Gravitational and viscous torques acting on swimming micro-organisms orient their trajectories. The horizontal component of the swimming velocity of individuals of the many algal genera having a centre of mass displaced toward the rear of the cell is therefore in the direction g × ([dtri ] × u), where g is the acceleration due to gravity. This phenomenon, called gyrotaxis, results in the cells swimming toward downward-flowing regions of their environment. Since the cells’ density is greater than that of water, regions of high (low) cell concentration sink (rise). The horizontal component of gyrotaxis reinforces this type of buoyant convection, whilst the vertical one maintains it. Gyrotactic buoyant convection results in the spontaneous generation of descending plumes containing high cell concentration, in spatially regular concentration/convection patterns, and in the perturbation of initially well-defined flow fields. This paper presents a height- and azimuth-independent steady-state solution of the Navier-Stokes and cell conservation equations. This solution, and the growth rate of a concentration fluctuation, are shown to be governed by a parameter similar to a Rayleigh number.