Inverse cascade and energy transfer in forced low-Reynolds number two-dimensional turbulence

Using numerical simulations of the forced two-dimensional Navier-Stokes equation, it is shown that the amount of energy transferred to large scales is related to the Reynolds number in a unique fashion. It is also observed that the critical value of the initial Reynolds number for the onset of an inverse cascade is lowered as the scale of the forcing approaches the size of the system, or in the presence of anisotropy. This study is motivated by recent experiments with bacterial colonies, and their description in terms of a hydrodynamic model.