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Introduction to Turbulence

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Handbook of Wind Energy Aerodynamics

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Abstract

The turbulent wind is the resource for wind turbines as well as the operating condition for the conversion process from wind into electrical energy. In this chapter, the fundamental aspects of turbulence are considered. The characteristics of turbulence are discussed based on common practices within the wind energy industry with the aim of a standardized characterization as well as the approaches of the scientific turbulence community. These different methods are discussed with respect to the description and quantification of statistical aspects. The aim of this chapter is to provide substantial background information on turbulence, important for an advanced understanding of the operating conditions of wind turbines.

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Notes

  1. 1.

    The concept of Taylor’s frozen turbulence hypothesis can be extended to higher turbulence degrees by the concept of local Taylor’s hypothesis.

  2. 2.

    Extreme wind speeds and gust wind speeds are defined by Vref via separate equations (cf. IEC Standard 2019).

  3. 3.

    For the covariances, one has to pay attention if u or u′ is taken; for the structure function, any mean value will drop out, due to the definition of the increment ur = u(x + r) − u(x) = u′(x + r) − u′(x).

  4. 4.

    As this was done during wartime, there was not much communication about this result; thus, these findings are also worked out independently by Weiszäcker and Heisenberg as well as by Onsager (cf. Frisch and Kolmogorov 1995).

  5. 5.

    The turbulent energy ε is defined as energy per mass and time.

  6. 6.

    One has to pay attention that the word intermittency is used also for other, different phenomena, like in chaos or for switches between laminar and turbulent phases.

  7. 7.

    The symbol \(\tilde {\lambda }\) is used to make a difference to the Taylor length.

  8. 8.

    An open-source software package is available to perform such analysis with given data (github.com/andre-fuchs-uni-oldenburg/).

References

  • IEC 61400-1:2019 ⒸIEC 2019 INTERNATIONAL ELECTROTECHNICAL COMMISSION, Geneva

    Google Scholar 

  • Arneodo A et al (1996) Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity. EPL (Europhysics Letters) 34(6):411

    Article  Google Scholar 

  • Babiano A, Dubrulle B, Frick P (1997) Some properties of two-dimensional inverse energy cascade dynamics. Phys Rev E 55(3):2693

    Article  Google Scholar 

  • Behnken C, Wächter M, Peinke J (2020) Multipoint reconstruction of wind speeds. Wind Energy Sci 5:1211–1223

    Article  Google Scholar 

  • Benzi R, Ciliberto S, Tripiccione R et al (1993) Extended self-similarity in turbulent flows. Phys Rev E 48(1):R29

    Article  Google Scholar 

  • Berg J, Natarajan A, Mann J, Patton,G (2016) Gaussian vs non- Gaussian turbulence: impact on wind turbine loads. Wind Energy 19:1975–1989. https://doi.org/10.1002/we.1963

    Article  Google Scholar 

  • Briscolini M, Santangelo P, Succi S et al (1994) Extended self-similarity in the numerical simulation of three-dimensional homogeneous flows. Phys Rev E 50(3):R1745

    Article  Google Scholar 

  • Carlson JA, Jaffe A, Wiles A (2006) The millennium prize problems. American Mathematical Society

    MATH  Google Scholar 

  • Castaing B, Gagne, Y, Hopfinger EJ (1990) Velocity probability density functions of high Reynolds number turbulence. Phys D Nonlinear Phenom 46(2):177–200

    Article  Google Scholar 

  • Castaing B (1996) The temperature of turbulent flows. J Physique II EDP Sci 6(1):105–114

    Google Scholar 

  • Chilla F, Peinke J, Castaing B (1996) Multiplicative process in turbulent velocity statistics: a simplified analysis. J Phys II 6(4):455–460

    Google Scholar 

  • Chevillard L, Castaing, B, Lévêque E, Arneodo A (2006) Unified multifractal description of velocity increments statistics in turbulence: intermittency and skewness. Phys D Nonlinear Phenom 218(1):77–82

    Article  Google Scholar 

  • Davidson PA, Kaneda Y, Moffatt K, Sreenivasan KR (eds) (2011) A voyage through turbulence. Cambridge University Press

    MATH  Google Scholar 

  • Davidson PA (2004) Turbulence. Cambridge University Press

    MATH  Google Scholar 

  • Dubrulle B (1994) Intermittency in fully developed turbulence: Log-Poisson statistics and generalized scale covariance. Phys Rev Lett 73(7):959

    Article  Google Scholar 

  • Forschungs- und Entwicklungszentrum Fachhochschule Kiel GmbH (2020) https://www.fino1.de/en/, visited 26 Nov 2020

  • Frisch U, Kolmogorov AN (1995) Turbulence: the legacy of AN Kolmogorov. Cambridge University Press

    Book  Google Scholar 

  • Frisch U, Sulem P-L, Nelkin M (1978) A simple dynamical model of intermittent fully developed turbulence. J Fluid Mech 87:719–736

    Article  Google Scholar 

  • Gagne Y, Marchand M, Castaing B (1994) Conditional velocity pdf in 3-D turbulence. J Phys II 4(1):1–8

    Google Scholar 

  • Gaudin E, Protas B, Goujon-Durand S et al (1998) Spatial properties of velocity structure functions in turbulent wake flows. Phys Rev E 57(1):R9

    Article  Google Scholar 

  • github.com/andre-fuchs-uni-oldenburg/ OPEN_FPE_IFT

    Google Scholar 

  • Hadjihosseini A, Wächter M, Hoffmann NP, Peinke J (2016) Capturing rogue waves by multi-point statistics. New J Phys 18:013017

    Article  MathSciNet  Google Scholar 

  • IEC Standard 61400-1 Ed. 4 (2019) Wind turbines, Part 1: design requirements, EN 61400-1:2018

    Google Scholar 

  • Khintchin A (1934) Korrelationstheorie der stationären stochastischen Prozesse. Mathematische Annalen 109:604–615. https://doi.org/10.1007/BF01449156

    Article  MathSciNet  Google Scholar 

  • Kolmogorov AN (1941a) Local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Proc USSR Acad Sci 30:301–305 (reprint Proc R Soc Lond A 434:9–13 (1991))

    Google Scholar 

  • Kolmogorov AN (1941b) Dissipation of energy in locally isotropic turbulence. Proc USSR Acad Sci 32:16–18 (reprint Proc R Soc Lond A 434:15–17 (1991))

    Google Scholar 

  • Kolmogorov AN (1962) A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J Fluid Mech 13:82–85

    Article  MathSciNet  Google Scholar 

  • L’vov VS, Procaccia I (2000) Analytic calculation of the anomalous exponents in turbulence: using the fusion rules to flush out a small parameter. Phys Rev E 62:8037

    Article  MathSciNet  Google Scholar 

  • Mann J (1994) The spatial structure of neutral atmospheric surface-layer turbulence. J Fluid Mech 273:141–168

    Article  Google Scholar 

  • Meneveau C, Sreenivasan KR (1991) The multifractal nature of turbulent energy dissipation. J Fluid Mech 224:429–484

    Article  Google Scholar 

  • Morales A, Wächter M, Peinke J (2012) Characterization of wind turbulence by higher-order statistics. Wind Energy 15:391–406

    Article  Google Scholar 

  • Naert A, Castaing B, Chabaud B, Hebral B, Peinke J (1998) Conditional statistics of velocity fluctuations in turbulence. Phys D Nonlinear Phenom 113(1):73–78

    Article  Google Scholar 

  • Peinke J, Tabar MRR, Wächter M (2019) The Fokker-Planck approach to complex disordered systems. Ann Rev Condensed Matter Phys 10:107–132

    Article  Google Scholar 

  • Polyakov AM (1995) Phys Rev E 52(6):6183

    Article  MathSciNet  Google Scholar 

  • St. B. Pope (2000) Turbulent flows. Cambridge University Press

    Book  Google Scholar 

  • Renner C, Peinke J (2012) A generalization of scaling models of turbulence. J Stat Phys 146:25–32. https://doi.org/10.1007/s10955-011-0345-1

    Article  MathSciNet  Google Scholar 

  • Renner C, Peinke J, Friedrich R (2001) Experimental indications for Markov properties of small-scale turbulence. J Fluid Mech 433:383–409

    Article  Google Scholar 

  • Richardson LF (1922) Weather prediction by numerical process. Cambridge University Press

    MATH  Google Scholar 

  • Schwarz CM, Ehrich S, Martín R et al (2018) Fatigue load estimations of intermittent wind dynamics based on a Blade Element Momentum method. J Phys Conf Ser. https://doi.org/10.1088/1742-6596/1037/7/072040

  • Schwarz CM, Ehrich S, Peinke J (2019) Wind turbine load dynamics in the context of turbulence intermittency. Wind Energy Sci 4:581–594

    Article  Google Scholar 

  • She ZS, Leveque E (1994) Universal scaling laws in fully developed turbulence. Phys Rev Lett 72(3):336–339

    Article  Google Scholar 

  • Siefert M, Peinke J (2004) Different cascade speeds for longitudinal and transverse velocity increments of small-scale turbulence. Phys Rev E 70:015302

    Article  Google Scholar 

  • Vassilicos JC (2001) Intermittency in turbulent flows. Cambridge University Press

    MATH  Google Scholar 

  • Veers PS (1988) Three-dimensional wind simulation, Technical Report SAND88-0152, Sandia National Laboratories

    Google Scholar 

  • Veers PS et al (2019) Grand challenges in the science of wind energy. Science 366. https://doi.org/10.1126/science.aau2027

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Author information

Authors and Affiliations

  1. ForWind, Institute of Physics, University of Oldenburg, Oldenburg, Germany

    Joachim Peinke & Matthias Wächter

  2. Department of Mechanical and Materials Engineering, Portland State University, Portland, OR, USA

    Raúl Bayoán Cal

Authors
  1. Joachim Peinke
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  2. Matthias Wächter
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  3. Raúl Bayoán Cal
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Corresponding author

Correspondence to Joachim Peinke .

Editor information

Editors and Affiliations

  1. Fraunhofer Institute for Wind Energy and, Oldenburg, Germany

    Bernhard Stoevesandt

  2. TNO-Energy Research Centre of the Nether, Netherlands Organisation for Applied Sci, Petten, The Netherlands

    Gerard Schepers

  3. Siemens Gamesa Renewable Energy, Brande, Denmark

    Peter Fuglsang

  4. Goldwind Americas, Chicago, IL, USA

    Sun Yuping

Section Editor information

  1. Aerodynamics, CFD and stochastic Dynamics, Fraunhofer Institute for Wind Energy Systems, Oldenburg, Germany

    Bernhard Stoevesandt

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Peinke, J., Wächter, M., Cal, R.B. (2021). Introduction to Turbulence. In: Stoevesandt, B., Schepers, G., Fuglsang, P., Yuping, S. (eds) Handbook of Wind Energy Aerodynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-05455-7_41-1

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  • DOI: https://doi.org/10.1007/978-3-030-05455-7_41-1

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