Gravity-modulated Weakly Nonlinear Oscillatory Bioconvection in a Densely Packed Porous Medium

In this paper, we investigate the effect of gravity modulation on Darcy–Brinkman bioconvection in a porous medium saturated with a Newtonian fluid containing gyrotactic microorganisms. A weakly nonlinear stability analysis is performed to examine the oscillatory mode of convection under low-amplitude modulation. Heat transport is quantified using the mean Nusselt number, evaluated through a complex Ginzburg–Landau equation (CGLE). The CGLE is derived from a solvability condition at the lowest order of the perturbation parameter. The results are presented graphically to illustrate the impact of system parameters on bioconvection. Both the Vadasz number and the modulation amplitude are found to have a significant influence on heat transfer. Conversely, an increase in the modified bioconvection Rayleigh–Darcy number and cell eccentricity leads to a decrease in heat transfer. It is also found that the convective transport process is more strongly influenced by the irregular shapes of microorganisms than by spherical-shaped ones. Gravity modulation is found to be effective in controlling heat transfer, highlighting the role of external modulation in regulating transport processes within the system.