Characteristics of space-time energy spectra in turbulent channel flows

Wu, Ting; Geng, Chenhui; Yao, Yichen; Xu, Chun-Xiao; He, Guowei

doi:10.1103/physrevfluids.2.084609

Cited by 15 publications

(17 citation statements)

References 30 publications

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“…The second-order conditional moments indicate the bandwidths of the energy spectra. The spectral bandwidths are used to study the well-known 'spectral broadening' in turbulent flows (Lumley 1965;Wilczek & Narita 2012;Wilczek et al 2015;Wu et al 2017).…”

Section: Mean Wavenumbers and Spectral Bandwidthsmentioning

confidence: 99%

“…The mean wavenumber and spectral bandwidth can be exactly expressed using temporal Fourier modes, given by (Wu et al 2017)…”

Section: Mean Wavenumbers and Spectral Bandwidthsmentioning

confidence: 99%

“…The second-order conditional moments represent spectral bandwidths that characterize the well-known spectral broadening. It has been shown that the mean wavenumbers are determined by phase derivatives alone and that spectral bandwidths are determined by both phase and amplitude derivatives (Wu et al 2017). Therefore, the goal of the present paper is to develop a statistical model to correctly predict mean wavenumbers and spectral bandwidths.…”

Section: Introductionmentioning

confidence: 99%

“…In both Taylor's model and the LW model, only phase velocities are used to determine space-time energy spectra. In fact, it has been shown that both the phase and amplitude derivatives contribute to the spectral bandwidth (Wu et al 2017). Spectral bandwidths are important indications of space-time energy spectra and characterize spectral broadening.…”

Section: Introductionmentioning

confidence: 99%

“…The previous paper (Wu et al 2017) focused on the exact expression of spectral bandwidths and found that Taylor's model and the LW model significantly underestimate the spectral bandwidths. To correctly predict the spectral bandwidths, we develop a new model (the LMW model) in the present paper and present the theoretical justification and numerical validation.…”

Section: Introductionmentioning

confidence: 99%

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Local modulated wave model for the reconstruction of space–time energy spectra in turbulent flows

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Section: Mean Wavenumbers and Spectral Bandwidthsmentioning

confidence: 99%

“…The mean wavenumber and spectral bandwidth can be exactly expressed using temporal Fourier modes, given by (Wu et al 2017)…”

Section: Mean Wavenumbers and Spectral Bandwidthsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Local modulated wave model for the reconstruction of space–time energy spectra in turbulent flows

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Modeling space‐time correlations of velocity fluctuations in wind farms

et al. 2018

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An analytical model for the streamwise velocity space-time correlations in turbulent flows is derived and applied to the special case of velocity fluctuations in large wind farms. The model is based on the Kraichnan-Tennekes random sweeping hypothesis, capturing the decorrelation in time while including a mean wind velocity in the streamwise direction. In the resulting model, the streamwise velocity space-time correlation is expressed as a convolution of the pure space correlation with an analytical temporal decorrelation kernel. Hence, the spatiotemporal structure of velocity fluctuations in wind farms can be derived from the spatial correlations only. We then explore the applicability of the model to predict spatiotemporal correlations in turbulent flows in wind farms. Comparisons of the model with data from a large eddy simulation of flow in a large, spatially periodic wind farm are performed, where needed model parameters such as spatial and temporal integral scales and spatial correlations are determined from the large eddy simulation.Good agreement is obtained between the model and large eddy simulation data showing that spatial data may be used to model the full spatiotemporal structure of fluctuations in wind farms. KEYWORDS large eddy simulation, power output fluctuations, space-time correlations, turbulent flows, wind farms 1 INTRODUCTION The wind energy market is strongly growing with a record in new installations in 2015 1,2 and increasing importance expected over the next years. 3 Wind energy is a fluctuating resource that is converted into electrical power in a nonlinear fashion (see, eg, Burton et al 4 ). These characteristics constitute challenges with respect to power quality and grid stability, cf Milan et al, 5 which raise significant interest in predicting short-term power output fluctuations in wind farms. Understanding and predicting the spatiotemporal structure of velocity fluctuations in wind farms, which is a main source of the power output fluctuations, is a crucial step towards this goal. The atmospheric conditions of wind approaching a wind farm can be described by basic atmospheric boundary layer (ABL) theory. For a recent overview, we refer to Stevens and Meneveau. 6 Wind speed fluctuations in the ABL occur on different time scales, ranging from annual or seasonal variations, down to minutes and seconds. 4,7 The short-term fluctuations on scales shorter than around, say, 10 minutes are usually referred to as turbulent fluctuations. 4 An introduction to the characteristics of atmospheric wind including typical turbulence intensities and naturally occurring extreme wind gusts (cf Böttcher et al 8 ), as well as other factors such as geographical (onshore and offshore), landscape, and climate influences is given in Burton et al. 4 The evolution of wind velocities in the wind farm itself is influenced by the aerodynamics of the turbines (see, eg, Hansen andButterfield 9 ), the design of the whole wind farm, eg, in terms of turbine spacing, 10,11 and by the influence of turbines onto each ...

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Modeling probability density functions of velocity fluctuations in wind farms

Wilczek

2022

Wind Energy

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The flow in large wind farms is a complex multiscale phenomenon, making comprehensive analytical or computational studies of velocity fluctuations challenging. Motivated by the need for simple, physics-based analytical approaches to short-time wind velocity prediction, we derive a statistical model for the spatio-temporal evolution of streamwise velocity fluctuations in wind farms. Here, we show that the one-pointone-time probability density function of velocity fluctuations can be modeled by a weighted superposition of two Ornstein-Uhlenbeck processes. The model is extended to a one-particle advection model assuming Taylor's hypothesis of frozen turbulence. We find that our advection model captures the decorrelation process of streamwise velocity fluctuations observed in experiments.

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Characteristics of space-time energy spectra in turbulent channel flows

Cited by 15 publications

References 30 publications

Local modulated wave model for the reconstruction of space–time energy spectra in turbulent flows

Local modulated wave model for the reconstruction of space–time energy spectra in turbulent flows

Modeling space‐time correlations of velocity fluctuations in wind farms

Modeling probability density functions of velocity fluctuations in wind farms

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