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Settling-driven instability in two-component stably stratified Hele-Shaw flows

Published online by Cambridge University Press:  22 March 2018

Rafael M. Oliveira Open the ORCID record for Rafael M. Oliveira [Opens in a new window]  and
Eckart Meiburg Open the ORCID record for Eckart Meiburg [Opens in a new window]
Rafael M. Oliveira
Affiliation:
Departamento de Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ 22451-900, Brazil
Eckart Meiburg*
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the onset of instability in a stably stratified two-component fluid in a vertical Hele-Shaw cell when the unstably stratified scalar has a settling velocity. This linear stability problem is analysed on the basis of Darcy’s law, for constant-gradient base states. The settling velocity is found to trigger a novel instability mode characterized by pairs of inclined waves. For unequal diffusivities, this new settling-driven mode competes with the traditional double-diffusive mode. Below a critical value of the settling velocity, the double-diffusive elevator mode dominates, while, above this threshold, the inclined waves associated with the settling-driven instability exhibit faster growth. The analysis yields neutral stability curves and allows for the discussion of various asymptotic limits.

JFM classification

Convection: Double diffusive convection Low-Reynolds-number flows: Hele-Shaw flows Geophysical and Geological Flows: Stratified flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 843 , 25 May 2018 , R1
Copyright
© 2018 Cambridge University Press 

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