Instabilities in variable density flows: Stability and sensitivity analyses for homogeneous and heterogeneous media

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Abstract
This study improves our understanding of instability phenomena that may accompany the transport of dense plumes of dissolved contaminants. One major objective is to test how well analytic stability theory developed by List [1965] applies to the transport of dense plumes in both homogeneous and heterogeneous media. The data to test the prediction come from numerical model experiments in which instability growth is generated by perturbing the interface between fluids of differing density. Stability criteria, as determined by the transverse Rayleigh number, the ratio of transverse to longitudinal Rayleigh numbers, and the nondimensional wave number, compare very well with results observed in the numerical experiments for isotropic media. Comparisons involving correlated random fields were much less successful because plume stability is determined on a local basis as a function of the changing permeability field. Instabilities tend to dissipate in zones of lower permeability and grow in zones of higher permeability. Another objective of the study is to determine the factors that contribute to stability and instability in homogeneous and heterogeneous systems. Sensitivity analyses using a transport model within the framework of List's stability theory show that stability is promoted by low medium permeability, small density differences, and significant dispersion. In heterogeneous media, stability is promoted by increased correlation length scales and increased log permeability variance. Furthermore, the simulations illustrate the intimate relationship that exists between instability growth and decay and the heterogeneous nature of the permeability field. Thus stability criteria that do not incorporate characteristics of the permeability field will not be suitable for natural or field‐scale porous media.

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