| dc.description.abstract | With increasing driving, the turbulent transition from the ordered to the turbulent states, is a common process which can be found in various nonlinear extended media, such as hydrodynamic flows and nonlinear waves. For hydrodynamic flows, such as channel, pipe and Taylor-Couette flows, recent studies demonstrated that the turbulent transition starts with intermittently spreading and decaying turbulent puffs identified as local domains with disordered flow fields in the laminar background, followed by the emergence of one percolating turbulent puff occupying the entire space, leading to fully developed turbulence [1-5]. It is found that laminar-turbulent transition belongs to the directed-percolation universality class, which has been used to describe forest fire spreading and epidemic propagation. Yet, the scenario of turbulent transition in nonlinear waves and the corresponding spatiotemporal waveform dynamics from ordered to turbulent waves still remain unclear.
In this work, the transition scenario and the corresponding spatiotemporal waveform dynamics from the ordered plane wave to wave turbulent states through intermediate weakly disordered state are investigated in self-excited three-dimensional (3D) dust acoustic waves by direct observing dust density fluctuations over a large area. Turbulent sites (TSs) with wide local bandwidth in the 2+1D space-time space are identified through wavelet analysis. By measuring local instantaneous energy and the degree of local instantaneous phase incoherence, low (high) amplitude extreme events can be viewed as the local incoherent (coherent) TSs with low (high) local energy, due to the destructive (constructive) interference of wide-band excitations. With decreasing background dissipation, the transition from the ordered plane wave to the wave turbulent states starts with a small fraction of intermittently emerging and decaying TSs mainly clustering around defect filaments with null amplitude, followed by spreading and percolating scale-free TS clusters with high amplitude. The transition with a smoothly but rapidly increasing fraction of TSs with high local energy, scale-free TS cluster size distributions, and histograms of spatiotemporal gaps between clusters following the transition from power-law to exponential distributions, are similar to the percolating turbulent transition found in hydrodynamic flows.
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