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The effect of the rigid top surface on the onset of phototactic bioconvectionis investigated using linear stability theory for a suspension offorward-scattering phototactic algae in this article. The suspension isuniformly illuminated by both diffuse and oblique collimated flux. The natureof disturbance of bio-convective instability transits from a stationary(overstable) to an overstable (stationary) state as the forward scatteringcoefficient varies under fixed parameters. In presence of rigid top surface,the suspension becomes more stable as the forward scattering coefficientincreases.

Effect of forward scattering and rigid top surface on the onset of  phototactic bioconvection in an algal suspension illuminated by both oblique  collimated and diffuse irradiation