SAIKIRAN RAPAKAa1, SHIYI CHENa1a2, RAJESH J. PAWARa3, PHILIP H. STAUFFERa3 and DONGXIAO ZHANGa4

a1 Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA saikiran@jhu.edu

a2 COE & CCSE, Peking University, Beijing, China

a3 EES-6, Los Alamos National Laboratory, Los Alamos, NM 87544, USA

a4 Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA 90089, USA

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.

(Received April 16 2007)

(Revised May 20 2008)

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