Gyrotactic clustering from turbulent acceleration

We study self-propelled particles advected by a turbulent flow as a model of microorganisms swimming in a turbulent environment. In particular, we consider (spherical) gyrotactic microorganisms, whose swimming direction results from vortical overturning and fluid acceleration. In such conditions self-propelled particles forms (multi)fractal aggregates, which can be rationalized, in some limits, in terms of an effective compressibility.