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Turbulent characteristics in the intensity fluctuations of a solar quiescent prominence observed by the \textit{Hinode} Solar Optical Telescope

We focus on Hinode Solar Optical Telescope (SOT) calcium II H-line observations of a solar quiescent prominence (QP) that exhibits highly variable dynamics suggestive of turbulence. These images capture a sufficient range of scales spatially ($\sim$0.1-100 arc seconds) and temporally ($\sim$16.8 s - 4.5 hrs) to allow the application of statistical methods used to quantify finite range fluid turbulence. We present the first such application of these techniques to the spatial intensity field of a long lived solar prominence. Fully evolved inertial range turbulence in an infinite medium exhibits multifractal \emph{scale invariance} in the statistics of its fluctuations, seen as power law power spectra and as scaling of the higher order moments (structure functions) of fluctuations which have non-Gaussian statistics; fluctuations $δI(r,L)=I(r+L)-I(r)$ on length scale $L$ along a given direction in observed spatial field $I$ have moments that scale as $<δI(r,L)^p>\sim L^{ζ(p)}$. For turbulence in a system that is of finite size, or that is not fully developed, one anticipates a generalized scale invariance or extended self-similarity (ESS) $<δI(r,L)^p>\sim G(L)^{ζ(p)}$. For these QP intensity measurements we find scaling in the power spectra and ESS. We find that the fluctuation statistics are non-Gaussian and we use ESS to obtain ratios of the scaling exponents $ζ(p)$: these are consistent with a multifractal field and show distinct values for directions longitudinal and transverse to the bulk (driving) flow. Thus, the intensity fluctuations of the QP exhibit statistical properties consistent with an underling turbulent flow.