Abstract
The prevalent multifractal characteristics of turbulent velocity fluctuations in the atmosphere are important for estimating various wind effects in wind engineering. Here, the multifractal characteristics of turbulent velocity fluctuations, including the small-scale multiscaling, the long-tail distributions and the intermittency, are thoroughly investigated by using a high-frequency dataset of three-dimensional velocities (100 Hz) collected at three levels during one month. To reduce uncertainties in the estimate of multiscaling exponents, a new method, the sequential extended self-similarity, is proposed. Based on this method, we obtain the multiscaling exponents of qth-order moments of velocity increments as a function of q, that is the so-called multifractal spectrum. The multifractal random walk (MRW) model is then shown to describe the various multifractal spectra of turbulent velocity fluctuations. With the help of this model, we find a connection between the small-scale multiscaling and the long-tail distributions, which is generally observed in our dataset, again validating the MRW model. A non-linear multifractal spectrum is commonly considered to be related to the intermittency of turbulent velocity fluctuations at small scales and its curvature is usually used as a quantification of intermittency intensity. However, we suggest that models capturing the non-linear multifractal spectrum may fail to represent the long-tail distribution, which is a more direct quantification of intermittency. Finally, qualitative variations of validated indicators with specific boundary-layer parameters are investigated. Results show that the intermittency of turbulent velocity fluctuations is more relevant to the friction velocity, compared with the average wind speed, the average temperature, and the surface-layer stability.
Highlights
The small-scale multiscaling phenomenon has been found to be prevalent in the time series of turbulent velocity fluctuations in the atmosphere (Schmitt et al 1994; Cho et al 2001; Vindel and Yagüe 2011; Liu and Hu 2013; Xu and Hu 2015)
Studies have shown that small-scale multiscaling is important for estimating wind loads (Peinke et al 2004; Fitton et al 2014) and wind power (Milan et al 2013; Calif and Schmitt 2014), and it is becoming a new feature in the statistical simulation of atmospheric turbulence (Nawroth and Peinke 2006; Guo et al 2011; Calif and Schmitt 2012; Baile and Muzy 2016)
We have shown that the log–normal multifractal random walk (MRW) model is a good model to describe the small-scale multiscaling and the long-tail distributions of turbulent velocity fluctuations
Summary
The small-scale multiscaling phenomenon has been found to be prevalent in the time series of turbulent velocity fluctuations in the atmosphere (Schmitt et al 1994; Cho et al 2001; Vindel and Yagüe 2011; Liu and Hu 2013; Xu and Hu 2015). Multiscaling at small scales in the inertial range close to the energycontaining range may be contaminated by large-scale motions (Katul et al 1994; Mahrt 2014) This phenomenon is referred to as external intermittency, which is distinguished from so-called internal intermittency in the inertial range far from the energy-containing range. A united mathematical framework on small-scale multiscaling and the long-tail distribution is helpful for understanding, simulating and predicting the external intermittency of atmospheric turbulence. We note that the multifractal random walk (MRW) model can be used to resolve this problem (Muzy and Bacry 2002; Bacry and Muzy 2003) In this model, the small-scale multiscaling, the long-tail distribution, and the intermittency all emerge from a continuous construction of random multiplicative cascades. We briefly review relevant characteristics of the multifractal random walk (MRW) model; for mathematical details, see Muzy and Bacry (2002) and references therein
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