Percolating transition from weak to strong turbulence in wind-induced water surface waves

Abstract

Recent studies in hydrodynamic flows and nonlinear plasma waves have demonstrated the turbulent transitions from ordered laminar flows and ordered plane waves, respectively, with the formation of a large percolating turbulent cluster, after the sporadic emergence and decay of turbulent puffs in the spatiotemporal space. These transitions follow the similar order–disorder transition scenario in nonequilibrium extended systems, governed by percolation theory. Here, we experimentally investigate the unexplored issue of whether a similar transition scenario can be extended to wind-driven water waves, especially for the transition from weak to strong turbulent states. Localized sites in the y–t (y is normal to the wind direction) space are binarized into hot turbulent sites (HTSs) and cold turbulent sites depending on the instantaneous energy of the local wave height fluctuations. It is found that increasing the fetch (the distance x from the wind entrance) as increasing the effective drive leads to the transition from the weak to the strong turbulent state with a smooth rapid rise of the area fraction occupied by HTSs, and the formation of a large HTS cluster percolating through the y–t space after the sporadic emergence of HTS clusters. This generic transition behavior and the scaling exponents of the HTS fraction around the critical (percolating) fetch, and of the quiescent time and the quiescent distance between adjacent HTS clusters at the critical fetch, are akin to those around and at the critical point, respectively, for the 1 + 1D (dimensional) nonequilibrium system governed by the directed percolation theory.