Waveform dynamics in undulated dust acoustic waves

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蔡雅怡(Ya-Yi Tsai) 查詢紙本館藏

畢業系所

物理學系

論文名稱

(Waveform dynamics in undulated dust acoustic waves)

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摘要(中)

弱失穩態為介於規則與紊流波之中介態，藉由調升系統外部驅動，其振幅與相位均被調制，造成波面扭曲與位於低振幅洞(low amplitude hole)上拓樸缺陷的產生，伴隨著豐富的動力學行為，此現象廣泛地存在於其他非線性波動系統中。然而，在弱失穩疏密波中，其缺陷形成原因與三維波型卻未曾被探討過。此外，同樣藉由調制不穩定性所產生之超高突波(rogue wave)，也是非線性波動系統中相當重要的現象。超高突波是否存在於弱失穩疏密波中與其產生機制仍然為未解之議題。
微粒電漿系統由懸浮於電漿中微米尺度的帶電顆粒組成。透過微粒的慣性、屏蔽效應下之庫倫作用力、背景電漿壓力與離子風之交互作用所產生之不穩定性，產生由微米粒子縱向震盪組成之自發性微粒電漿聲波。藉由直接觀測其聲波場密度變化與追蹤微米粒子影像，微粒電漿聲波提供一個很好的研究平台，用以探討疏密波之波動現象與其微觀動力學行為。
在此研究中，藉由觀測弱失穩微粒電漿聲波三度空間波型之時空變化與追蹤微粒運動軌跡，我們首度在三維波狀微粒電漿聲波中，觀測到聲渦(acoustic vortex)與超高突波之存在，並探討其非線性動力程序。透過微粒電漿平面波之自發性對稱破缺，環繞低振幅洞之聲渦可視為不規則疏密波之基礎激發態。藉由因調制不穩定性造成之波峰面彎曲、斷裂與重聯，帶著相反手性之雙聲渦產生。此外，透過統計分析其波高分佈，我們驗證了超高突波在三維不規則疏密波之存在。並指出在超高突波產生前的兩項跡象：因調制不穩定性造成之緩慢波包振幅成長與較高出現機率之低振幅洞伴隨著較強的波峰面扭曲。在平行密度波中，垂直於波前(波後)的力場對進入(離開)波峰微粒進行的壓縮(舒張)為造成波行進與波型演化的主因，而扭曲之波峰所產生額外的橫向力更可造成進入波前粒子的聚焦與散焦，此為形成超高突波與影響缺陷運動的主因。

摘要(英)

The weakly disordered intermediate state, changed from the ordered wave by increasing the excitation before entering the wave turbulence with power-law spectrum, is a ubiquitous phenomenon in many nonlinear open dissipative systems. Through amplitude and phase modulations, the waveforms are distorted associated with the uncertain generation of defects, located at points with null amplitudes and undefined phases. However, defect dynamics of 3D traveling waves had only been demonstrated recently, without showing the surrounding 3D waveforms and explaining the generation mechanism. In addition to the low amplitude singular objects (defects), the generations of the uncertain and highly localized large amplitude events, rogue waves, is also a ubiquitous fundamental excitation in various nonlinear wave systems. Whether rogue waves exist in the nonlinear acoustic type traveling waves and their generation mechanism still remain elusive, especially from the Eulerian-Lagrangian view of wave-particle interaction.
Dust acoustic wave (DAW) is a density wave with longitudinal oscillations of negatively charged dust particles suspended in weakly ionized discharges. In this work, using the undulated DAW as a platform, the above unexplored issues are experimentally addressed by direct imaging the large area dust density evolutions and tracking the individual dust particle motions. For the first time, we demonstrate the observations of acoustic vortex (AV) and rogue wave event (RWE), and construct pictures explaining their generation mechanisms. AVs with helical waveforms winding around the low amplitude hole (LAH) filaments, generated from the spontaneous symmetry breaking are identified as the basic excitations. Under the modulation instability induced stretching of crest surfaces, the sequential rupturing of crest surfaces, followed by the reconnections between two adjacent crest surfaces, leads to the pair generation of AVs carrying opposite chirality. The above processes are reversed when AVs are pairwise annihilated.
On the other hand, the identification of RWEs is confirmed by observing the tail beyond two significant wave heights in the probability distribution function. It is found that, RWEs tend to be led by the slow growth of wave envelope in a few leading cycles and the higher probability of LAHs before RWE emergences. For a traveling DAW, the particle compression and rarefaction in the crest front and rare control waveform evolution. The presences of AVs tend to be associated with distorted waveforms. The particle focusing and defocusing induced by the additional transverse forces of the distorted waveforms are the key factors for emergences of RWEs and motions of AVs, respectively.

關鍵字(中)

★ 微粒電漿聲波
★ 低振幅洞
★ 聲渦
★ 超高突波

關鍵字(英)

★ Dust acoustic wave
★ Low amplitude hole
★ Acoustic vortex
★ Rogue wave

論文目次

1 Introduction 1
2 Background and theory 6
2.1 Defect mediated turbulence in nonlinear extend media . . . . 6
2.2 Acoustic vortex . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Rogue wave event . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Dust acoustic wave . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 Dusty plasma system . . . . . . . . . . . . . . . . . . . 11
2.4.2 Dust acoustic wave . . . . . . . . . . . . . . . . . . . . 12
2.4.3 Undulated dust acoustic wave with ﬂuctuating defects . 13
2.4.4 Particle-wave interaction . . . . . . . . . . . . . . . . . 15
3 Experiment and data analysis 19
3.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Result and discussion 25
4.1 Identiﬁcation of acoustic vortex as basic excitation . . . . . . . 25
4.1.1 Undulated dust acoustic wave . . . . . . . . . . . . . . 25
4.1.2 Helical waveform winding around defect . . . . . . . . 27
4.1.3 Pair generation and annihilation of acoustic vortices:
kinked, ruptured, and reconnected crest surfaces . . . . 31
4.1.4 Spatiotemporal waveform undulation . . . . . . . . . . 34
4.1.5 Distorted waveform around defects . . . . . . . . . . . 36
4.1.6 Another example of 3D waveforms surrounding AVs . 37
4.2 Observation of dust acoustic rogue wave . . . . . . . . . . . . 37
4.2.1 Identiﬁcation of rogue wave from local dust density
oscillations . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.2 Relation between rogue wave and low amplitude hole . 41
4.2.3 Waveform evolution from the view of particle-wave in-
teraction in the distorted waves . . . . . . . . . . . . . 44
4.2.3.1 Pitchfork waveform evolution . . . . . . . . . 45
4.2.3.2 Generation of rogue waves through three-dimensional
particle focusing . . . . . . . . . . . . . . . . 49
5 Conclusion 55

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指導教授

伊林(Lin I)

審核日期

2016-1-21

推文