Clustering of gyrotactic microorganisms in turbulent flows

We study the spatial distribution of gyrotactic microorganisms swimming in a three-dimensional turbulent flow by means of direct numerical simulations. We find that gyrotaxis combines with turbulent fluctuations to produce small scales patchiness with fractal clustering. We explain our observations by showing that gyrotactic swimming cells behave like tracers transported by an effective compressible flow. We derive an explicit expression for the compressibility in the limit of fluid acceleration much smaller than gravity.