Applications of biorthogonal decompositions in fluid–structure interactions

Hémon, Pascal; Santi, F.

doi:10.1016/s0889-9746(03)00057-4

Cited by 27 publications

(18 citation statements)

References 19 publications

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“…By multiplication with ? α k , the spatial information of the signal can be separated from its temporal information [23,41]. Since the norm of the series Upx, tq converges, it is possible to truncate the series to the first k terms [23].…”

Section: Biorthogonal Decompositionmentioning

confidence: 99%

“…The explained variance of each k-th term in the series Upx, tq, called the relative eigenvalue λ rk , can be calculated according to [41]:…”

Section: Biorthogonal Decompositionmentioning

confidence: 99%

“…Information about phase lags in time and space between the time series of Upx, tq are contained in the different behavior of the chronos and topos [24,25,41].…”

Section: Biorthogonal Decompositionmentioning

confidence: 99%

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Coherent Momentum Exchange above and within a Scots Pine Forest

Mohr

Schindler

2016

Atmosphere

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Biorthogonal decomposition (BOD) is used to detect and study synchronous coherent structures occurring at multiple levels in the vertical momentum flux (u 1 w 1 ) within and above a planted Scots pine forest during a 12-week continuous measurement period. In this study, the presented method allowed for the simultaneous detection and quantification of the number of coherent structures (N), their duration (D) and separation (S) at five measurement heights (z 1 -z 5 ) covering the range z 1 /h = 0.11 to z 5 /h = 1.67, with h being the mean stand height at the measurement site. Results presented for five different exchange regimes (C1-C5) and for four different atmospheric stability conditions (stable, transition to stable, near-neutral, forced convection) demonstrate that during the measurement period, above-canopy momentum flux was only to a limited extent involved in the evolution of spatiotemporal momentum flux patterns found within the below-canopy space. Fully-coupled turbulent momentum exchange over the investigated height range occurred during 19% of all analyzed half-hourly datasets. Across the analyzed exchange regimes, the median contribution of strong sweeps and ejections to total momentum transfer above the canopy varied between 30% and 39% while covering 28%-32% of the time. In the below-canopy space, the contribution of coherent structures varied between 19% and 21% while covering the same amount of time. This suggests that momentum transfer through synchronous coherent structures is very efficient above the forest canopy, but attenuated in the below-canopy space. Since the majority of the presented results agrees well with the results from previous studies that analyzed coherent structures at single levels, the BOD is a promising tool for the consistent investigation of synchronous coherent structures at multiple measurement heights.

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Section: Biorthogonal Decompositionmentioning

confidence: 99%

“…The explained variance of each k-th term in the series Upx, tq, called the relative eigenvalue λ rk , can be calculated according to [41]:…”

Section: Biorthogonal Decompositionmentioning

confidence: 99%

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Coherent Momentum Exchange above and within a Scots Pine Forest

Mohr

Schindler

2016

Atmosphere

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“…Based on video-recorded canopy motion and the application of the bi-orthogonal decomposition (Aubry et al 1991;Hémon and Santi 2003), they were able to detect large coherent patterns in the crop canopy motion that scaled with typical wavelengths of wind fluctuations over the canopies. In flat terrain, it has been shown that intermittent, organised airflow structures in the streamwise direction control turbulence over even-aged, uniform plant canopies to a large extent (Raupach et al 1996;Finnigan 2000).…”

Section: Introductionmentioning

confidence: 99%

Coherent response of a group of plantation-grown Scots pine trees to wind loading

et al. 2011

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Wind-induced motion of 29 neighbouring trees growing in a Scots pine plantation was measured over the period 14 March to 24 March 2008. The bi-orthogonal decomposition (BOD) of the complex tree motion field into a limited number of spatio-temporal modes provided the basis for the analysis of the response behaviour to wind excitation of the group of sample trees. It is shown that the first BOD-mode was the most energetic and differed from all other BOD-modes. The BOD-results as well as the results from wavelet analysis of the temporal eigenvectors of the BOD-modes demonstrate that two concomitant lowfrequency components in the streamwise wind velocity component stimulated coherent response of the sample trees at the tree group level. However, in the range of the wind speed measured close to the top of the Scots pine forest canopy (hourly mean wind speed values lower than 6 m s -1 ), the wind loads associated with these low-frequency airflow structures were too low to harmonise the motion of the sample trees completely. It is shown that instantaneous single tree responses to wind excitation were highly irregular in magnitude and direction. Results from Fourier and wavelet analysis demonstrate that sway in the first mode dominated the wind-induced sway behaviour at the tree level.

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“…POD technique represents a random process as a linear combination of the orthogonal eigenmodes and principal components, which are uncorrelated with each other. The POD technique has been applied in many fields including random variable, signal analysis, process identification, and many others [7][8][9][10]. This paper focuses on the applications of POD to wind engineering of structures.…”

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confidence: 99%

Wind Pressures on Structures by Proper Orthogonal Decomposition

Li¹,

Gu²,

Ni³

et al. 2012

JCEA

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Abstract:Proper orthogonal decomposition (POD) is an effective statistical technique for data reduction and feature extraction of the random field including the wind field. This paper introduces the theory of the POD and illustrates engineering of structures. Using the POD technique, it is shown that wind pressure data can be accurately reconstructed with a limited number of modes using the wind pressure data from wind tunnel test. Comparing the reconstructed values by POD with the original measured values from the wind tunnel test both in the time and frequency domains, it is concluded that the proper orthogonal decomposition(POD) is an efficient and practical technique for deriving the random wind pressure field from limited known data as shown in the pitched roof example in this paper.

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Applications of biorthogonal decompositions in fluid–structure interactions

Cited by 27 publications

References 19 publications

Coherent Momentum Exchange above and within a Scots Pine Forest

Coherent Momentum Exchange above and within a Scots Pine Forest

Coherent response of a group of plantation-grown Scots pine trees to wind loading

Wind Pressures on Structures by Proper Orthogonal Decomposition

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