Stability analysis and numerical simulation of gravitactic bioconvection in a rectangular cavity

The bioconvection of gravitactic microorganisms, through linear analysis and numerical simulation is presented. Using the basic state as initial condition for both microorganisms and streamlines, the critical Rayleigh number and the bioconvection are predicted. The dynamic microorganisms’ behavior is influenced by the initial spatial distribution. The stability of the system is dependent on the horizontal wave component that is inversely related to wavelength. The pattern length and the instability of the process are associated with the horizontal component of the wave number and the characteristic wavelength, respectively. Using complex and real eigenvalues, five unstable and three stable rolls are found respectively. The three stable rolls is the dominant pattern when varying the principal variables of this bioconvective process.