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Articles

Multi-scale/fractal processes in the wake of a wind turbine array boundary layer

ORCID Icon, , , &
Pages 93-120 | Received 10 Jul 2018, Accepted 20 Feb 2019, Published online: 20 Mar 2019

References

  • Ali N, Cortina G, Hamilton N, et al. Turbulence characteristics of a thermally stratified wind turbine array boundary layer via proper orthogonal decomposition. J Fluid Mech. 2017;828:175–195.
  • Ali N, Hamilton N, Cortina G. Anisotropy stress invariants of thermally stratified wind turbine array boundary layers using Large Eddy simulations. J Renew Sust Energy. 2018;10(1):013301.
  • Ali N, Hamilton N, DeLucia D, et al. Assessing spacing impact on coherent features in a wind turbine array boundary layer. Wind Energy Sci. 2018;3(1):43–56.
  • Stresing R, Peinke J. Towards a stochastic multi-point description of turbulence. New J Phys. 2010;12(10):103046.
  • Keylock CJ, Stresing R, Peinke J. Gradual wavelet reconstruction of the velocity increments for turbulent wakes. Phys Fluids. 2015;27(2):025104.
  • Ali N, Kadum HF, Cal RB. Focused-based multifractal analysis of the wake in a wind turbine array utilizing proper orthogonal decomposition. J Renew Sust Energy. 2016;8(6):63306-1–63306-19.
  • Ali N, Aseyev AS, Melius M. Evaluation of higher order moments and isotropy in the wake of a wind turbine array. Whither turbulence and big data in the 21st century? Berlin: Springer; 2017. p. 273–292.
  • Chevillard L, Castaing B, Lévêque E. On the rapid increase of intermittency in the near-dissipation range of fully developed turbulence. Eur Phys J B-Condens Matter Complex Syst. 2005;45(4):561–567.
  • Chevillard L, Roux SG, Lévêque E. Intermittency of velocity time increments in turbulence. Phys Rev Lett. 2005;95(6):064501.
  • Chevillard L, Castaing B, Lévêque E, et al. Unified multifractal description of velocity increments statistics in turbulence: intermittency and skewness. Phys D. 2006;218(1):77–82.
  • Meneveau C, Sreenivasan KR. The multifractal nature of turbulent energy dissipation. J Fluid Mech. 1991;224:429–484.
  • Meneveau C, Sreenivasan KR. Simple multifractal cascade model for fully developed turbulence. Phys Rev Lett. 1987;59(13):1424.
  • Kolmogorov AN. Dissipation of energy in locally isotropic turbulence. 1941. p. 16–18. (Dokl. Akad. Nauk SSSR; vol. 32).
  • Kolmogorov AN. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high reynolds number. J Fluid Mech. 1962;13(1):82–85.
  • Frisch U, Sulem PL, Nelkin M. A simple dynamical model of intermittent fully developed turbulence. J Fluid Mech. 1978;87(4):719–736.
  • She ZS, Leveque E. Universal scaling laws in fully developed turbulence. Phys Rev Lett. 1994;72(3):336.
  • Benzi R, Ciliberto S, Tripiccione R, et al. Extended self-similarity in turbulent flows. Phys Rev E. 1993;48(1):R29.
  • Dubrulle B. Intermittency in fully developed turbulence: log-poisson statistics and generalized scale covariance. Phys Rev Lett. 1994;73(7):959.
  • Babiano A, Dubrulle B, Frick P. Some properties of two-dimensional inverse energy cascade dynamics. Phys Rev E. 1997;55(3):2693.
  • Ali N, Aseyev AS, Cal RB. Structure functions, scaling exponents and intermittency in the wake of a wind turbine array. J Renew Sust Energy. 2016;8(1):013304.
  • Keylock CJ, Nishimura K, Peinke J. A classification scheme for turbulence based on the velocity-intermittency structure with an application to near-wall flow and with implications for bed load transport. J Geophys Res. 2012;117(F1):F01037.
  • Praskovsky AA, Gledzer EB, Karyakin MY, et al. The sweeping decorrelation hypothesis and energy–inertial scale interaction in high reynolds number flows. J Fluid Mech. 1993;248:493–511.
  • Sreenivasan KR, Stolovitzky G. Statistical dependence of inertial range properties on large scales in a high-reynolds-number shear flow. Phys Rev Lett. 1996;77(11):2218.
  • Hosokawa I. A paradox concerning the refined similarity hypothesis of Kolmogorov for isotropic turbulence. Progress Theor Phys. 2007;118(1):169–173.
  • Stresing R, Peinke J, Seoud R. Defining a new class of turbulent flows. Phys Rev Lett. 2010;104(19):194501.
  • Renner C, Peinke J, Friedrich R. Experimental indications for markov properties of small-scale turbulence. J Fluid Mech. 2001;433:383–409.
  • Risken H. Fokker-Planck equation. The Fokker-Planck equation. Berlin: Springer;1984. p. 63–95.
  • Friedrich R, Peinke J. Description of a turbulent cascade by a Fokker-Planck equation. Phys Rev Lett. 1997;78(5):863.
  • Melius MS, Tutkun M, Cal RB. Identification of Markov process within a wind turbine array boundary layer. J Renew Sust Energy. 2014;6(2):1–18.
  • Melius MS, Tutkun M, Cal RB. Solution of the Fokker-Planck equation in a wind turbine array boundary layer. Phys D. 2014;280:14–21.
  • Nickelsen D, Engel A. Probing small-scale intermittency with a fluctuation theorem. Phys Rev Lett. 2013;110(21):138701.
  • Reinke N, Fuchs A, Nickelsen D, et al. On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics. J Fluid Mech. 2018;848:117–153.
  • Vidal Y, Acho L, Cifre I, et al. Wind turbine synchronous reset pitch control. Energies. 2017;10(6):770.
  • Mücke T, Kleinhans D, Peinke J. Atmospheric turbulence and its influence on the alternating loads on wind turbines. Wind Energy. 2011;14(2):301–316.
  • DeCarolis JF, Keith DW. The economics of large-scale wind power in a carbon constrained world. Energy Policy. 2006;34(4):395–410.
  • Calif R, Schmitt FG. Multiscaling and joint multiscaling description of the atmospheric wind speed and the aggregate power output from a wind farm. Nonlinear Process Geophys. 2014;21(2):379–392.
  • Schottler J, Reinke N, Hölling A, et al. On the impact of non-gaussian wind statistics on wind turbines–an experimental approach. Wind Energy Sci. 2017;2(1):1–13.
  • Schmietendorf K, Peinke J, Kamps O. The impact of turbulent renewable energy production on power grid stability and quality. Eur Phys J B. 2017;90(11):222.
  • Keylock CJ. A criterion for delimiting active periods within turbulent flows. Geophys Res Lett. 2008;35(11):L11804.
  • Gottschall J, Peinke J. On the definition and handling of different drift and diffusion estimates. New J Phys. 2008;10(8):083034.
  • Honisch C, Friedrich R. Estimation of Kramers-Moyal coefficients at low sampling rates. Phys Rev E. 2011;83(6):066701.
  • Kleinhans D, Friedrich R, Nawroth A, et al. An iterative procedure for the estimation of drift and diffusion coefficients of Langevin processes. Phys Lett A. 2005;346(1):42–46.
  • Nawroth AP, Peinke J, Kleinhans D. Improved estimation of fokker-planck equations through optimization. Phys Rev E. 2007;76(5):056102.
  • Nickelsen D. Master equation for she-leveque scaling and its classification in terms of other markov models of developed turbulence. Preprint, 2017, arXiv:170205766.
  • Feller W. An introduction to probability theory and its applications. Vol. 1. New York: Wiley; 1968.
  • Jarzynski C. Nonequilibrium equality for free energy differences. Phys Rev Lett. 1997;78(14):2690.
  • Seifert U. Entropy production along a stochastic trajectory and an integral fluctuation theorem. Phys Rev Lett. 2005;95(4):040602.
  • Parisi G, Ghil M. Turbulence and predictability in geophysical fluid dynamics and climate dynamics. Proceedings of the International School of Physic Enrico Fermi, Course lxxxviii, Varenna on lake como, Villa monastero, 1983 Jun 14–24. North-Holland; 1985.
  • Muzy JF, Bacry E, Arneodo A. Wavelets and multifractal formalism for singular signals: application to turbulence data. Phys Rev Lett. 1991;67(25):3515.
  • Keylock CJ, Chang KS, Constantinescu GS. Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes. J Fluid Mech. 2016;805:656–685.
  • Kolwankar KM, Lévy-Véhel J. A time domain characterization of the fine local regularity of functions. J Fourier Anal Appl. 2002;8(4):319–334.
  • Jaffard S. Multifractal formalism for functions part I: results valid for all functions. SIAM J Math Anal. 1997;28(4):944–970.
  • Seuret S, Lévy-Véhel J. A time domain characterization of 2-microlocal spaces. J Fourier Anal Appl. 2003;9(5):473–495.
  • Tricot C. Curves and fractal dimension. Berlin: Springer Science & Business Media; 1994.
  • Trujillo L, Legrand P, Lévy-Véhel J. The estimation of Hölderian regularity using genetic programming. Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation. ACM; 2010. p. 861–868.
  • Keylock CJ. Characterizing the structure of nonlinear systems using gradual wavelet reconstruction. Nonlinear Process Geophys. 2010;17(6):615.
  • Nakagawa H, Nezu I. Prediction of the contributions to the reynolds stress from bursting events in open-channel flows. J Fluid Mech. 1977;80(1):99–128.
  • Bogard DG, Tiederman WG. Burst detection with single-point velocity measurements. J Fluid Mech. 1986;162:389–413.
  • Keylock CJ, Singh A, Venditti JG, et al. Robust classification for the joint velocity-intermittency structure of turbulent flow over fixed and mobile bedforms. Earth Surf Proc Land. 2014;39(13):1717–1728.
  • Ali N, Hamilton N, Calaf M. Turbulence kinetic energy budget and conditional sampling of momentum, scalar, and intermittency fluxes in thermally stratified wind farms. J Turbul. 2019;20(1):1–32.
  • Keylock CJ, Ganapathasubramani B, Monty J. The coupling between inner and outer scales in a zero pressure boundary layer evaluated using a Hölder exponent framework. Fluid Dyn Res. 2016;48(2):021405.
  • Cal RB, Lebrón J, Castillo L. Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer. J Renew Sust Energy. 2010;2(1):013106.
  • Carter DW, Coletti F. Scale-to-scale anisotropy in homogeneous turbulence. J Fluid Mech. 2017;827:250–284.
  • Pope SB. Turbulent flows. Cambridge: Cambridge University Press; 2000.
  • Tardu S. Statistical approach to wall turbulence. Hoboken: John Wiley & Sons; 2013.
  • Aseyev AS, Cal RB. Vortex identification in the wake of a model wind turbine array. J Turbul. 2016;17(4):357–378.
  • Viggiano B, Gion MS, Ali N. Inverse structure functions in the canonical wind turbine array boundary layer. J Renew Sust Energy. 2016;8(5):053310.
  • Kullback S, Leibler RA. On information and sufficiency. Ann Math Stat. 1951;22(1):79–86.
  • Murphy KP. Machine learning a probabilistic perspective. Cambridge: MIT press; 2012.
  • Shannon CE, Weaver W. The mathematical theory of communication. Urbana: University of Illinois press; 1998.
  • Li TF. An efficient algorithm to find the MLE of prior probabilities of a mixture in pattern recognition. Pattern Recognit. 1996;29(2):337–339.
  • Sotoca JM, Pla F. Supervised feature selection by clustering using conditional mutual information-based distances. Pattern Recognit. 2010;43(6):2068–2081.
  • Abou-Moustafa KT, De La Torre F, Ferrie FP. Pareto models for discriminative multiclass linear dimensionality reduction. Pattern Recognit. 2015;48(5):1863–1877.
  • Moacir P, Kittler J, Riva M, et al. A decision cognizant Kullback-Leibler divergence. Pattern Recognit. 2017;61:470–478.
  • Tsuji Y, Nakamura I. Probability density function in the log-law region of low reynolds number turbulent boundary layer. Phys Fluids. 1999;11(3):647–658.
  • Lindgren B, Johansson AV, Tsuji Y. Universality of probability density distributions in the overlap region in high reynolds number turbulent boundary layers. Phys Fluids. 2004;16(7):2587–2591.
  • Tsuji Y, Lindgren B, Johansson AV. Self-similar profile of probability density functions in zero-pressure gradient turbulent boundary layers. Fluid Dyn Res. 2005;37(5):293–316.
  • Zhou A, Klewicki J. Properties of the streamwise velocity fluctuations in the inertial layer of turbulent boundary layers and their connection to self-similar mean dynamics. Int J Heat Fluid Flow. 2015;51:372–382.
  • Buxton ORH. Modulation of the velocity gradient tensor by concurrent large-scale velocity fluctuations in a turbulent mixing layer. J Fluid Mech. 2015;777:R1-1–R1-12.
  • Granero-Belinchon C, Roux SG, Garnier NB. A Kullback-Leibler divergence measure of intermittency: application to turbulence. Preprint, 2017. arXiv:170707950.
  • Willmarth WW, Lu SS. Structure of the reynolds stress near the wall. J Fluid Mech. 1972;55(1):65–92.
  • Raupach MR. Conditional statistics of reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J Fluid Mech. 1981;108:363–382.
  • Katul G, Poggi D, Cava D, et al. The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer. Boundary Layer Meteorol. 2006;120(3):367–375.

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