Percolating transition to acoustic wave turbulence in dusty plasmas

In various nonlinear extended media, increasing driving causes the transition from the ordered state to the turbulent state. For the hydrodynamic flow, the transition starts with spreading and decaying intermittent turbulent puffs in the laminar background, followed by the emergence of one percolating turbulent puff leading to full turbulence. Nevertheless, for nonlinear waves, the transition scenario and the corresponding spatiotemporal waveform dynamics from the ordered wave to wave turbulence still remain elusive. Here, these issues are experimentally explored in three dimensional traveling dust acoustic waves of the dusty plasma system through direct visualization. Turbulent sites (TSs) with a wide instantaneous bandwidth in the 2 + 1D spatiotemporal space are identified through wavelet transform. It is found that the transition from the plane wave to the weakly disordered states starts with a small fraction of emerging and decaying TSs mainly clustering around defect filaments with null wave amplitude, in the ordered wave background. Further transition to turbulence with a smooth rapid increase in the fraction of TSs, which exhibit scale-free cluster size distributions and eventually percolate through the 2 + 1D space, is similar to the percolating turbulent transition in hydrodynamic flows.