18,694 research outputs found
Spectral proper orthogonal decomposition
The identification of coherent structures from experimental or numerical data
is an essential task when conducting research in fluid dynamics. This typically
involves the construction of an empirical mode base that appropriately captures
the dominant flow structures. The most prominent candidates are the
energy-ranked proper orthogonal decomposition (POD) and the frequency ranked
Fourier decomposition and dynamic mode decomposition (DMD). However, these
methods fail when the relevant coherent structures occur at low energies or at
multiple frequencies, which is often the case. To overcome the deficit of these
"rigid" approaches, we propose a new method termed Spectral Proper Orthogonal
Decomposition (SPOD). It is based on classical POD and it can be applied to
spatially and temporally resolved data. The new method involves an additional
temporal constraint that enables a clear separation of phenomena that occur at
multiple frequencies and energies. SPOD allows for a continuous shifting from
the energetically optimal POD to the spectrally pure Fourier decomposition by
changing a single parameter. In this article, SPOD is motivated from
phenomenological considerations of the POD autocorrelation matrix and justified
from dynamical system theory. The new method is further applied to three sets
of PIV measurements of flows from very different engineering problems. We
consider the flow of a swirl-stabilized combustor, the wake of an airfoil with
a Gurney flap, and the flow field of the sweeping jet behind a fluidic
oscillator. For these examples, the commonly used methods fail to assign the
relevant coherent structures to single modes. The SPOD, however, achieves a
proper separation of spatially and temporally coherent structures, which are
either hidden in stochastic turbulent fluctuations or spread over a wide
frequency range
Incremental Algorithms for Lattice Problems
In this short note we give incremental algorithms for the following lattice
problems: finding a basis of a lattice, computing the successive minima, and
determining the orthogonal decomposition. We prove an upper bound for the
number of update steps for every insertion order. For the determination of the
orthogonal decomposition we efficiently implement an argument due to Kneser.Comment: 5 page
Guide to Spectral Proper Orthogonal Decomposition
This paper discusses the spectral proper orthogonal decomposition and its use in identifying modes, or structures, in flow data. A specific algorithm based on estimating the cross-spectral density tensor with Welch’s method is presented, and guidance is provided on selecting data sampling parameters and understanding tradeoffs among them in terms of bias, variability, aliasing, and leakage. Practical implementation issues, including dealing with large datasets, are discussed and illustrated with examples involving experimental and computational turbulent flow data
Proper orthogonal decomposition of solar photospheric motions
The spatio-temporal dynamics of the solar photosphere is studied by
performing a Proper Orthogonal Decomposition (POD) of line of sight velocity
fields computed from high resolution data coming from the MDI/SOHO instrument.
Using this technique, we are able to identify and characterize the different
dynamical regimes acting in the system. Low frequency oscillations, with
frequencies in the range 20-130 microHz, dominate the most energetic POD modes
(excluding solar rotation), and are characterized by spatial patterns with
typical scales of about 3 Mm. Patterns with larger typical scales of 10 Mm, are
associated to p-modes oscillations at frequencies of about 3000 microHz.Comment: 8 figures in jpg in press on PR
- …