We studied linear and nonlinear instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media. We studied the critical Rayleigh number and traced marginal stability curves at different parameters Q, italicTa, Pr1, and Pr2. We obtained Takens‐Bogdanov and co‐dimension two bifurcation points. The Newell‐Whitehead multiple scheme was employed to derive amplitude equations at Pitchfork and Hopf bifurcation. At the onset of Pitchfork bifurcation we identified Eckhaus and Zigzag instability regions and studied Nusselt number. The system of coupled Landau Ginzburg equations were derived at the onset of Hopf bifurcation and identified secondary instability regions for fixed parameters, steady state mode shifted to standing and traveling waves as Q increases.
Linear and weakly non-linear thermohaline rotating convection in a sparsely packed porous medium with an imposed horizontal magnetic eld is studied analytically. In the linear stability analysis, the normal mode technique is employed to nd the critical Rayleigh number and it is calculated as a function of q, Ta, Q, Λ, Da, Pr 1, and Pr 2 . In order to study the secondary instabilities and heat transport by convection, the well-known equation Ginzburg-Landau equation is derived. The system of one dimensional coupled amplitude equations arederived at the onset of oscillatory convection to study the stability regions of steady state, Standing waves and Travelling waves.
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