紊流可以視為相互糾纏的多尺度渦漩在其自生速度場下演化和交互作用，這些多尺度渦旋可以分別簡化為2+1維時空間和 3維空間中以細絲形式存在的渦核絲，這些渦核絲是拓撲缺陷，彼此之間會相互作用並可用於研究紊流複雜動力學行為。 然而，先前紊流的研究主要集中在一些統計性質上的歐拉行為，如頻譜冪律衰減的斜率、非高斯速度分佈和速度結構函數，但對多尺度渦旋的拉格朗日動力學及其相互作用的研究較少。雖然相鄰尺度渦旋之間的單向能量傳遞是導致頻譜冪律衰減的關鍵已被廣泛接受，但對於上述傳遞是否存在雙向能量傳遞，目前尚不清楚，而多尺度渦旋核心的擴散行為和其相關的渦度變化也從未被探究過。 此研究中，我們使用電磁驅動的二維湍流研究多尺度渦旋的拉格朗日動力學中所涉及的問題。利用水平直流電場和隨空間交替極化磁場形成的勞侖茲力驅動低濃度（0.9 M）的硫酸銅電解液，進而生成了渦旋。通過帶通濾波將多尺度渦漩於空間上拆解成不同的模態。我們發現渦核絲可在時空間中生成或消失，且其壽命各不相同。渦核絲壽命表現出多尺度拉伸冪律分佈，且隨著模態數的增加而減短。不同模態的渦核均方位移和均方渦度變化都表現出超擴散。在一段時間內對能量（位渦擬能）的變化進行相關概率測量可發現相鄰模式之間具有強烈的反相關性，表明能量（位渦擬能）可以從注入尺度瞬時且局部地以雙向方式在不同尺度中傳遞。然而，模態3和模態4渦核心的能量（位渦擬能）變化相關概率為正相關，表明它們的能量（位渦擬能）變化可能來自同一個根源的影響。 ;Hydrodynamic turbulence can be viewed as a zoo of multiscale vortices evolving and interacting under their self-induced velocity field. Those multiscale vortices can be simplified to vortex cores (VCs) in the form of unstable filaments in the 2+1D spatiotemporal space and 3D spatial space for the two and three dimensional turbulences, respectively. Those filaments are the topological defects, i.e. the singular objects which can interact with one another and be used to characterize the complicated dynamics of the turbulence. Nevertheless, previous studies on turbulence have mainly focus on the statistical Eulerian behaviors such as the scaling of power-law decays in the power spectra of fluctuating turbulent flows, non-Gaussian velocity distribution, and velocity structure function, but to a much less extent on the Lagrangian dynamics of multiscale vortices and their mutual interaction. Although the scale free one-way energy transfer between vortices of adjacent scales have been accepted as the key leading the scale-free decay of the turbulent power spectrum, there has been no other direct statistical evidence for the above transfer scenario. Whether there are two-way energy transfers are unknown. The diffusive behaviors and associated vorticity changes of multi-scale vortex cores have also never been explored. In this work, we use the electromagnetically driven 2D (two dimensional) turbulence as a platform to investigate the above issues of the Lagrangian dynamics of multi-scale vortices. Vortices are generated in the low concentration (0.9 M) electrolyte CuSO4, driven by Lorentz force from a DC horizontal electric field and a spatially alternating polarization magnetic field. The velocity field of each frame is decomposed into different spatial modes by band pass filtering. It is found that vortex core filaments (VCFs) can be generated and annihilate in the xyt space with different lifetimes. The life times of VCFs of each mode show multiscale stretched power law distribution, which can be rescaled by the mode number. The mean square displacements and the mean square vorticity variations of VCs of different modes all exhibits anomalous super-diffusion. The correlation probability measurements of energy/enstrophy variations over a time interval show strong anti-correlation for adjacent modes are anti-correlated, indicating that energy/enstrophy can be instantaneously and locally transferred two-ways cascaded from the injection scale to the larger scale modes. However, the positively correlated energy (enstrophy) variations between two nearby VCs of modes 4 and 3 reveals that their energy (enstrophy) variations might share the common sources of injection and retraction from the interaction of flow field and background DC electric field and lattice type magnetic field.
