Phototactic bioconvection with the combined effect of diffuse and oblique collimated flux on an algal suspension

Abstract

The objective of this paper is mainly to investigate the combined effect of diffuse and oblique collimated flux on the onset of phototactic bioconvection. The onset of phototactic bioconvection is examined numerically in a finite-depth algal suspension via linear stability theory. At bioconvective instability, an unstable mode of disturbance shifts from a non-oscillatory (an overstable) to an overstable (a non-oscillatory) state at the variation in oblique incidence angle/diffuse flux for fixed parameters. If n convection cells are piled up on another vertically, then the bioconvective solution of the linear stability problem is called mode n. For some parameters, mode 2 instability is switched to mode 1 instability as the angle of incidence/diffuse flux varies. In addition, diffuse flux (or oblique collimated flux) enhances algal suspension stability (or instability).