  This article explores how a rigid top surface with diffuse and oblique
collimated irradiation affect isotropic scattering algal suspensions. When the
fluid flow becomes zero, the suspension reaches a steady (basic) state where
up-and-down swimming occurs due to interplay of phototaxis and diffusion. For
purely scattering suspensions, a bimodal steady state occurs due to scattering,
which reverts to a unimodal steady state as the angle of incidence increases
with fixed other governing parameters. To check the linear stability of the
suspension, a small perturbation to the basic state are considered and the
perturbed equations are solved by using the Newton-Raphson-Kantorovich (NRK)
iterative method. The linear stability of the same suspension predicts both
stable and oscillatory nature of disturbance for specific parameter ranges. A
rigid top surface, as well as diffuse and oblique collimated irradiation, make
the suspension more stable.
