Dual cascade of two-dimensional turbulence arising from collective swimming

Abstract

Abstract Using high-resolution numerical simulations, supported by shallow-water tank experiments, we show that the collective swimming of fish at finite Reynolds numbers can spontaneously generate two-dimensional (2D) turbulence. The resulting flow exhibits a robust dual-cascade structure, with an inverse energy cascade transferring energy from intermediate to large scales and a direct enstrophy cascade transporting vorticity towards smaller scales. The interscale energy transfer is driven by broadband, spatially heterogeneous forcing arising from the undulatory motion of individual swimmers, whose localized and intermittent activity nevertheless sustains coherent large-scale structures. Furthermore, the organization of the school strongly influences the cascade dynamics: disordered swarming promotes vortex merging and a pronounced inverse energy cascade, whereas coordinated milling constrains the development of large-scale vortex mergers. These findings reveal a previously unrecognized form of biologically driven 2D turbulence and suggest that collective animal behaviour can generate turbulent flows consistent with classical theoretical predictions, most clearly in the swarming state, even under complex, realistic conditions.