Penetrative phototactic bioconvection

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Abstract
Using the generic model of Vincent and Hill [J. Fluid Mech. 327, 343 (1996)] for phototaxis in a suspension of swimming algae, we investigate two-dimensional phototactic bioconvection in a suspension confined between a rigid bottom boundary, and stress-free top and lateral boundaries. Phototaxis denotes swimming towards (positive) or away (negative) from light. The model of Vincent and Hill also incorporates the effect of shading where microorganisms close to the light source absorb and scatter light before it reaches those further away. The system is governed by the Navier–Stokes equations for an incompressible fluid coupled with a microorganism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. Convection driven by phototactic microorganisms, which are slightly denser than water, has been investigated in a series of numerical experiments. The solutions show transition from steady state to periodic oscillations, and periodic oscillations to steady state to periodic oscillations again, as the governing parameters are varied. The mechanism driving the oscillatory solution just above the critical parameter values is explained.