| Abstract: | 受外力驅動下，紊波 (Wave turbulence) 存在於許多非線性系統中，其振幅與相位均被強力地調製，造成連續頻譜與多尺度動力行為。過去的研究主要探討色散關係、非高斯動力學、以及多重碎形等，但鮮少著重於時空間多尺度同調波形的動力行為。此外，先前研究主要著重巨觀連續系統，在不連續系統中紊波是否存在跟其時空間同調波形動力學仍為未探討重要議題。
微觀不連續尺度下，冷液體為強耦合、非線性、多體的系統，粒子之間的作用力與熱擾動相互競爭下，導致不同三角晶格排列的多重晶塊，並被缺陷環繞，其粒子呈現多尺度動力行為，晶塊的形成使受熱擾動激發的聲波能傳遞於冷液體中，但尚未以紊波的觀點探討相對應的動力學行為。
本研究藉由接近凝固點的微粒電漿冷液體，探討微觀不連續紊波系統中，受熱擾動激發的多尺度聲子如何在晶格中傳遞，利用Hilbert Huang transform拆解粒子間震盪之連續頻譜，首次將多尺度粒子運動拆解成許多不同尺度的聲波模態，不同尺度聲波模態能於時空間受激發、傳播、以及湮滅，其中不同尺度模態之同調(coherence)團簇在時空中呈現冪次律分布。另外發現小尺度和大尺度聲波模態分別容易出現在穩定與不穩定結構處，且相鄰尺度的聲波模態之間存在著交互作用。也發現導致粒子滯-滑式(stick-slip type)區塊旋轉的原因為熱擾動誘發時空中聲波模態的同步消長。
;Under strong external drive, macroscopic wave turbulence with a continuous power spectrum ubiquitously occurs in various nonlinear continuous media, such as water surface, chemical systems, nonlinear optical media, and plasmas. Previous studies mainly focused on dynamical behaviors such as dispersion relations, scaling behaviors, energy cascades, non-Gaussian behaviors, and multifractalities, but have paid less attention on the spatiotemporal coherent behaviors at various scales. Beyond the continuous limit, whether thermally excited microscopic acoustic wave turbulence occurs, and the corresponding spatiotemporal coherent behaviors at various scales at the discrete level still remain open fundamental issues.
Microscopically, the cold liquid around freezing is a nonlinear discrete many-body system. The competition between mutual interaction and thermal agitation leads to the crystalline ordered domains (CODs) with different lattice orientations surrounded with defects. Waves are allowed to propagate in CODs. However, those waves have never been investigated from the wave turbulence view, especially their spatiotemporal coherence at different scales.
In this work, we experimentally demonstrate the observation of thermally excited microscopic acoustic wave turbulence at the discrete level in a quasi-2D cold dusty plasma liquid formed by negatively charged micro-meter sized particle suspended in a low pressure Ar discharge. Through multidimensional complementary ensemble empirical mode decomposition from Hilbert-Huang transform, the relative transverse displacement of dust particle with continuous power spectrum is decomposed into several traveling wave modes with different spatiotemporal scales. It is found that all coherent wave modes exhibit intermittent excitation, propagation, scattering, and annihilation in the form of clusters in the xyt space. Their cluster size distributions rescaled by their own spatiotemporal scales collapse into a single power-law distribution, which manifests the self-similar behavior of different wave modes, akin to the self-similar dynamics of coherent excitations in other nonlinear systems. The poor particle interlocking in the region with poor structural order allows easier excitations of the slow modes with large envelope, which leads to the positive correlation between the envelopes of adjacent modes. The sudden spatiotemporal phase synchronization of slow wave modes with large envelopes can switch the particle motion from cage rattling to cooperative hopping. |
