A General Approach to the Linear Stability Analysis of Miscible Viscous Fingering in Porous Media
- 411 Downloads
We analyse the linear growth of the viscous fingering instability for miscible, non-reactive, neutral buoyant fluids using the non-modal analysis (NMA). The onset of instability is obscured due to the continually changing base state, and the normal mode analysis is not applicable to the non-autonomous linearized perturbed equations. Commonly used techniques such as frozen time method or amplification theory approach with random initial condition using transient amplifications yield substantially different results for the threshold of instability. We present the classical non-modal methods in the short-time limit using singular value decomposition of the propagator matrix. Using the non-modal approach we characterize the existence of a transition region between a domain exhibiting strong convection and a domain where initial perturbations are damped due to diffusion. Further, at the early times the algebraic growth of perturbations is possible which suggest that NMA could play an important role in describing the onset of instability in the physical phenomenon involving VF.
KeywordsLinear Stability Analysis Numerical Range Stability Matrix Propagator Matrix Miscible Fluid
The authors would like to thank the three reviewers for their helpful critics and suggestions. This helped us in improving the standard of the manuscript. S.P. gratefully acknowledges the National Board for Higher Mathematics, Department of Atomic Energy, Government of India for the financial support through a Ph.D. fellowship.
- 15.Schmid PJ, Henningson DS (2001) Stability and transition in shear flows. Applied mathematics science, vol 142. Springer, New YorkGoogle Scholar