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\begin{document}

\title{A theoretical modeling framework for motile and colonial harmful algae}



\author[1]{Jackie Taylor}%
\author[1]{M. Carme Calderer}%
\author[1]{Miki Hondzo}%
\author[1]{Vaughan Voller}%
\affil[1]{University of Minnesota Twin Cities}%


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  \date{May 25, 2024}


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\begin{abstract}
1. Harmful algal blooms are increasing in both severity and frequency
across the globe. Many bloom-forming species are capable of vertical
motility and colony formation. The cyanobacterium \emph{Microcystis
aeruginosa} is a common example of such a species, yet current models
poorly predict vertical distributions of \emph{M. aeruginosa}. 2. To
couple the hydrodynamics, buoyancy, and the colony dynamics of
\emph{Microcystis}, we present a system of one-dimensional
advection-diffusion-aggregation equations with Smoluchowski aggregation
terms. 3. Results indicate Smoluchowski aggregation accurately describes
the colony dynamics of \emph{M. aeruginosa}. Further, transport dynamics
are strongly dependent on colony size, and aggregation processes are
highly sensitive to algal concentration and wind-induced mixing. Both of
these findings have direct consequences to harmful algal bloom
formation. 4. While the theoretical framework outlined in this
manuscript was derived for \emph{M. aeruginosa}, both motility and
colony formation are common among bloom-forming algae. As such, this
coupling of vertical transport and colony dynamics is a useful step for
improving forecasts of surface harmful algal blooms.%
\end{abstract}%



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