On the Statistics of Wind Gusts

Boettcher, F.; Renner, C.; Waldl, Hans-Peter; Peinke, Joachim

doi:10.1023/a:1023009722736

Cited by 102 publications

(85 citation statements)

References 10 publications

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“…Additionally, for very large τ the increment distribution approaches a Gaussian, which is shown in Figure 3 and in agreement with references [13][14][15][16]. The figure depicts the estimated increment distribution in a semi-logarithmic plot.…”

Section: Wind Datasupporting

confidence: 87%

“…Regarding the ABL wind speed increments with fixed increment length τ , several studies, such as [13][14][15][16], give empirical evidence that it is in good approximation of the symmetric Castaing distribution. The latter is developed by Castaing et al [17] under the assumption of the Taylor hypothesis [18] stating that spatial correlations can be translated into temporal correlations.…”

Section: Wind Datamentioning

confidence: 99%

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A first order geometric auto regressive process for boundary layer wind speed simulation

Laubrich

Kantz

2009

Eur. Phys. J. B

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Abstract. Under certain conditions the first order geometric auto regressive (AR) process has statistical properties similar to atmospheric boundary layer wind speed. In this contribution, we investigate this similarity and analyse the extent to which this stochastic process is a suitable model for wind speed simulation. In particular, we focus on the fluctuation of the process around its moving average over a given number of time steps. We show that the fluctuation conditioned on the value V of the moving average are of a symmetric normal distribution with a proportionality between its standard deviation and V . This proportionality is empirically observed in wind speed data. Furthermore, we show that the increment distribution of the geometric AR(1) process is in good agreement with the symmetric Castaing distribution which is empirically found in wind speed data.

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Section: Wind Datasupporting

confidence: 87%

Section: Wind Datamentioning

confidence: 99%

A first order geometric auto regressive process for boundary layer wind speed simulation

Laubrich

Kantz

2009

Eur. Phys. J. B

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“…Thus, in this paper we focus on wind speed changes within seconds, i.e., by the corresponding increments. Numerous studies have reported on non-Gaussian characteristics of wind speed increments; see, e.g., Boettcher et al (2003), Liu et al (2010), Morales et al (2012), and. Furthermore, findings of non-Gaussian wind statistics have been implemented in simulations by a variety of methods; see, e.g., Nielsen et al (2007), Mücke et al (2011), andGong andChen (2014).…”

Section: Introductionmentioning

confidence: 99%

On the impact of non-Gaussian wind statistics on wind turbines – an experimental approach

et al. 2017

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Abstract. The effect of intermittent and Gaussian inflow conditions on wind energy converters is studied experimentally. Two different flow situations were created in a wind tunnel using an active grid. Both flows exhibit nearly equal mean velocity values and turbulence intensities but strongly differ in their two point statistics, namely their distribution of velocity increments on a variety of timescales, one being Gaussian distributed, and the other one being strongly intermittent. A horizontal axis model wind turbine is exposed to both flows, isolating the effect on the turbine of the differences not captured by mean values and turbulence intensities. Thrust, torque and power data were recorded and analyzed, showing that the model turbine does not smooth out intermittency. Intermittent inflow is converted to similarly intermittent turbine data on all scales considered, reaching down to sub-rotor scales in space. This indicates that it is not correct to assume a smoothing of intermittent wind speed increments below the size of the rotor.

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“…They account for the fact that rare events, which initiate crashes, are much more frequent than in Gaussian distributions. These are events in the so-called Lévy tails ∝ 1/|x| 1+λ of the distributions, whose description requires a Hamiltonian [3]Such tail-events are present in the self-similar distribution of matter in the universe [8][9][10], in velocity distributions of many body sytems with long-range forces [11], and in the distributions of windgusts [12], oceanic moster waves [13], and earthquakes [14], with often catastrophic consequences. They are a consequence of rather general…”

mentioning

confidence: 99%

Fractional quantum field theory, path integral, and stochastic differential equation for strongly interacting many-particle systems

Kleinert¹

2012

EPL

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While free and weakly interacting particles are well described by a second-quantized nonlinear Schrödinger field, or relativistic versions of it, with various approximations, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal Lévy walks rather than Gaussian random walks with perturbations.PACS numbers: 95.35+d.04.60,04.20C,04.90 Quantum-mechanical physics is explained with high accuracy by Schrödinger theory. The wave equation for many particles can convenienty be reformulated as a second-quantized field theory, with an action that is the sum of quadratic and an interacting termwhere the term A 2 has typically the formwith D being the space timension, m the mass, and V (x) some external potential. The interaction term A int may be approximated in molecular systems by a fourth-order term in the fieldwhere V 12 (x, x ′ ) is some two-body potential. If relativistic velocities are present, the field is generalized to a scalar Klein-Gordon field, or a quantized Dirac field. In molecular physics, the fourth-order term is due to the exchange of a minimally coupled quantized photon field and is proportional to e 2 , where e is the electric charge. The field equations may be studied with any standard method of quantum field theory, and corrections can be derived using perturbation theory in powers of α ≡ e 2 / ≈ 1/137. Since α is very small, this appeoch is quite successful.If time is continued analytically to imaginary values t = iτ , one is faced with the so-called Euclidean version of quantum field theory. Then perturbation theory may be understood as developing a theory of particle physics from an expansion around Gaussian random walks. Indeed, the relativistic scalar free-particle propagator of mass m in D + 1-dimensional euclidean energymomentum space p µ = (p, p 4 ), has the formwhere the energy has been continued analytically to p 4 = −iE. The Fourier transform of e −s(p 2 +p 2 4 ) is the distribution of Gaussian random walks of length s in D + 1 euclidean dimensionswhich makes the propagator (4) a superposition of such walks with lenghts distributed like e −sm -3]. This propagator is the relativistic version of the free-field propagator of the action (2). The second-quantized field theory described by (1) accounts for grand-canical ensembles of orbits with their two-body interactions [4].Gaussian random walks are a natural and rather universal starting point for many stochastic processes. For instance, they form the basis of the most important tool in the theory of financial markets, the Black-Scholes option price theory [5] (Nobel Prize 1997), by which a portfolio of assets is hoped to remain steadily growing through hedging. In fact, the famous central-limit theorem permits us to prove that many independent random movements of finite variance always pile up to display a Gaussian distribution [6].However, since the last stock market crash and the still ongoing financial cris...

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On the Statistics of Wind Gusts

Cited by 102 publications

References 10 publications

A first order geometric auto regressive process for boundary layer wind speed simulation

A first order geometric auto regressive process for boundary layer wind speed simulation

On the impact of non-Gaussian wind statistics on wind turbines – an experimental approach

Fractional quantum field theory, path integral, and stochastic differential equation for strongly interacting many-particle systems

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