3D Gyrotactic Bioconvection Simulations

We introduce a new code for solving the continuum equations for gyrotactic bioconvection [1] in \emph{three spatial dimensions} to study pattern formation in suspensions of swimming micro-organisms such as the single-celled alga, \emph{Clamydomonas nivalis}. The governing equations consist of Navier--Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved efficiently using a semi-implicit second-order accurate conservative finite-difference method. The structure and stability of a three-dimensional plume in a deep chamber with stress-free sidewalls are investigated. The solutions are compared with previous studies on two-dimensional [2] and axisymmetric bioconvection [3]. The evolution of the plumes is rich and varied, with quasi-steady states giving way to varicose and then meandering modes. 1. Pedley, T.J., Hill, N.A. \& Kessler, J.O., 1988. The growth of bioconvection patterns in a uniform suspension of gyrotactic microorganisms. J.~Fluid Mech.~\textbf{195}, 223---238. 2. Ghorai, S. \& Hill, N.A., 2000. Wavelengths of gyrotactic plumes in bioconvection. Bull.~Math.~Biol.~\textbf{62}, 429---450. 3. Ghorai, S. \& Hill, N.A., 2002. Axisymmetric bioconvection in a cylinder. J.~Theor.~Biol.~\textbf{219}, 137---152.