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@PHDTHESIS{Boschung:697733,
author = {Boschung, Jonas Peter Maria},
othercontributors = {Pitsch, Heinz and Schröder, Wolfgang},
title = {{S}tructure function analysis of turbulent flows},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {Shaker},
reportid = {RWTH-2017-07234},
isbn = {978-3-8440-5449-1},
series = {Berichte aus der Strömungstechnik},
pages = {1 Online-Ressource (xxi, 245 Seiten) : Illustrationen,
Diagramme},
year = {2017},
note = {Auch veröffentlicht auf dem Publikationsserver der RWTH
Aachen University; Dissertation, RWTH Aachen University,
2017},
abstract = {The present work focuses on structure functions in
homogeneous isotropic turbulence. Structure functions are
statistics (more precisely, higher-order moments) of the
velocity difference evaluated at two points in space,
separated by some distance $r$. While most of the work found
in the literature is based on phenomenology and thus
requires additional assumptions besides homogeneity and
continuity, the present thesis aims at examining structure
functions based on the Navier-Stokes equations, the
governing equations of motion for incompressible fluids. For
that reason, firstly the system of structure function
equations is discussed and analysed, with emphasis on their
dissipative and pressure source terms. It is found that the
dissipative source terms and equations derived thereof
contain the higher moments of the (pseudo-)dissipation.
Next, the viscous range is examined more closely. It is
found that there are exact solutions for even-order
longitudinal structure functions, which are determined by
the higher moments of the dissipation $\langle
\varepsilon^{N/2} \rangle$ and the viscosity $\nu$. These
findings are then used to define exact order-dependent
dissipative cut-off scales $\eta_{C,N}$ and $u_{C,N}$, which
reduce to the well-known Kolmogorov scales $\eta$ and
$u_\eta$ for the second order $N=2$. Considering the
inertial range, one may use the previous dissipative range
results to match both regimes and relate inertial range
scaling exponents of longitudinal structure functions to the
Reynolds number scaling of the moments of the dissipation
when assuming Kolmogorov's refined similarity hypothesis
(RSH). Furthermore, the inertial range scaling exponent of
the trace of the fifth-order structure functions is examined
with regard to the system of equations. It is found that the
fifth order is mostly determined by the dissipation source
term, which contains the second moment of the
(pseudo)-dissipation. In the inertial range, terms acting on
the large scales and viscous terms are usually neglected.
However at finite Reynolds numbers, these terms contribute
to the structure function equation balances. For that
reason, their influence is examined for the second-order
equations for decaying turbulence. It is found that both the
unsteady and the viscous terms contribute significantly to
the second-order balances at moderate Reynolds numbers and
their influence decreases only slowly. Finally, streamline
segment statistics are briefly considered, because the
higher conditional moments are conceptually similar to the
longitudinal structure functions.},
cin = {411410},
ddc = {620},
cid = {$I:(DE-82)411410_20140620$},
typ = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2017-07234},
url = {https://publications.rwth-aachen.de/record/697733},
}
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