NDLI: Numerical simulation of the Rayleigh–Taylor instability of a miscible slice in a porous medium

Content Provider	Springer Nature Link
Author	Kim, Min Chan
Copyright Year	2015
Abstract	Convective instability in miscible slices is important in understanding the contaminant spreading in groundwater and sample dispersion in a chromatographic column. In the present study, the temporal evolution of the Rayleigh–Taylor instability of a miscible high-density slice in a porous medium is analyzed theoretically using nonlinear numerical simulations. Nonlinear governing equations are derived and solved with the Fourier spectral method. To connect the previous linear stability analysis and the present nonlinear simulation, the most unstable disturbance which was identified in the linear analysis is employed as an initial condition for the nonlinear study. In contrast to the fingering between two semi-infinite regions, the nonlinear fingering of a finite slice is influenced by the depth of the high-density region. The present nonlinear analysis shows that there exists a critical depth below which the system is linearly unstable, but nonlinear phenomena cannot be expected. The nonlinear simulation results show that nonlinear competition yields a series of cells of slightly different widths and amplitudes. Also, it is found that the upper stable region hinders the development of instability motions and stabilizes the system.
Ending Page	94
Page Count	14
Starting Page	81
File Format	PDF
ISSN	00220833
e-ISSN	15732703
Journal	Journal of Engineering Mathematics
Issue Number	1
Volume Number	100
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-12-26
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Analysis Nonlinear simulation Mechanics Miscible slice Rayleigh–Taylor instability Applications of Mathematics Mathematical Modeling and Industrial Mathematics Fourier spectral method Convection Nonlinear effects
Content Type	Text
Resource Type	Article
Subject	Mathematics Engineering

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