A Note on Algae Population Dynamics

Abstract

All three authors had the pleasure of extensive technical interactions with John Blake during his career in the UK, USA and Australia and benefited both professionally and personally from his friendship. John’s work in developing fundamental mathematical solutions for Stokes’ flows and his application of those mathematical tools to analyses of micro-organism locomotion led to special new insights into that world of small-scale swimming. This special issue devoted to John’s memory seems an appropriate occasion to present another fluid mechanical challenge associated with micro-organisms, namely the dynamics of algae blooms. Though it is a special reduced-order model that is of limited practical value, John would have particularly enjoyed the analytical solution to the dynamics of algae that was presented by Rutherford Aris (1997) in a somewhat eccentric paper. We revisit that solution in this paper and present an extension to Aris’ solution that includes sedimentation of the algae. We think that John would have enjoyed this solution and would, in all likelihood, have been able to expand upon it to include other features such as micro-organism buoyancy variations (see, for example, Kromkamp et al. 1990, Belov and Giles 1997, Brookes and Ganf 2001), the death of algae (see, for example, Serizawa et al. 2008a, Reynolds 1984), the swimming of algae (see, for example, Pedley 2016), and other relevant hydrodynamic matters.