穩定平面波可在非線性耗散系統中自發產生。藉由調升系統外部驅動，穩定平面波相轉換至弱失穩波(weakly disordered wave)現象廣泛存在於各種非線性波動系統如聲學、光學、電漿、微粒電漿系統等。因調制失穩導致的振幅與相位調制，造成波面扭曲並伴生振幅為零且相位無法定義之拓樸缺陷絲(topological defect filament)。此等不規則的波動狀亦稱缺陷紊流波 (defect-mediated turbulence)，為介於規則波動與紊流波之中介狀態。
過去在類聲波發現，調制失穩造成之波面扭曲使波面撕裂並與鄰近扭曲波面重連造就對偶(正反手性)生成之單尺度螺旋聲渦螺旋(acoustic vortex)，並環繞於對應之對偶拓樸缺陷絲上。此等自發性對稱破缺產生之聲渦，為具調制失穩的三維非線性縱波中的普世行為。然而，過去鮮少著重於探討因調制失穩導致的穩定平面波至缺陷紊波相轉換，也鮮少討論缺陷紊流波中拓樸缺陷絲的交互作用、動力行為與環繞其周圍的扭曲波形變化之動力行為。
微粒電漿系統由微米尺度帶負電顆粒懸浮於低壓電漿中，可藉由調控系統驅動使產生縱向震盪之自發性微粒電漿聲波。此研究中則以微粒電漿聲紊波為實驗平台，探討上述未被仔細研究之時空間中波形演化。
在小系統增加外部驅動使其由穩定平面波相轉換至缺陷紊波發現，平面波能從邊界撕裂出單一左旋或右旋聲渦或從中間對偶產生之聲渦推擠至邊界並保留單聲渦。單聲渦在三維空間中的軌跡調制附近扭曲波形之振幅與相位，使波譜中主頻和倍頻產生邊帶尖點(sideband peak)。增強系統驅動後，其產生多個聲渦並進入缺陷紊流波狀態。多聲渦紊亂軌跡和數量上多尺度的擾動使波形扭曲，其對應波譜中的主頻和倍頻也形成平滑寬帶。在缺陷紊流波中發現，一個波長內同(異)轉的成對洞絲相斥(相吸)，且局部曲率在三維中為負(正)相關。波形形變造成的波面拉展，使波的局部振幅梯度成為低振幅洞位移的早期指標。

With increasing driving, the transition from the ordered state to the weakly disordered state before entering the turbulence state is a universal phenomenon in many nonlinear wave systems such as acoustic, plasma, optical, and dusty plasma systems. Through modulation instability, the waveforms in the weakly disordered states are spatiotemporally modulated, causing the generation of defect filaments with null amplitudes and undefined phases. It also leads to the name defect mediated turbulence (DMT).
In the weakly disordered plane traveling waves such as acoustic and optical waves, defect filaments are winded by helical waves named acoustic vortices (AVs) and optical vortices, respectively. Previous studies in acoustic type waves found that the modulation instability causes waveform undulation and induces sequential rupture and reconnection of adjacent wave crest surfaces. It is the key to generate a pair of AVs with opposite helicities winding around a pair of defect filaments with opposite topological charges. Nevertheless, the transition from the ordered plane wave state to the DMT state with many fluctuating defect filaments and the generic dynamical behaviors of defect filaments, remain unexplored fundamental issues.
In this work, those issues are experimentally addressed in a self-excited dust acoustic wave (DAW) in the dusty plasma system composed of micro-size particles with negatively charged oscillating longitudinally and suspended in a low pressure discharge, by monitoring the spatiotemporal waveform evolution in the 2+1D space-time space.
It is found that, with increasing driving in a small size system, the sequential ruptures of the crest surfaces from the cluster boundary followed by their reconnection with adjacent ruptured crest surfaces, or repelling one of the pairwise generated defects out of the boundary is the key for the single AV generation. The gyration motion of this single AV in 2+1D space-time space modulates the amplitude and phase of neighbor distorted waveforms, causing the emergence of side band peaks at the main peak and its harmonics in the power spectrum. Further increasing driving makes the system enter the state with few short-lived AV and the DMT state with multiple AVs. Gradually increasing defect filament fluctuations and defect number in the transition to the DMT more strongly distort the nearby waveforms. It leads to the transition from the emergence of the distinct side band peaks to the broadened peaks in the power spectra of temporal dust density fluctuation. In the DMT state, two defect filaments with the same (opposite) topological charges repel (attract) each other within a wavelength scale. The local filament curvature in the space is also positively correlated in that scale. Furthermore, the local wave amplitude and phase gradient caused by the wave crest surface stretching due to waveform undulation can be used as an early indicator for the subsequent propagating velocity of the defect.

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