63 research outputs found
Towards a Simplified Dynamic Wake Model using POD Analysis
We apply the proper orthogonal decomposition (POD) to large eddy simulation
data of a wind turbine wake in a turbulent atmospheric boundary layer. The
turbine is modeled as an actuator disk. Our analyis mainly focuses on the
question whether POD could be a useful tool to develop a simplified dynamic
wake model. The extracted POD modes are used to obtain approximate descriptions
of the velocity field. To assess the quality of these POD reconstructions, we
define simple measures which are believed to be relevant for a sequential
turbine in the wake such as the energy flux through a disk in the wake. It is
shown that only a few modes are necessary to capture basic dynamical aspects of
these measures even though only a small part of the turbulent kinetic energy is
restored. Furthermore, we show that the importance of the individual modes
depends on the measure chosen. Therefore, the optimal choice of modes for a
possible model could in principle depend on the application of interest. We
additionally present a possible interpretation of the POD modes relating them
to specific properties of the wake. For example the first mode is related to
the horizontal large scale movement. Besides yielding a deeper understanding,
this also enables us to view our results in comparison to existing dynamic wake
models
The Langevin Approach: An R Package for Modeling Markov Processes
We describe an R package developed by the research group Turbulence, Wind
energy and Stochastics (TWiSt) at the Carl von Ossietzky University of
Oldenburg, which extracts the (stochastic) evolution equation underlying a set
of data or measurements. The method can be directly applied to data sets with
one or two stochastic variables. Examples for the one-dimensional and
two-dimensional cases are provided. This framework is valid under a small set
of conditions which are explicitly presented and which imply simple preliminary
test procedures to the data. For Markovian processes involving Gaussian white
noise, a stochastic differential equation is derived straightforwardly from the
time series and captures the full dynamical properties of the underlying
process. Still, even in the case such conditions are not fulfilled, there are
alternative versions of this method which we discuss briefly and provide the
user with the necessary bibliography
An open source MATLAB package to perform basic statistical analysis of turbulence data and other complex systems along with its application to Fokker-Planck equation and Integral fluctuation theorem
We present a user-friendly open-source
\proglang{MATLAB\textsuperscript{\textregistered}} package developed by the
research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von
Ossietzky University of Oldenburg. This package enables to perform a standard
analysis of given turbulent data and extracts the stochastic equations
describing the scale-dependent cascade process in turbulent flows through
Fokker-Planck equations. As a precondition, Markovian properties of the process
in scale are tested. Such a stochastic scale-dependent cascade process allows a
comprehensive statistical description in terms of the complexity of the data.
Cascade trajectories can be defined as single events, for each of which a total
entropy production can be determined. For such entropy fluctuations a rigorous
law of non-equilibrium stochastic thermodynamics, namely the integral
fluctuation theorem, will be verified. As the analysis of the scale-dependent
cascade process through a hierarchy of spatial and temporal scales in turbulent
flows is an integral part of turbulence theory, this interdisciplinary
treatment of the turbulent cascade process has the potential for a new way to
link the statistical description of turbulence (via common two-point increment
statistics), non-equilibrium stochastic thermodynamics and local turbulent flow
structures. The presented package can be used also for the analysis of other
data with turbulent like complexity.Comment: This open source MATLAB package can be downloaded with all the
supplementary material (data, source code and standalone applications
(64-bit) for Windows, macOS and Linux) to replicate all the results presented
in this paper from the repository on GitHub
https://github.com/andre-fuchs-uni-oldenburg/OPEN_FPE_IF
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