Skip to main content Accessibility help

On the interaction of very-large-scale motions in a neutral atmospheric boundary layer with a row of wind turbines

  • Asim Önder (a1) and Johan Meyers (a1)


Recent experiments have revealed the existence of very long streamwise features, denoted as very-large-scale motions (VLSMs), in the thermally neutral atmospheric boundary layer (ABL) (Hutchins et al., Boundary-Layer Meteorol., vol. 145(2), 2012, pp. 273–306). The aim of our study is to elaborate the role of these large-scale anisotropic patterns in wind-energy harvesting with special emphasis on the organization of turbulent fields around wind turbines. To this end, we perform large-eddy simulation (LES) of a turbine row operating under neutral conditions. The ABL data are produced separately in a very long domain of $240\unicode[STIX]{x1D6FF}$ , where $\unicode[STIX]{x1D6FF}$ is the ABL thickness, to ensure a realistic representation for very large scales of $O(10\unicode[STIX]{x1D6FF})$ . VLSMs are extracted from the LES database using a cutoff at streamwise wavelength $\unicode[STIX]{x1D706}_{x}=5\unicode[STIX]{x1D6FF}$ , or $\unicode[STIX]{x1D706}_{x}=50D$ in terms of turbine diameter. Reynolds averaging of low-pass filtered fields shows that the interaction of VLSMs and turbines produce very-long-wavelength motions in the wake region, which contain approximately $20\,\%$ of the resolved Reynolds shear stress, and $30\,\%$ of the resolved streamwise kinetic energy in the shear layers. To further elucidate these statistics, we conduct a geometrical analysis using conditional averaging based on large-scale low- and high-velocity events. The conditional eddies provide evidence for very long ( ${\sim}10\unicode[STIX]{x1D6FF}$ ) and wide ( ${\sim}\unicode[STIX]{x1D6FF}$ ) streak–roller structures around the turbine row. Although all of these eddies share the same streak–roller topology, there are remarkable modifications in the morphology of the conditional eddies whose cores are located sideways to the turbines. In these cases, the turbine row pushes the whole low- or high-momentum streak aside, and prevails as a sharp boundary to the low–high-momentum streak pair. In this process, accompanying rollers remain relatively unaffected. This creates a two-way flux towards the turbine row. These observations provide some insights about the high lateral spreading observed in the large-scale Reynolds stress fields.



Hide All
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 154.
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41L44.
Allaerts, D. & Meyers, J. 2015a Large eddy simulation of a large wind-turbine array in a conventionally neutral atmospheric boundary layer. Phys. Fluids 27 (6), 065108.
Allaerts, D. & Meyers, J. 2018 Simulation of large wind farms in the conventionally neutral atmospheric boundary layer using LES. In Direct and Large-Eddy Simulation X, pp. 469474. Springer.
Bailey, S. C. C. & Smits, A. J. 2010 Experimental investigation of the structure of large-and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 651, 339356.
Bou-Zeid, E., Meneveau, C. & Parlange, M. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17 (2), 025105.
Boyd, J. P. 2001 Chebyshev and Fourier Spectral Methods. Courier Corporation.
Brost, R., Lenschow, D. H. & Wyngaard, J. C. 1982 Marine stratocumulus layers. Part 1: mean conditions. J. Atmos. Sci. 39 (4), 800817.
Calaf, M., Meneveau, C. & Meyers, J. 2010 Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys. Fluids 22 (1), 015110.
Calaf, M., Parlange, M. B. & Meneveau, C. 2011 Large eddy simulation study of scalar transport in fully developed wind-turbine array boundary layers. Phys. Fluids 23 (12), 126603.
Carper, M. A. & Porté-Agel, F. 2004 The role of coherent structures in subfilter-scale dissipation of turbulence measured in the atmospheric surface layer. J. Turbul. 5, 3232.
Chauhan, K., Hutchins, N., Monty, J. & Marusic, I. 2013 Structure inclination angles in the convective atmospheric surface layer. Boundary-Layer Meteorol. 147 (1), 4150.
Chung, D. & McKeon, B. J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341364.
Del Álamo, J. C. & Jimenez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205213.
Del Alamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.
Del Álamo, J. C., Jimenez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329358.
Etling, D. & Brown, R. A. 1993 Roll vortices in the planetary boundary layer: a review. Boundary-Layer Meteorol. 65 (3), 215248.
Fang, J. & Porté-Agel, F. 2015 Large-eddy simulation of very-large-scale motions in the neutrally stratified atmospheric boundary layer. Boundary-Layer Meteorol. 155 (3), 397416.
Farrell, B. F., Ioannou, P. J., Jiménez, J., Constantinou, N. C., Lozano-Durán, A. & Nikolaidis, M.-A. 2016 A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow. J. Fluid Mech. 809, 290315.
Fishpool, G. M., Lardeau, S. & Leschziner, M. A. 2009 Persistent non-homogeneous features in periodic channel-flow simulations. Flow Turbul. Combust. 83 (3), 323342.
Goit, J. P. & Meyers, J. 2015 Optimal control of energy extraction in wind-farm boundary layers. J. Fluid Mech. 768, 550.
Grant, A. L. M. 1986 Observations of boundary layer structure made during the 1981 Kontur experiment. Q. J. R. Meteorol. Soc. 112 (473), 825841.
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.
Hambleton, W. T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 5364.
Högström, U., Hunt, J. C. R. & Smedman, A.-S. 2002 Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorol. 103 (1), 101124.
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.
Hutchins, N., Chauhan, K., Marusic, I., Monty, J. & Klewicki, J. 2012 Towards reconciling the large-scale structure of turbulent boundary layers in the atmosphere and laboratory. Boundary-Layer Meteorol. 145 (2), 273306.
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254289.
Hwang, Y. & Cossu, C. 2010 Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105 (4), 044505.
Jimenez, A., Crespo, A., Migoya, E. & Garcia, J. 2007 Advances in large-eddy simulation of a wind turbine wake. J. Phys.: Conf. Ser. 75, 012041–15.
Jiménez, J. 1998 The largest scales of turbulent wall flows. CTR Annu. Res. Briefs 137, 54.
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25 (10), 101302.
Khanna, S. & Brasseur, J. G. 1998 Three-dimensional buoyancy- and shear-induced local structure of the atmospheric boundary layer. J. Atmos. Sci. 55 (5), 710743.
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.
Kunkel, G. J. & Marusic, I. 2006 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375402.
Lee, J. H. & Sung, H. J. 2011 Very-large-scale motions in a turbulent boundary layer. J. Fluid Mech. 673, 80120.
Lee, M. J., Kim, J. & Moin, P. 1990 Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561583.
Lignarolo, L. E. M., Mehta, D., Stevens, R. J. A. M., Yilmaz, A. E., van Kuik, G., Andersen, S. J., Meneveau, C., Ferreira, C. J., Ragni, D., Meyers, J. et al. 2016 Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an actuator disc and a wind turbine. J. Renew. Energy 94, 510523.
Liu, H., Wang, G. & Zheng, X. 2017 Spatial length scales of large-scale structures in atmospheric surface layers. Phys. Rev. Fluids 2 (6), 064606.
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100130.
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to Re 𝜏 = 4200. Phys. Fluids 26 (1), 011702.
Marusic, I. & Heuer, W. D. C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99 (11), 114504.
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.
Marušić, I. & Perry, A. E. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support. J. Fluid Mech. 298, 389407.
Mason, P. J. & Thomson, D. J. 1992 Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech. 242, 5178.
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311337.
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336382.
Metzger, M. M. & Klewicki, J. C. 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13 (3), 692701.
Meyers, J. & Meneveau, C. 2010 Large eddy simulations of large wind-turbine arrays in the atmospheric boundary layer. In Proceedings of the 48th AIAA Aerospace Sciences Meeting, Including the New Horizons Forum and Aerospace Exposition, Orlando, FL, AIAA-2010-827.
Meyers, J. & Meneveau, C. 2013 Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms. J. Fluid Mech. 715, 335358.
Moeng, C.-H. & Sullivan, P. P. 1994 A comparison of shear-and buoyancy-driven planetary boundary layer flows. J. Atmos. Sci. 51 (7), 9991022.
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431442.
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147156.
Munters, W., Meneveau, C. & Meyers, J. 2016a Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows. Phys. Fluids 28 (2), 025112.
Munters, W., Meneveau, C. & Meyers, J. 2016b Turbulent inflow precursor method with time-varying direction for large-eddy simulations and applications to wind farms. Boundary-Layer Meteorol. 159 (2), 305328.
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601639.
Shah, S. & Bou-Zeid, E. 2014 Very-large-scale motions in the atmospheric boundary layer educed by snapshot proper orthogonal decomposition. Boundary-Layer Meteorol. 153 (3), 355387.
Sillero, J. A., Jiménez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 26 (10), 105109.
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weath. Rev. 91 (3), 99164.
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353375.
Tjernström, M. & Smedman, A.-S. 1993 The vertical turbulence structure of the coastal marine atmospheric boundary layer. J. Geophys. Res. 98 (C3), 48094826.
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
VerHulst, C. & Meneveau, C. 2014 Large eddy simulation study of the kinetic energy entrainment by energetic turbulent flow structures in large wind farms. Phys. Fluids 26 (2), 025113.
Verstappen, R. W. C. P. & Veldman, A. E. P. 2003 Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 187 (1), 343368.
Wang, G. & Zheng, X. 2016 Very large scale motions in the atmospheric surface layer: a field investigation. J. Fluid Mech. 802, 464489.
Wu, Y.-T. & Porté-Agel, F. 2011 Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations. Boundary-Layer Meteorol. 138 (3), 345366.
Wu, Y.-T. & Porté-Agel, F. 2013 Simulation of turbulent flow inside and above wind farms: model validation and layout effects. Boundary-Layer Meteorol. 146 (2), 181205.
Young, G. S., Kristovich, D. A. R., Hjelmfelt, M. R. & Foster, R. C. 2002 Rolls, streets, waves, and more: a review of quasi-two-dimensional structures in the atmospheric boundary layer. Bull. Am. Meteorol. Soc. 83 (7), 9971001.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed