A General Approach to the Linear Stability Analysis of Miscible Viscous Fingering in Porous Media

  • Tapan Kumar HotaEmail author
  • Satyajit Pramanik
  • Manoranjan Mishra
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


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.


Linear Stability Analysis Numerical Range Stability Matrix Propagator Matrix Miscible Fluid 
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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.


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Tapan Kumar Hota
    • 1
    Email author
  • Satyajit Pramanik
    • 1
  • Manoranjan Mishra
    • 1
  1. 1.Department of MathematicsIndian Institute of Technology RoparPunjabIndia

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