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

TL;DR

This paper analyzes how rotation, porous media properties, and light intensity influence the stability of phototactic bioconvection patterns, revealing stabilizing and destabilizing effects through linear stability analysis.

Contribution

It introduces a mathematical model examining the combined effects of rotation, porosity, and light on bioconvection stability, providing new insights into pattern formation in such systems.

Findings

Higher Darcy numbers increase instability and pattern wavelength.

Rotation stabilizes the system by restricting vertical motion.

Critical light intensity amplifies bioconvection instability.

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.