  Shear flow significantly affects the transport of swimming algae in
suspension. For example, viscous and gravitational torques bias bottom-heavy
cells to swim towards regions of downwelling fluid (gyrotaxis). It is necessary
to understand how such biases affect algal dispersion in natural and industrial
flows, especially in view of growing interest in algal photobioreactors.
Motivated by this, we here study the dispersion of gyrotactic algae in laminar
and turbulent channel flows using direct numerical simulation (DNS) and the
analytical swimming dispersion theory of Bees and Croze (2010). Time-resolved
dispersion measures are evaluated as functions of the Peclet and Reynolds
numbers in upwelling and downwelling flows. For laminar flows, DNS results are
compared with theory using competing descriptions of biased swimming cells in
shear flow. Excellent agreement is found for predictions that employ
generalized-Taylor-dispersion. The results highlight peculiarities of
gyrotactic swimmer dispersion relative to passive tracers. In laminar
downwelling flow the cell distribution drifts in excess of the mean flow,
increasing in magnitude with Peclet number. The cell effective axial
diffusivity increases and decreases with Peclet number (for tracers it merely
increases). In turbulent flows, gyrotactic effects are weaker, but discernable
and manifested as non-zero drift. These results should significantly impact
photobioreactor design.
