Abstract:
The influence of dispersion or equivalently of the Péclet number (Pe) on miscible viscous fingering in
a homogeneous porous medium is examined. The linear optimal perturbations maximizing finite-time energy gain
is demonstrated with the help of the propagator matrix approach based non-modal analysis (NMA). We show that
onset of instability is a monotonically decreasing function of Pe and the onset time determined by NMA emulates
the non-linear simulations. Our investigations suggest that perturbations will grow algebraically at early times,
contrary to the well-known exponential growth determined from the quasi-steady eigenvalues. One of the overarching objective of the present work is to determine whether there are alternative mechanisms which can describe
the mathematical understanding of the spectrum of the time-dependent stability matrix. Good agreement between
the NMA and non-linear simulations is observed. It is shown that within the framework of L2-norm, the non-normal
stability matrix can be symmetrizable by a similarity transformation and thereby we show that the non-normality
of the linearized operator is norm dependent. A framework is thus presented to analyze the exchange of stability
which can be determined from the eigenmodes.
