| 摘要: | 在逐漸增加系統能量輸入的過程中，系統從有序態失穩至紊亂態的至亂動力過程是一個常見於流體和波動等非線性動力系統的現象。
在流體系統，例如管流和渠道流中，區域性的無序流場被識別為紊流團塊(turbulent puffs)，而近期的研究展示出紊流轉換(turbulent transition)始於紊流團塊在層流的環境中間歇性地在時空間上出現。隨著雷諾數提升，紊流團塊從間歇出現與消失轉變成在空間迅速擴散，並逐漸展透(percolate)整個時空間使流體系統進入完全紊流態[1-5]，而研究也指出流體中紊流相轉換符合用於描述森林野火與傳染病擴散之定向展透理論(directed percolation theory)。然而鮮少研究從波形演化觀點看待週期性平面波到波動紊流之間的轉換過程。
在此研究中，我們以微粒聲波系統做為平台，並以時空間波形動力行為說明了穩定平面波動態失穩至波動紊流態中波形動力行為。而微粒電漿系統是由懸浮於電漿中微米尺度的帶負電顆粒組成，因正離子流可以導致疏密聲波自發產生。又因其適當的時空間尺度，可以透過光學顯微數位影像技術，直接追蹤粒子運動及大面積粒子密度起伏，因此微粒電漿聲波是一個適合研究疏密波之波形的動力學平臺，並可用來建構立體聲波結構。我們藉由小波分析可以找出在三維時空間中具有多重頻率寬頻激發態的區域波動紊流(localized turbulent sites)。藉由量測區域瞬時能量以及區域瞬時相位不同調的程度，我們可以看待極低(高)振幅事件為寬頻模態破壞性(建設性)干涉出的非同調(同調)且低(高)能量的區域波動紊流。
我們發現區域波動紊流在微失穩態下間歇性的出沒於具有低振幅的波形缺陷附近。隨著增加系統能量輸入，區域波動紊流體積占比快速提升且區域波動紊流可以快速散播並且團簇於高振幅區域，最終形成一個可以展透時空間的巨型團簇。我們發現了波動紊流轉換伴隨著平穩且快速紊流體積占比提升、無尺度(scale-free)區域紊流團簇尺寸分布、從冪次衰減轉換至指數衰減之時空間上區域波動紊流間格分布。上述發現驗證了波動紊流轉換過程屬於展透理論中一種形式，而它也相似於在流體中發現的紊流轉換現象。
;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. |
