紊流廣泛存於各類非線性系統中，透過外部驅動，可使平穩的系統轉換成紊亂狀態，時空上其頻譜皆呈現冪次下降(power law decay)。然而，紊流並非完全隨機且不可預測，過去研究在流體紊流(hydrodynamic turbulence)中發現蟲狀(worm-like)與絲狀(filament-like)多重尺度單調節構(coherent structures)，因此，可將紊流看成相互糾纏的多尺度漩渦。 細菌紊流為經典二維自驅系統，在高細菌濃度下，透過自驅力、長條形細胞體與非線性強耦合，細菌形成團簇並展現紊流般集體運動行為如多重尺度渦旋(vortex)及噴射流(jet)，能量可由單細胞尺度傳遞至大尺度，多尺度渦絲(vortex filament)之時空動力行為與其交互作用仍為重要且未解議題，此外連續頻譜中缺少譜隙之特性使上述議題更加困難。 此研究中，我們以二維自驅大腸桿菌紊流為平台並利用二維經驗模態拆解自驅紊流成空間多尺度模態，研究多尺度同調激發渦漩之時空動力行為與各模態間交互作用。發現不同尺度渦絲在時空中可展現單調激發、移動、互相糾纏與湮滅運動，其中相鄰模態但不同螺旋性(helicity)的渦漩對較其他漩渦對更喜歡座落在一起。更發現渦旋等值線可用以了解渦旋運動如渦旋分裂與合併(splitting and merging events)的重要指標，當漩渦等值線變成細長狀時，漩渦核可能在下時刻分解或合併。此外，我們亦發現漩渦分解與合併經常伴隨馬鞍狀奇異點在周遭流場產生。 ;Turbulence is a ubiquitous phenomenon, exhibiting a continuous spectrum with a power law decay over a wide range of spatiotemporal scales, in various nonlinear extended systems. However, turbulence is not completely random. Intermittent coherent structures in the forms of vortices with worm- or filament like cores have been found in hydrodynamic turbulence. Based on these features, turbulence is usually viewed as a tangle of interacting multiscale vortices. Bacterial systems, a model active system, exhibits self-driven turbulent-like motion with multiscale vortex excitation through the interplay of self-propulsion and nonlinear couplings from anisotropic excluded volume and strong mutual interaction. It is intriguing to ask how multiscale coherent vortices behave and how they are correlated spatiotemporally. In addition, the absence of spectral gaps in the continuous turbulent spectrum hinders the decomposition of the turbulent spectrum into multi-scale modes through Fourier analysis. This makes the above issues more difficult. In this work, we experimentally investigate the above issues in two dimensional (2D) E. coli suspension in thin liquid films. Through bi-dimensional empirical mode decomposition, two dimensional turbulent-like vorticity field is adaptively decomposed into modes with different scales. It is found that the multi-mode vortex filaments exhibit coherent excitation, propagation and annihilation in 2+1D space time. The vortex cores of different modes with the same helicity tend to entangle and co-localize with those of their neighboring mode at short range. Interestingly, the shape of a contour line of a vortex core can serve as an indicator for vortex splitting and merging events, which are further found to be associated with the emergence of saddle-type singularity at the surrounding flow field.
