Clustering of gyrotactic microorganisms in turbulent flows

We study the spatial distribution of gyrotactic microorganisms transported by a three-dimensional turbulent flow generated by direct numerical simulations. We find that gyrotaxis combines with turbulent fluctuations to produce small scales (multi-)fractal clustering. We explain this result by showing that gyrotactic swimming cells behave like tracers in a compressible flow. The effective compressibility is derived in the limits of fluid acceleration much larger and smaller than the gravity.