Ejected Fungal Spores, and Solutions to the Moderate Reynolds number Navier Stokes Equation

Michael Brenner
Harvard U

ABSTRACT:

Coprophilic fungi must eject their spores long distance in order for
the species to survive. For that reason it has been suggested that the
shapes of the spores have been optimized to minimize their drag. We
present this argument, and present an analysis of the shapes of objects
that minimize their fluid drag as a function of Reynolds number (in the
relevant range form 1-100). We compare these shapes with those
collected from a family tree of fungi that forcibly eject spores. The
optimal shapes exhibit a surprising feature: they are very nearly
fore-aft symmetric, despite the fact that the flow field around them is
very asymmetric. We use this observation as a basis for constructing a
surprisingly accurate linear approximation to steady flows of the
Navier Stokes equations that works at least up to Reynolds number of
order 100.