Phototactic Bioconvection in a Rotating Isotropic Porous Medium: Linear Stability Analysis

Abstract

This study investigates the linear stability of phototactic bioconvection in a rotating porous medium under collimated light, incorporating the effects of critical intensity, Darcy number, and Taylor number. Using a mathematical model and the MATLAB Bvp4c solver, the critical Rayleigh number and wavenumber for instability onset are identified. The results reveal that higher Darcy numbers enhance instability, increasing the wavelength of bioconvection patterns, while rotation exerts a stabilizing effect by limiting vertical motion and confining fluid dynamics to the horizontal plane. Additionally, an increase in critical intensity amplifies instability. Furthermore, the study explores the transition between oscillatory and stationary solutions, highlighting the role of rotational dynamics in altering instability modes. These findings provide novel insights into the interplay of phototaxis, rotation, and porous media, advancing the understanding of bioconvective systems with potential applications in environmental engineering, biophysics, and geophysical fluid dynamics.

Figures (10)

• Figure 1: Geometrical view of the porous rotating medium.
• Figure 2: Neutral curves plotted against the wavenumber for the fixed parameters $W=10$, $\chi=0.5$, $\mathbb{J}_c=0.63$, (a) $T_a=0$, (b) and $T_a=1000$ as the Darcy number $D_a$ varies.
• Figure 3: Growth rate curves are plotted against the wavenumber for the following fixed parameters $W=10$, $\chi=0.5$, $\mathbb{J}_c=0.63$, $R_a=2030$. (a) Displays growth rate curves for $T_a=0$ as the Darcy number $D_a$ varies. (b) Displays growth rate curves for $D_a=0.1$ as the Taylor number $T_a$ varies.
• Figure 4: Neutral curves plotted against the wavenumber for the fixed parameters $W=15$, $\chi=0.5$, $\mathbb{J}_c=0.68$, (a) $T_a=0$, (b) and $T_a=1000$ as the Darcy number $D_a$ varies. The oscillating branches are represented by dotted lines.
• Figure 5: Neutral curves plotted against the wavenumber for the fixed parameters $W=15$, $\chi=1.0$, $\mathbb{J}_c=0.51$, (a) $T_a=0$, (b) and $T_a=2000$ as the Darcy number $D_a$ varies. The oscillating branches are represented by dotted lines.