| 摘要: | 隨外加驅動增強，非平衡系統可以觀察到如展透模型描述之由規則至紊亂態轉換。例如管流研究顯示隨雷諾數提升，層流到紊流態的轉始於局域性無序流場之紊流團塊(local turbulent puffs)在規則層流中間歇性的出現、擴散以及消失，進而形成巨大的紊流團塊展透(percolate)至整個時空間。相似的展透轉換(percolating transition)也在微粒電漿系統之規則平面微粒聲波至紊波轉換研究中發現。然上述的展透理行為研究僅限於由有序狀態至紊亂轉換，未曾觸及多尺度弱紊波到強紊波之轉換過程，特別是此轉換是否遵循在非平衡系統中由規則態至紊態紊展透轉換的普世規律。
風驅水面波，廣存於自然界，展現豐富的非線性時空動力行為，然過去研究未曾以展透模型的觀點探討其在驅動增強下之轉換過程。此研究中，我們透過在長型水槽上方安裝風洞提供穩定風流，由數位影像記錄水面高度起伏，通過小波分析計算出局域瞬時能量，決定局域熱區，以風行距 x (fetch,即觀測點離入風口距離)為控制參數，探討隨其增加水波由弱紊波至強紊波的轉換程序。
我們發現隨x增加，高振幅熱點會形成團簇並逐漸占據整個yt(y為垂直風行方向)空間，最終形成一個可以展透yt空間的巨型團簇，熱點團簇大小呈現無尺(scale-free)冪次分布。而熱點團簇相鄰團簇在時間與空間的距離，則伴隨著熱點的擴散類似stretch exponential 的形式遞減。諸多重要在臨界點的尺度指數(scaling exponent) 亦展現類似在非平衡系統中由規則態至紊態紊展透轉換的普世規律。
;With increasing driving, the percolating type transition from the ordered state to the turbulent state has been observed in non-equilibrium systems, as forest fires, epidemic hydrodynamic flows, and nonlinear waves. For example, recent studies on pipe flows demonstrated that the transition from the laminar flow to turbulence is associated with the uncertain emergence, spreading, and decaying of the localized disordered flow, called turbulent puff, in the form of clusters, followed by the emergence of a large cluster percolating through the space. Similar scenario was also demonstrated in recent study on turbulent transition from ordered plane waves in nonlinear dust acoustic waves. However, the above percolating transitions were only limited to the turbulent transition from the ordered state.
Wind-driven water surface wave widely exist in nature. The large numbers of degrees of freedom of water and wind, and their complicated mutual interaction makes the wind-driven water surface wave exhibit rich spatiotemporal behaviors. However, the transition scenario from weak to strong wave turbulence and the associated waveform dynamics, especially whether the transition scenario belongs to the general class of percolating transition found in previous studies on non-equilibrium systems remain elusive.
In this work, the above unexplored issues are experimentally investigated in a shallow water wave system driven by steady wind. The spatiotemporal wave height evolution can be directly monitored through diffusion light photography. Hot and cold turbulent sites (HTSs and CTSs, respectively) in the 1+1D spatiotemporal (yt) space are identified through wavelet transform. Here, y is normal to the wave propagation direction. It is found that, with increasing fetch (x, the distance from the wind entrance), the transition from the weakly turbulent state to the strong turbulent state is associated with the sporadic emergence of HTSs in the form of clusters following power-law cluster size distribution in the yt space, followed by the formation of a large HTSs cluster percolating through the yt space. The quiescent space and quiescent time between two neighboring clusters also exhibit stretched exponential distributions. The scaling exponents around the transition point are also similar to those found in the model and experimental studies of direct percolating transition in hydrodynamic flows. |
