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Wind-farm wake recovery mechanisms in conventionally neutral boundary layers

Published online by Cambridge University Press:  15 July 2025

Luca Lanzilao Open the ORCID record for Luca Lanzilao [Opens in a new window]  and
Johan Meyers Open the ORCID record for Johan Meyers [Opens in a new window]
Luca Lanzilao*
Affiliation:
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300 – Box 2421, Leuven B-3001, Belgium
Johan Meyers
Affiliation:
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300 – Box 2421, Leuven B-3001, Belgium
*
Corresponding author: Luca Lanzilao, luca.lanzilao@kuleuven.be
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Abstract

Synthetic-aperture radar images and mesoscale models show that wind-farm wakes differ from single-turbine wakes. For instance, wind-farm wakes often narrow and do not disperse over long distances, contrasting the broader and more dissipating wakes of individual turbines. In this work, we aim to better understand the mechanisms that govern wind-farm wake behaviour and recovery. Hence we study the wake properties of a $1.6$ GW wind farm operating in conventionally neutral boundary layers with capping-inversion heights $203$, $319$, $507$ and $1001$ m. In shallow boundary layers, we find strong flow decelerations that reduce the Coriolis force magnitude, leading to an anticlockwise wake deflection in the Northern Hemisphere. In deep boundary layers, the vertical turbulent entrainment of momentum adds clockwise-turning flow from aloft into the wake region, leading to a faster recovery rate and a clockwise wake deflection. To estimate the wake properties, we propose a simple function to fit the velocity magnitude profiles along the spanwise direction. In the vertical direction, the wake spreads up to the capping-inversion height, which significantly limits vertical wake development in shallow-boundary-layer cases. In the horizontal direction and for shallow boundary layers, the wake behaves as two distinct mixing layers located at the lateral wake edges, which expand and turn towards their low-velocity side, causing the wake to narrow along the streamwise direction. A detailed analysis of the momentum budget reveals that in deep boundary layers, the wake is predominantly replenished through turbulent vertical entrainment. Conversely, in shallow boundary layers, wakes are mostly replenished by mean flow advection in the spanwise direction.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Turbulent boundary layers Wakes/Jets: Wakes

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JFM Papers
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Journal of Fluid Mechanics , Volume 1015 , 25 July 2025 , A5
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© The Author(s), 2025. Published by Cambridge University Press

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References

Abraham, A., Hamilton, N., Bodini, N., Hirth, B., Schroeder, J., Letizia, S., Krishnamurthy, R., Newsom, R. & Moriarty, P. 2024 Land-based wind plant wake characterization using dual-Doppler radar measurements at AWAKEN. J. Phys.: Conf. Ser. 2767 (9), 092037.Google Scholar
Ahsbahs, T., Badger, M., Volker, P., Hansen, K.S. & Hasager, C.B. 2018 Applications of satellite winds for the offshore wind farm site Anholt. Wind Energ. Sci. 3 (2), 573–588.10.5194/wes-3-573-2018CrossRefGoogle Scholar
Ahsbahs, T., Nygaard, N.G., Newcombe, A. & Badger, M. 2020 Wind farm wakes from SAR and Doppler radar. Remote Sens. 12 (3), 462.10.3390/rs12030462CrossRefGoogle Scholar
Akhtar, N., Geyer, B., Rockel, B., Sommer, P.S. & Schrum, C. 2021 Accelerating Deployment of Offshore Wind Energy Alter Wind Climate and Reduce Future Power Generation Potentials. Scientific reports..10.1038/s41598-021-91283-3CrossRefGoogle Scholar
Allaerts, D. 2016 Large-eddy simulation of wind farms in conventionally neutral and stable atmospheric boundary layers. PhD thesis, KU Leuven, Leuven, Belgium.Google Scholar
Allaerts, D. & Meyers, J. 2015 Large eddy simulation of a large wind-turbine array in a conventionally neutral atmospheric boundary layer. Phys. Fluids 27 (6), 065108.10.1063/1.4922339CrossRefGoogle Scholar
Allaerts, D. & Meyers, J. 2017 Boundary-layer development and gravity waves in conventionally neutral wind farms. J. Fluid Mech. 814, 95–130.10.1017/jfm.2017.11CrossRefGoogle Scholar
Allaerts, D. & Meyers, J. 2018 Gravity waves and wind-farm efficiency in neutral and stable conditions. Boundary-Layer Meteorol. 166 (2), 269–299.10.1007/s10546-017-0307-5CrossRefGoogle ScholarPubMed
Allaerts, D. & Meyers, J. 2019 Sensitivity and feedback of wind-farm induced gravity waves. J. Fluid Mech. 862, 990–1028.10.1017/jfm.2018.969CrossRefGoogle ScholarPubMed
Andreas, P. et al. 2018 First in situ evidence of wakes in the far field behind offshore wind farms. Sci. Rep. 8 (1), 2163.Google Scholar
Baas, P. & Verzijlbergh, R. 2022 The impact of wakes from neighboring wind farms on the production of the IJmuiden Ver wind farm zone. Whiffle Report. Available at: https://whiffle.nl/wp-content/uploads/The-impact-of-wakes-from-neighboring-wind-farms-IJmuiden.pdf.Google Scholar
Baas, P., Verzijlbergh, R., van Dorp, P. & Jonker, H. 2023 Investigating energy production and wake losses of multi-gigawatt offshore wind farms with atmospheric large-eddy simulation. Wind Energy Sci. 8 (5), 787–805.10.5194/wes-8-787-2023CrossRefGoogle Scholar
Bastankhah, M., Mohammadi, M.-M., Lees, C., Diaz, G., Buxton, O.R.H. & Ivanell, S. 2024 A fast-running physics-based wake model for a semi-infinite wind farm. J. Fluid Mech. 985, A43.10.1017/jfm.2024.282CrossRefGoogle Scholar
Bastankhah, M. & Porté-Agel, F. 2014 A new analytical model for wind-turbine wakes. Renew. Energy 70, 116–123.10.1016/j.renene.2014.01.002CrossRefGoogle Scholar
Bleeg, J. & Montavon, C. 2022 Blockage effects in a single row of wind turbines. J. Phys.: Conf. Ser. 2265 (2), 022001.Google Scholar
Bleeg, J., Purcell, M., Ruisi, R. & Traiger, E. 2018 Wind farm blockage and the consequences of neglecting its impact on energy production. Energies 11 (6), 1609.10.3390/en11061609CrossRefGoogle Scholar
Blondel, F. & Cathelain, M. 2020 An alternative form of the super-Gaussian wind turbine wake model. Wind Energy Sci. 5 (3), 1225–1236.10.5194/wes-5-1225-2020CrossRefGoogle Scholar
Borgers, R., Dirksen, M., Wijnant, I.L., Stepek, A., Stoffelen, A., Akhtar, N., Neirynck, J., Van de Walle, J., Meyers, J. & van Lipzig, N.P.M. 2024 Mesoscale modelling of North Sea wind resources with COSMO-CLM: model evaluation and impact assessment of future wind farm characteristics on cluster-scale wake losses. Wind Energy Sci. 9 (3), 697–719.10.5194/wes-9-697-2024CrossRefGoogle Scholar
Bortolotti, P., Tarrés, H.C., Dykes, K., Merz, K., Sethuraman, L., Verelst, D. & Zahle, F. 2019 IEA Wind TCP task 37: systems engineering in wind energy – WP2.1 reference wind turbines. Technical Report. National Renewable Energy Laboratory (NREL).10.2172/1529216CrossRefGoogle Scholar
Brost, R.A., Lenschow, D.H. & Wyngaard, J.C. 1982 Marine stratocumulus layers. Part 1: Mean conditions. J. Atmos. Sci. 39 (4), 800–817.10.1175/1520-0469(1982)039<0800:MSLPMC>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Calaf, M., Meneveau, C. & Meyers, J. 2010 Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys. Fluids 22 (1), 015110.10.1063/1.3291077CrossRefGoogle Scholar
Canuto, C., Hussaini, M.Y., Quarteroni, A. & Zang, T.A. 1988 Spectral Methods in Fluid Dynamics. Springer-Verlag.10.1007/978-3-642-84108-8CrossRefGoogle Scholar
Chamorro, L.P. & Porté-Agel, F. 2009 A wind-tunnel investigation of wind-turbine wakes: boundary-layer turbulence effects. Boundary-Layer Meteorol. 132 (5), 1573–1472.10.1007/s10546-009-9380-8CrossRefGoogle Scholar
Christiansen, M.B. & Hasager, C.B. 2005 Wake effects of large offshore wind farms identified from satellite SAR. Remote Sens. Environ. 98 (2), 251–268.10.1016/j.rse.2005.07.009CrossRefGoogle Scholar
Crespo, A. & Hernandez, J. 1996 Turbulence characteristics in wind-turbine wakes. J. Wind. Engng Ind. Aerodyn. 61 (1), 71–85.10.1016/0167-6105(95)00033-XCrossRefGoogle Scholar
Delport, S. 2010 Optimal control of a turbulent mixing layer. PhD thesis, KU Leuven, Leuven, Belgium.Google Scholar
Djath, B., Schulz-Stellenfleth, J. & Cañadillas, B. 2018 Impact of atmospheric stability on X-band and C-band synthetic aperture radar imagery of offshore windpark wakes. J. Renew. Sustain. Energy 10 (4), 043301.10.1063/1.5020437CrossRefGoogle Scholar
Emeis, S., Siedersleben, S., Lampert, A., Platis, A., Bange, J., Djath, B., Schulz-Stellenfleth, J. & Neumann, T. 2016 Exploring the wakes of large offshore wind farms. J. Phys.: Conf. Ser. 753 (9), 092014.Google Scholar
Finserås, E., Herrera Anchustegui, I., Cheynet, E., Gebhardt, C.G. & Reuder, J. 2024 Gone with the wind? Wind farm-induced wakes and regulatory gaps. Mar. Policy 159, 105897.10.1016/j.marpol.2023.105897CrossRefGoogle Scholar
Fischereit, J., Brown, R., Larsén, X.G., Badger, J. & Hawkes, G. 2022 a Review of mesoscale wind-farm parametrizations and their applications. Boundary-Layer Meteorol. 182 (2), 1573–1472.10.1007/s10546-021-00652-yCrossRefGoogle Scholar
Fischereit, J., Larsén, X.G. & Hahmann, A.N. 2022 b Climatic impacts of wind–wave–wake interactions in offshore wind farms. Front. Energy Res. 10, 881459.10.3389/fenrg.2022.881459CrossRefGoogle Scholar
Fitch, A.C., Olson, J.B., Lundquist, J.K., Dudhia, J., Gupta, A.K., Michalakes, J. & Barstad, I. 2012 Local and mesoscale impacts of wind farms as parameterized in a mesoscale NWP model. Mon. Weather Rev. 140 (9), 3017–3038.10.1175/MWR-D-11-00352.1CrossRefGoogle Scholar
Fornberg, B. 1996 A Practical Guide to Pseudospectral Methods. Cambridge University Press.10.1017/CBO9780511626357CrossRefGoogle Scholar
Goit, J.P. & Meyers, J. 2015 Optimal control of energy extraction in wind-farm boundary layers. J. Fluid Mech. 768, 5–50.10.1017/jfm.2015.70CrossRefGoogle Scholar
Göçmen, T., van der Laan, P., Réthoré, P.-E., Diaz, A.P., Larsen, G.C. & Ott, S. 2016 Wind turbine wake models developed at the Technical University of Denmark: a review. Renew. Sustain. Energy Rev. 60, 752–769.10.1016/j.rser.2016.01.113CrossRefGoogle Scholar
GWEC 2024 Global wind report. Available at: https://www.gwec.net/reports/globalwindreport/2024, accessed 2025-06-27.Google Scholar
Hasager, C.B., Vincent, P., Badger, J., Badger, M., Di Bella, A., Peña, A., Husson, R. & Volker, P.J.H. 2015 Using satellite SAR to characterize the wind flow around offshore wind farms. Energies 8 (6), 5413–5439.10.3390/en8065413CrossRefGoogle Scholar
Heck, K.S. & Howland, M.F. 2025 Coriolis effects on wind turbine wakes across neutral atmospheric boundary layer regimes. J. Fluid Mech. 1008, A7.10.1017/jfm.2025.35CrossRefGoogle Scholar
Howland, M.F., Ghate, A.S. & Lele, S.K. 2018 Influence of the horizontal component of Earth’s rotation on wind turbine wakes. J. Phys.: Conf. Ser. 1037 (7), 072003.Google Scholar
Kenis, M., Lanzilao, L., Bruninx, K., Meyers, J. & Delarue, E. 2023 Trading rights to consume wind in presence of farm-farm interactions. Joule 7 (7), 1394–1398.10.1016/j.joule.2023.05.015CrossRefGoogle Scholar
Kirby, A., Nishino, T. & Dunstan, T.D. 2022 Two-scale interaction of wake and blockage effects in large wind farms. J. Fluid Mech. 953, A39.10.1017/jfm.2022.979CrossRefGoogle Scholar
van der Laan, M.P., García-Santiago, O., Kelly, M., Meyer Forsting, A., Dubreuil-Boisclair, C., Sponheim Seim, K., Imberger, M., Peña, A., Sørensen, N.N. & Réthoré, P.-E. 2023 A new RANS-based wind farm parameterization and inflow model for wind farm cluster modeling. Wind Energy Sci. 8 (5), 819–848.10.5194/wes-8-819-2023CrossRefGoogle Scholar
van der Laan, M.P., Hansen, K.S., Sørensen, N.N. & Réthoré, P.-E. 2015 Predicting wind farm wake interaction with RANS: an investigation of the Coriolis force. J. Phys.: Conf. Ser. 625, 012026.Google Scholar
van der Laan, M.P. & Sørensen, N.N. 2017 Why the Coriolis force turns a wind farm wake clockwise in the northern hemisphere. Wind Energy Sci. 2 (1), 285–294.10.5194/wes-2-285-2017CrossRefGoogle Scholar
Lanzilao, L. 2023 Modelling of self-induced atmospheric gravity waves in large-scale wind farms. PhD thesis. Available at: https://kuleuven.limo.libis.be/discovery/fulldisplay?docid=lirias4088811&context=SearchWebhook&vid=32KUL_KUL:Lirias&lang=en&search_scope=lirias_profile&adaptor=SearchWebhook&tab=LIRIAS&query=any,contains,LIRIAS4088811&offset=0.Google Scholar
Lanzilao, L. & Meyers, J. 2022 a Effects of self-induced gravity waves on finite wind-farm operations using a large-eddy simulation framework. J. Phys.: Conf. Ser. 2265 (2), 022043.Google Scholar
Lanzilao, L. & Meyers, J. 2022 b A new wake-merging method for wind-farm power prediction in the presence of heterogeneous background velocity fields. Wind Energy 25 (2), 237–259.10.1002/we.2669CrossRefGoogle Scholar
Lanzilao, L. & Meyers, J. 2023 An improved fringe-region technique for the representation of gravity waves in large eddy simulation with application to wind farms. Boundary-Layer Meteorol. 186, 567–593.10.1007/s10546-022-00772-zCrossRefGoogle Scholar
Lanzilao, L. & Meyers, J. 2024 a A reference database for the analysis of wind-farm wake recovery mechanisms in a large-eddy simulation framework. Available at: https://rdr.kuleuven.be/dataset.xhtml?persistentId=doi:10.48804/LRSENQ.CrossRefGoogle Scholar
Lanzilao, L. & Meyers, J. 2024 b A parametric large-eddy simulation study of wind-farm blockage and gravity waves in conventionally neutral boundary layers. J. Fluid Mech. 979, A54.10.1017/jfm.2023.1088CrossRefGoogle Scholar
Lignarolo, L.E.M. 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. Renew. Energy 94, 510–523.10.1016/j.renene.2016.03.070CrossRefGoogle Scholar
Lundquist, J.K., DuVivier, K.K., Kaffine, D. & Tomaszewski, J.M. 2019 Costs and consequences of wind turbine wake effects arising from uncoordinated wind energy development. Nat. Energy 4, 26–34.10.1038/s41560-018-0281-2CrossRefGoogle Scholar
Maas, O. 2023 a From gigawatt to multi-gigawatt wind farms: wake effects, energy budgets and inertial gravity waves investigated by large-eddy simulations. Wind Energy Sci. 8 (4), 535–556.10.5194/wes-8-535-2023CrossRefGoogle Scholar
Maas, O. 2023 b Large-eddy simulation of a 15 GW wind farm: flow effects, energy budgets and comparison with wake models. Frontiers Mech. Eng. 9. 10.3389/fmech.2023.1108180.10.3389/fmech.2023.1108180CrossRefGoogle Scholar
Maas, O. & Raasch, S. 2022 Wake properties and power output of very large wind farms for different meteorological conditions and turbine spacings: a large-eddy simulation case study for the German Bight. Wind Energy Sci. 7 (2), 715–739.10.5194/wes-7-715-2022CrossRefGoogle Scholar
Martínez-Tossas, L.A., Churchfield, M.J., Yilmaz, A.E., Sarlak, H., Johnson, P.L., Sørensen, J.N., Meyers, J. & Meneveau, C. 2018 Comparison of four large-eddy simulation research codes and effects of model coefficient and inflow turbulence in actuator-line-based wind turbine modeling. J. Renew. Sustain. Energy 10 (3), 033301.10.1063/1.5004710CrossRefGoogle Scholar
Mason, P.J. & Thomson, D.J. 1992 Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech. 242, 51–78.10.1017/S0022112092002271CrossRefGoogle Scholar
McTavish, S., Rodrigue, S., Feszty, D. & Nitzsche, F. 2015 An investigation of in-field blockage effects in closely spaced lateral wind farm configurations. Wind Energy 18 (11), 1989–2011.10.1002/we.1806CrossRefGoogle Scholar
Meyers, J. & Meneveau, C. 2010 Large eddy simulations of large wind-turbine arrays in the atmospheric boundary layer. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition}. Available at: https://arc.aiaa.org/doi/abs/10.2514/6.2010-827.CrossRefGoogle Scholar
Meyers, J. & Sagaut, P. 2007 Is plane-channel flow a friendly case for the testing of large-eddy simulation subgrid-scale models? Phys. Fluids 19 (4), 048105.10.1063/1.2722422CrossRefGoogle Scholar
Moeng, C.H. 1984 A large-eddy-simulation model for the study of the planetary boundary-layer turbulence. J. Atmos. Sci. 41 (13), 2052–2062.10.1175/1520-0469(1984)041<2052:ALESMF>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Munters, W., Adiloglu, B., Buckingham, S. & van Beeck, J. 2022 Wake impact of constructing a new offshore wind farm zone on an existing downwind cluster: a case study of the Belgian Princess Elisabeth zone using FLORIS. J. Phys.: Conf. Ser. 2265 (2), 022049.Google Scholar
Munters, W. & Meyers, J. 2018 Dynamic strategies for yaw and induction control of wind farms based on large-eddy simulation and optimization. Energies 11 (1), 177.10.3390/en11010177CrossRefGoogle Scholar
Nappo, C.J. 2002 An introduction to atmospheric gravity waves. In International Geophysics Series, vol. 85. Academic Press.Google Scholar
Nygaard, N.G. 2014 Wakes in very large wind farms and the effect of neighbouring wind farms. J. Phys.: Conf. Ser. 524, 012162.Google Scholar
Nygaard, N.G. & Newcombe, A.C. 2018 Wake behind an offshore wind farm observed with dual-Doppler radars. J. Phys.: Conf. Ser. 1037, 072008.Google Scholar
Nygaard, N.G., Steen, S.T., Poulsen, L. & Pedersen, J.G. 2020 Modelling cluster wakes and wind farm blockage. J. Phys.: Conf. Ser. 1618 (6), 062072.Google Scholar
Pedersen, J.G., Gryning, S.E. & Kelly, M. 2014 On the structure and adjustment of inversion-capped neutral atmospheric boundary-layer flows: large-eddy simulation study. Boundary-Layer Meteorol. 153 (1), 43–62.10.1007/s10546-014-9937-zCrossRefGoogle Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Pryor, S.C. & Barthelmie, R.J. 2001 Comparison of potential power production at on- and offshore sites. Wind Energy 4 (4), 173–181.10.1002/we.54CrossRefGoogle Scholar
Pryor, S.C., Barthelmie, R.J. & Shepherd, T.J. 2021 Wind power production from very large offshore wind farms. Joule 5 (10), 2663–2686.10.1016/j.joule.2021.09.002CrossRefGoogle Scholar
Pryor, S.C., Barthelmie, R.J., Shepherd, T.J., Hahmann, A.N. & Garcia Santiago, O.M. 2022 Wakes in and between very large offshore arrays. J. Phys.: Conf. Ser. 2265 (2), 022037.Google Scholar
Pryor, S.C. & Barthelmie, R.J. 2024 Wind shadows impact planning of large offshore wind farms. Appl. Energy 359, 122755.10.1016/j.apenergy.2024.122755CrossRefGoogle Scholar
Pryor, S.C., Shepherd, T.J., Barthelmie, R.J., Hahmann, A.N. & Volker, P. 2019 Wind farm wakes simulated using WRF. J. Phys.: Conf. Ser. 1256 (1), 012025.Google Scholar
Rampanelli, G. & Zardi, D. 2004 A method to determine the capping inversion of the convective boundary layer. J. Appl. Meteorol. 43 (6), 925–933.10.1175/1520-0450(2004)043<0925:AMTDTC>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Rosencrans, D., Lundquist, J.K., Optis, M., Rybchuk, A., Bodini, N. & Rossol, M. 2024 Seasonal variability of wake impacts on us mid-Atlantic offshore wind plant power production. Wind Energy Sci. 9 (3), 555–583.10.5194/wes-9-555-2024CrossRefGoogle Scholar
Sachsperger, J., Serafin, S. & Grubišić, V. 2015 Lee waves on the boundary-layer inversion and their dependence on free-atmospheric stability. Frontiers Earth Sci. 3. 10.3389/feart.2015.00070. 10.3389/feart.2015.00070CrossRefGoogle Scholar
Sanchez Gomez, M., Lundquist, J.K., Mirocha, J.D. & Arthur, R.S. 2023 Investigating the physical mechanisms that modify wind plant blockage in stable boundary layers. Wind Energy Sci. Discuss. 2023, 1–28.Google Scholar
Schneemann, J., Rott, A., Dorenkamper, M., Steinfeld, G. & Kuhn, M. 2020 Cluster wakes impact on a far-distant offshore wind farm’s power. Wind Energy Sci. 5 (1), 29–49.10.5194/wes-5-29-2020CrossRefGoogle Scholar
Sood, I., Simon, E., Vitsas, A., Blockmans, B., Larsen, G.C. & Meyers, J. 2022 Comparison of large eddy simulations against measurements from the Lillgrund offshore wind farm. Wind Energy Sci. 7 (6), 2469–2489.10.5194/wes-7-2469-2022CrossRefGoogle Scholar
Stevens, B., Moeng, C.H. & Sullivan, P.P. 2000 Entrainment and subgrid length scales in large-eddy simulations of atmospheric boundary-layer flows. Symp. Dev. Geophys. Turbul. 58, 253–269.Google Scholar
Stieren, A. & Stevens, R.J.A.M. 2021 Evaluating wind farm wakes in large eddy simulations and engineering models. J. Phys.: Conf. Ser. 1 (1), 012018.Google Scholar
Stieren, A. & Stevens, R.J.A.M. 2022 Impact of wind farm wakes on flow structures in and around downstream wind farms. Flow 2, E21.10.1017/flo.2022.15CrossRefGoogle Scholar
Stipa, S., Ahmed Khan, M., Allaerts, D. & Brinkerhoff, J. 2024 An LES model for wind farm-induced atmospheric gravity wave effects inside conventionally neutral boundary layers. Wind Energy Sci. Discuss. 2024, 1–22.Google Scholar
Taylor, P.K. & Yelland, M.J. 2000 The dependence of sea surface roughness on the height and steepness of the waves. J. Phys. Oceanogr. 31, 572–590.10.1175/1520-0485(2001)031<0572:TDOSSR>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Verstappen, R.W.C.P. & Veldman, A.E.P. 2003 Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 187 (1), 343–368.10.1016/S0021-9991(03)00126-8CrossRefGoogle Scholar
Virtanen, P. et al. 2020 SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Meth. 17 (3), 261–272.10.1038/s41592-019-0686-2CrossRefGoogle ScholarPubMed
Vosper, S.B. 2004 Inversion effects on mountain lee waves. Q. J. Roy. Meteorol. Soc. 130 (600), 1723–1748.10.1256/qj.03.63CrossRefGoogle Scholar
Zilitinkevich, S.S. 1989 Velocity profiles, the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer. Boundary-Layer Meteorol. 46 (4), 367–387.10.1007/BF00172242CrossRefGoogle Scholar