Effect of scattered/diffuse flux on the phototactic bioconvection in the absence of collimated flux

Abstract

The main objective of this paper is to investigate the impact of diffuse/scattered flux in the absence of collimated flux on the stability of an isotropic scattering algal suspension. The linear stability analysis predicts an unstable mode of disturbance shifts from a non-oscillatory (an overstable) to an overstable (a non-oscillatory) state at the variation of diffuse flux for fixed parameters at the bioconvective instability. However, overstable solutions are observed only at the higher cell swimming speed and a higher extinction coefficient. The critical Rayleigh number increases as the magnitude of diffuse flux intensifies. This indicates that a suspension illuminated by higher levels of diffuse flux is more stable. Furthermore, the lower (higher) swimming speed enhances (diminishes) the suspension's stability, especially in low (high) light conditions. Also, the horizontal component of swimming orientation becomes more influential with a higher level of diffuse flux, particularly at smaller pattern wavelengths, resulting in behavior akin to gyrotaxis in certain instances.