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Quantifying finite range plasma turbulence
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Leonardis, Ersilia (2013) Quantifying finite range plasma turbulence. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2689303~S1
Abstract
Turbulence is a highly non-linear 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 self-similarity. 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 self-similar processes).
Experimentally, it has been observed that turbulent systems exhibit an extended
self-similarity 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 cut-offs 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 spatio-temporal
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 self-similarity 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 self-similar and quasi self-similar systems,
allowing us to distinguish turbulence from other processes that show
statistical scaling.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QC Physics | ||||
Library of Congress Subject Headings (LCSH): | Plasma turbulence, Scaling laws (Statistical physics) | ||||
Official Date: | June 2013 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Physics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Chapman, Sandra C. | ||||
Extent: | ix, 133 leaves : illustrations. | ||||
Language: | eng |
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