Effect of Variable Gravity on Linear and Nonlinear Stability of Double Diffusive Hadley Flow in Porous Media

Matta, A and P A, Lakshmi Narayana (2016) Effect of Variable Gravity on Linear and Nonlinear Stability of Double Diffusive Hadley Flow in Porous Media. Journal of Porous Media, 19 (4). pp. 287-301. ISSN 1091-028X

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Abstract

The present study analyzes the influence of variable gravity on the mechanism of instability of the double diffusive Hadley convection in a horizontal porous layer by applying linear and nonlinear stability analysis. This instability is analyzed using three-dimensional normal modes in the linear theory and the nonlinear theory using energy approach. The vertical thermal Rayleigh number is treated as the eigenvalue. The system that constitutes the eigenvalue problem is solved by applying Shooting and Runga−Kutta methods for various modes of instability. The detailed analysis is carried out for both the linear and nonlinear cases. The stability results are graphically presented, and it is notified that the flow undergoes the influence of gravity parameter along with other flow-governing parameters. This study brings out the drawbacks of linear stability theory over energy stability theory by showing the possible occurrence of subcritical instabilities in the flow parameter space.

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