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Stability of triple-diffusive convection in a vertical porous layer

Published online by Cambridge University Press:  29 July 2024

B.M. Shankar Open the ORCID record for B.M. Shankar [Opens in a new window]  and
I.S. Shivakumara Open the ORCID record for I.S. Shivakumara [Opens in a new window]
B.M. Shankar*
Affiliation:
Department of Mathematics, PES University, Bangalore 560 085, India
I.S. Shivakumara
Affiliation:
Department of Mathematics, Bangalore University, Bangalore 560 056, India
*
†Email address for correspondence: bmshankar@pes.edu
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Abstract

The classical Gill's problem, focusing on the stability of thermal buoyancy-driven convection in a vertical porous slab with impermeable isothermal boundaries, is studied from a different perspective by considering a triple-diffusive fluid system having different molecular diffusivities. The assessment of stability/instability of the basic flow entails a numerical solution of the governing equations for the disturbances as Gill's proof of linear stability falls short. The updated problem formulation is found to introduce instability in contrast to Gill's original set-up. A systematic examination of neutral stability curves is undertaken for KCl–NaCl–sucrose and heat–KCl–sucrose aqueous systems which are found to exhibit an anomalous behaviour on the stability of base flow. It is found that, in some cases, the KCl–NaCl–sucrose system necessitates the requirement of four critical values of the Darcy–Rayleigh number to specify the linear stability criteria ascribed to the existence of two isolated neutral curves positioned one below the other. Conversely, the heat–KCl–sucrose system demands only two critical values of the Darcy–Rayleigh number to decide the stability of the system. The stability boundaries are presented and the emergence of a travelling-wave mode supported back and forth with stationary modes is observed due to the introduction of a third diffusing component. In addition, some intriguing outcomes not recognized hitherto for double-diffusive fluid systems are manifested.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 989 , 25 June 2024 , A8
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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