Instability Analysis of Gyrotactic Microorganisms: A Combined Effect of High-Frequency Vertical Vibration and Porous Media

A linear stability analysis is carried out to predict the instability analysis in a dilute suspension of gyrotactic microorganisms in horizontal fluid-saturated porous layer influenced by high-frequency vertical vibration. The governing equations, describing the mean flow, are the time-averaged Boussinesq equations and the analytical solution of the problem has been obtained using Galerkin method. A secular relation involving bioconvection Rayleigh number and its vibrational analogs and other parameters have been established. The graphical interpretations for dependence of bioconvection Rayleigh-Darcy number and corresponding wave number, on gyrotactic number and bioconvection P,clet number in the presence of vibration are utilized to understand the problem.