Please use this identifier to cite or link to this item: http://dspace.iitrpr.ac.in:8080/xmlui/handle/123456789/1531
Title: Transient growth and symmetrizability in rectilinear miscible viscous fingering
Authors: Hota, T.K.
Mishra, M.
Keywords: Dispersion
Non-modal analysis
Viscous fingering
Issue Date: 13-Mar-2020
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.
URI: http://localhost:8080/xmlui/handle/123456789/1531
Appears in Collections:Year-2020

Files in This Item:
File Description SizeFormat 
Full Text.pdf1.27 MBAdobe PDFView/Open    Request a copy


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.