The vertical current sheet (VCS) trailing coronal mass ejections (CMEs) is the key place where the flare energy release and the CME buildup take place through magnetic reconnection. It is often studied from the edge-on perspective for the morphological similarity with the two-dimensional ``standard picture, but its three dimensional structure can only be revealed when the flare arcade is observed side on. The structure and dynamics in the so-called supra-arcade region thus contain important clues to the physical processes in flares and CMEs. Here we focus on the supra-arcade spikes (SASs), interpreted as the VCS viewed side-on, to study their spatiotemporal structures. By identifying each individual spike during the decay phase of four selected flares, in which the associated CME is traversed by a near-Earth spacecraft, we found that the widths of spikes are log-normal distributed, while the Fourier power spectra of the overall supra-arcade EUV emission, including bright spikes and dark downflows as well as the diffuse background, are power-law distributed, in terms of either spatial frequency $k$ or temporal frequency $ u$, which reflects the fragmentation of the VCS. We demonstrate that coronal emission-line intensity observations dominated by Kolmogorov turbulence would exhibit a power spectrum of $E(k)sim k^{-13/3}$ or $E( u)sim u^{-7/2}$, which is consistent with our observations. By comparing the number of SASs and the turns of field lines as derived from the ICMEs, we found a consistent axial length of $sim,$3.5 AU for three events with a CME speed of $sim,$1000 km/s in the inner heliosphere, but a much longer axial length $sim,$8 AU) for the fourth event with an exceptionally fast CME speed of $sim,$1500 km/s, suggesting that this ICME is flattened and its `nose has well passed the Earth when the spacecraft traversed its leg.
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