Localised inter-scale energy cascades in free-surface turbulence

The energy of fluid turbulence is transported, on average, to smaller and larger scales in three-dimensional and two-dimensional flows, respectively. The motion along the flat free surface of a turbulent liquid shares similarities with both classes of flows, therefore the direction of the energy cascade along it is ambiguous. We show experimentally that the process is linked to the local divergence of the surface velocity field: expansive motions, associated with flow upwelling towards the surface, transfer energy to larger scales, while compressive motions, associated with fluid plunging into the bulk, do the opposite. The net inter-scale energy flux is therefore vanishingly small, in stark contrast with homogeneous turbulence in both two- and three-dimensional systems. Moreover, we find that rare and intense compressive/expansive events are chiefly responsible for the instantaneous inter-scale fluxes, which are much stronger than their counterparts at depth.