Title:

Quantifying finite range plasma turbulence

Turbulence is a highly nonlinear process ubiquitous in Nature. The nonlinearity is responsible for the coupling of many degrees of freedom leading to an unpredictable dynamical evolution of a turbulent system. Nevertheless, experimental observations strongly support the idea that turbulence at small scales achieves a statistically stationary state. This has motivated scientists to adopt a statistical approach for the study of turbulence. In both hydrodynamics (HD) and magnetohydrodynamics (MHD), fluctuations of bulk quantities that describe turbulent flows exhibit the property of statistical scale invariance, which is a form of selfsimilarity. For fully evolved turbulence in an infinite medium, one interesting consequence of this scale invariance is the power law dependence of the physical observables of the flow such that, for instance, the velocity field fluctuations along a given direction show power law power spectra and multiscaling for the various orders of the structure function within a certain range of scales, known as the inertial range. The characterization of such scaling is crucial in turbulence since it would fully quantify the process itself, distinguishing the latter from a wider class of scaling processes (e.g., stochastic selfsimilar processes). Experimentally, it has been observed that turbulent systems exhibit an extended selfsimilarity when either turbulence is not completely evolved or the system has finite size. As consequence of this, the moments of the structure function exhibit a generalized scaling, which points to a universal feature of finite range MHD turbulent ows and, more generally, of scale invariant processes that have finite cutoffs of the fields or parameters. However, the underling physics of this generalized similarity is still an open question. This thesis focuses on the quantification of statistical scaling in turbulent systems of finite size. We apply statistical analyses to the spatiotemporal fluctuations associated with line of sight intensity measurements of a solar quiescent prominence and data of the reconnecting fields in simulations of magnetic reconnection. We find that in both environments these fluctuations exhibit the hallmarks of finite range turbulence. In particular, an extended selfsimilarity is observed to hold the inertial range of turbulence, which is consistent with a generalized scaling for the structure function. Importantly, this generalized scaling is found to be multifractal in character as a signature of intermittency in the turbulence cascade. The generalized scaling recovered for finite range turbulence exhibits dependence on a function, the generalized function, which contains important information about the bounded turbulent flow such as some characteristics scale of the flow, the crossover from the small scale to the outer scale of turbulence and perhaps some characteristic features of the boundaries (future work). The quantification of the generalized scaling is performed thank to the application of statistical tools, some of which have been here introduced for the first time, which allow to identify the statistical properties of a wide class of scaling processes. Importantly, these techniques are powerful methodologies for testing fractal/multifractal scaling in selfsimilar and quasi selfsimilar systems, allowing us to distinguish turbulence from other processes that show statistical scaling.
