Hydrodynamically induced aggregation of two dimensional oriented active particles

We investigate a system of co-oriented active particles interacting only via hydrodynamic and steric interactions in a two-dimensional fluid. We offer a new method of calculating the flow created by any active particle in such a fluid, focusing on the dynamics of flow fields with a high-order spatial decay, which we analyze using a geometric Hamiltonian. We show that when the particles are oriented and the flow has a single, odd power decay, such systems lead to stable, fractal-like aggregation, with the only exception being the force dipole. We discuss how our results can easily be generalized to more complicated force distributions and to other effective two-dimensional systems.