Phototaxis denotes swimming towards (positive) or away (negative) from light. The suspension containing phototactic algae is illuminated by both the diffuse and collimated solar radiation. The algae absorb the incident light and scatter it. We use the phototaxis model of Ghorai et al. [“Bioconvection in a suspension of isotropically scattering phototactic algae,” Phys. Fluids 22, 071901 (2010)] and investigate the onset of bioconvection with particular emphasis on the effects of diffuse irradiation. The basic equilibrium state of the bioconvective governing system is defined by assuming that the bulk velocity of the fluid to be zero and the up and down swimming, caused by the positive and negative phototaxis, is balanced with the diffusion. For some values of the parameters, the bimodal steady-state profile transits to a unimodal equilibrium state as the diffuse irradiation is increased. For a small scattering albedo, at the onset of bioconvective instability, this model differs significantly from the up-swimming model of Vincent and Hill [“Bioconvection in a suspension of phototactic algae,” J. Fluid Mech. 327, 343 (1996)], even for small wavelengths. Furthermore, the solutions show a transition of the most unstable mode from the stationary to oscillatory state, and then back to the stationary state again, as the governing parameters are varied. A significant stabilizing effect on suspension has also been observed due to the effects of diffuse irradiation. The effect of the diffuse irradiation on a dominant bioconvection pattern wavelength at instability is also qualitatively in good agreement with the bioconvection experiments.

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