Multiscale coherent excitations and extreme events in dust acoustic wave turbulence

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姓名

林柏丞(Po-Cheng Lin) 查詢紙本館藏

畢業系所

物理學系

論文名稱

(Multiscale coherent excitations and extreme events in dust acoustic wave turbulence)

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摘要(中)

隨著調升系統外部驅動，水流甚至是波動等非線性系統皆具從規則至紊亂態的相轉換。一般來說，此紊亂態具有極高和極低的不穩定振幅擾動，但非是完全無序的。過去在水流系統中的研究發現，具有絲狀奇異核心的多尺度漩渦是水流紊流中的基礎擬序激發態(coherent excitation)。
在轉換成紊亂態前，過去在弱失穩微粒電漿聲波的研究中，發現環繞著絲狀低振幅洞(Low amplitude hole filament)的正轉或反轉的單尺度聲渦(acoustic vortex)是單尺度擬序激發態，聲渦能對偶生成並對偶湮滅以維持拓樸守恆，這現象和弱失穩水流中的單尺度雙旋渦的對偶生成及煙滅類似。另一方面，極大振幅突波常伴隨著較高出現機率的低振幅洞，而低振幅洞旁較強的波面扭曲使粒子三維聚焦可被當成是突波形成的前驅跡象。
然而，在三維行進紊波中，多尺度擬序激發態是否存在、及其與極低和極高振幅突波(rogue wave)的關連皆為鮮少人研究的基礎問題。此外，因其連續頻譜中缺乏譜隙，紊亂狀態無法透過傅立葉帶通濾波拆解成多尺度模態，使得探討上述問題更加困難。
此研究中，我們以微粒電漿聲紊波作為平台並透過多維度經驗模態拆解紊波成多尺度模態，發現聲紊波中的多尺度聲渦(acoustic vortex)為其基礎擬序激發態並且說明多尺度聲渦與極高突波的關連。除了相同尺度的聲渦能對偶產生並對偶湮滅之外，不同尺度的聲渦能互相纏結並同步旋轉。這些現象皆和紊流中的多尺度旋渦有相近的現象。此外，我們也發現到極高突波皆座落於是大振幅多尺度扭曲波峰的交點。經過統計分析，我們也觀察到多尺度低振幅洞有較高的機率出現超高突波旁。多尺度低振幅洞扭曲了多尺度波峰，而扭曲的多尺度波峰產生額外的橫向推力使波前粒子能夠三維聚焦並導致極高突波能夠在紊波中產生。

摘要(英)

With increasing driving, the transition from ordered to the turbulence with fluctuating high and low amplitude events ubiquitously occurs in various nonlinear extended media ranging from hydrodynamics ﬂows to nonlinear wave media. Counterintuitively, turbulence is not completely disordered. In hydrodynamics turbulence, multi-scale interacting vortices surrounding filament-like singular cores, are basic coherent excitations.
Previous studies in dust acoustic waves demonstrated, for the weakly disordered single scale wave state before the transition to the wave turbulence state, the spontaneous pair-generation and pair-annihilation of single-scale acoustic vortices (AVs) with opposite helicities winding around low-amplitude hole filament (LAH filament) pairs, are the basic coherent excitation surrounding the low amplitude extreme events. Large-amplitude rogue wave events (RWEs) through 3D particle focusing by the preceding surrounding distorted waveforms were also observed.
Nevertheless in three-dimensional (3D) traveling wave turbulence, whether multi-scale coherent excitations also exist, how they are formed, and how they are correlated with high and low amplitude singular events are unexplored fundamental issues. Moreover, the absence of spectral gaps in the continuous turbulent spectrum disabling the decomposition of turbulent field into multiscale modes though Fourier band-pass filtering, makes the studies of above issues even more challenging.
In this work, the above unexplored issues are experimentally investigated using 3D dust acoustic wave turbulence as a platform, though multi-dimensional complementary ensemble empirical mode decomposition (MCEEMD). It is found, for the first time, the dust acoustic wave turbulence can be viewed as a zoo of self-similar interacting multi-scale AVs. In addition to the AV intra-mode interaction (e.g. pair generation/propagation/annihilation), the inter-mode interactions of AVs with same/opposite helicity, their entanglement and synchronization, are found to be the fundamental dynamical processes in acoustic wave turbulence, akin to the interacting multi-scale vortices around worm-like singular cores observed in hydrodynamic turbulence.
For RWEs in the acoustic wave turbulence, it is found that multiscale waveform focusing and the phase synchronization of multiscale wave crests as well as their envelopes are the keys for the generation of RWEs. In the 2+1D spatiotemporal space, RWEs are located at the intersection of distorted multiscale crest surfaces with large amplitudes and preceded by higher probability of finding LAHs in each mode. The synchronized multiscale distorted crests nearby multiscale LAHs assist 3D particle focusing for the generation of RWE in wave turbulence.

關鍵字(中)

★ 微粒電漿聲紊波
★ 多尺度聲渦
★ 瘋狗浪
★ 希爾伯特-黃轉換

關鍵字(英)

★ Dust acoustic wave turbulence
★ Multiscale acoustic vortices
★ Rogue wave
★ Hilbert-Huang transform

論文目次

1. Introduction 1
2. Background and theory 6
2.1 Hydrodynamic turbulence and wave turbulence 6
2.2 Weakly disordered single-scale wave 8
2.3 Dust acoustic wave 9
2.3.1 Dusty plasma system 9
2.3.2 Dust acoustic wave 11
2.3.3 Acoustic vortices as basic singular excitations in waves 12
2.3.4 Rogue waves and their correlation with defects 13

3. Experiment and data analysis 15
3.1 Experimental setup 15
3.2 Data analysis 18

4. Result and discussion 22
4.1 Decomposition of dust wave turbulence into multiscale modes 22
4.2 Multiscale undulated waveforms 24
4.3 Identification of multiscale acoustic vortices (AVs) 26
4.3.1 Helical waveform winding around defects 26
4.3.2 Self-similar dynamical behaviors of multiscale AVs 28
4.3.3 I nter- and intra-mode interactions between multiscale AVs 30
4.4 Observation of rogue waves in wave turbulence 32
4.4.1 Multiscale wave synchronization inducing rogue waves 32
4.4.2 Relation between rogue waves and multiscale defects 26
4.4.3 Multiscale focusing by preceding waveforms as the generation
mechanism of rogue wave events 38

5. Conclusion 41
6. Bibliography 43

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指導教授

伊林(Lin I)

審核日期

2019-6-26

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