Previous theoretical researchers successfully generated viscous finger patterns by assuming a randomly distributed boundary condition in their numerical models. Our objective is to identify a natural source of the randomness that underlies their success. A source of fluid flow instability is discerned by viewing fingering as a chaotic (nonlinear dynamical) phenomenon.
We begin by showing that miscible displacement models can be expressed as nonlinear generalizations of the linear convection-dispersion equation. A nonlinear dynamical analysis technique is used to study the stability of the nonlinear system. Detailed study of several ID and 2D cases illustrates the applicability of the stability analysis.