Articles | Volume 8, issue 6
https://doi.org/10.5194/wes-8-975-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-8-975-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
13 Jun 2023
Research article |
| 13 Jun 2023
| 13 Jun 2023
From shear to veer: theory, statistics, and practical application
Department of Wind Energy, Risø Lab/Campus, Danish Technical University, Frederiksborgvej 399, Roskilde 4000, Denmark
Maarten Paul van der Laan
Department of Wind Energy, Risø Lab/Campus, Danish Technical University, Frederiksborgvej 399, Roskilde 4000, Denmark
Related authors
Mark Kelly
Wind Energ. Sci., 10, 535–558, https://doi.org/10.5194/wes-10-535-2025, https://doi.org/10.5194/wes-10-535-2025, 2025
Short summary
Short summary
Industrial standards for wind turbine design are based on 10 min statistics of wind speed at turbine hub height, treating fluctuations as turbulence. But recent work shows that the effect of strong transients is described by flow acceleration. We devise a method to measure the acceleration that turbines encounter; the extremes offshore defy 10 min averages due to various phenomena beyond turbulence. These findings are translated into a recipe supporting statistical design.
Maarten Paul van der Laan, Mark Kelly, Mads Baungaard, Antariksh Dicholkar, and Emily Louise Hodgson
Wind Energ. Sci., 9, 1985–2000, https://doi.org/10.5194/wes-9-1985-2024, https://doi.org/10.5194/wes-9-1985-2024, 2024
Short summary
Short summary
Wind turbines are increasing in size and operate more frequently above the atmospheric surface layer, which requires improved inflow models for numerical simulations of turbine interaction. In this work, a novel steady-state model of the atmospheric boundary layer (ABL) is introduced. Numerical wind turbine flow simulations subjected to shallow and tall ABLs are conducted, and the proposed model shows improved performance compared to other state-of-the-art steady-state models.
Maarten Paul van der Laan, Oscar García-Santiago, Mark Kelly, Alexander Meyer Forsting, Camille Dubreuil-Boisclair, Knut Sponheim Seim, Marc Imberger, Alfredo Peña, Niels Nørmark Sørensen, and Pierre-Elouan Réthoré
Wind Energ. Sci., 8, 819–848, https://doi.org/10.5194/wes-8-819-2023, https://doi.org/10.5194/wes-8-819-2023, 2023
Short summary
Short summary
Offshore wind farms are more commonly installed in wind farm clusters, where wind farm interaction can lead to energy losses. In this work, an efficient numerical method is presented that can be used to estimate these energy losses. The novel method is verified with higher-fidelity numerical models and validated with measurements of an existing wind farm cluster.
Maarten Paul van der Laan, Mads Baungaard, and Mark Kelly
Wind Energ. Sci., 8, 247–254, https://doi.org/10.5194/wes-8-247-2023, https://doi.org/10.5194/wes-8-247-2023, 2023
Short summary
Short summary
Understanding wind turbine wake recovery is important to mitigate energy losses in wind farms. Wake recovery is often assumed or explained to be dependent on the first-order derivative of velocity. In this work we show that wind turbine wakes recover mainly due to the second-order derivative of the velocity, which transport momentum from the freestream towards the wake center. The wake recovery mechanisms and results of a high-fidelity numerical simulation are illustrated using a simple model.
Mads Baungaard, Stefan Wallin, Maarten Paul van der Laan, and Mark Kelly
Wind Energ. Sci., 7, 1975–2002, https://doi.org/10.5194/wes-7-1975-2022, https://doi.org/10.5194/wes-7-1975-2022, 2022
Short summary
Short summary
Wind turbine wakes in the neutral atmospheric surface layer are simulated with Reynolds-averaged Navier–Stokes (RANS) using an explicit algebraic Reynolds stress model. Contrary to standard two-equation turbulence models, it can predict turbulence anisotropy and complex physical phenomena like secondary motions. For the cases considered, it improves Reynolds stress, turbulence intensity, and velocity deficit predictions, although a more top-hat-shaped profile is observed for the latter.
Mads Baungaard, Maarten Paul van der Laan, and Mark Kelly
Wind Energ. Sci., 7, 783–800, https://doi.org/10.5194/wes-7-783-2022, https://doi.org/10.5194/wes-7-783-2022, 2022
Short summary
Short summary
Wind turbine wakes are dependent on the atmospheric conditions, and it is therefore important to be able to simulate in various different atmospheric conditions. This paper concerns the specific case of an unstable atmospheric surface layer, which is the lower part of the typical daytime atmospheric boundary layer. A simple flow model is suggested and tested for a range of single-wake scenarios, and it shows promising results for velocity deficit predictions.
Mark Kelly, Søren Juhl Andersen, and Ásta Hannesdóttir
Wind Energ. Sci., 6, 1227–1245, https://doi.org/10.5194/wes-6-1227-2021, https://doi.org/10.5194/wes-6-1227-2021, 2021
Short summary
Short summary
Via 11 years of measurements, we made a representative ensemble of wind ramps in terms of acceleration, mean speed, and shear. Constrained turbulence and large-eddy simulations were coupled to an aeroelastic model for each ensemble member. Ramp acceleration was found to dominate the maxima of thrust-associated loads, with a ramp-induced increase of 45 %–50 % plus ~ 3 % per 0.1 m/s2 of bulk ramp acceleration magnitude. The LES indicates that the ramps (and such loads) persist through the farm.
Maarten Paul van der Laan, Mark Kelly, and Mads Baungaard
Wind Energ. Sci., 6, 777–790, https://doi.org/10.5194/wes-6-777-2021, https://doi.org/10.5194/wes-6-777-2021, 2021
Short summary
Short summary
Wind farms operate in the atmospheric boundary layer, and their performance is strongly dependent on the atmospheric conditions. We propose a simple model of the atmospheric boundary layer that can be used as an inflow model for wind farm simulations for isolating a number of atmospheric effects – namely, the change in wind direction with height and atmospheric boundary layer depth. In addition, the simple model is shown to be consistent with two similarity theories.
Julia Steiner, Emily Louise Hodgson, Maarten Paul van der Laan, Leonardo Alcayaga, Mads Pedersen, Søren Juhl Andersen, Gunner Larsen, and Pierre-Elouan Réthoré
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-200, https://doi.org/10.5194/wes-2025-200, 2025
Preprint under review for WES
Short summary
Short summary
Wake steering is a promising strategy for wind farm optimization, but its success hinges on accurate wake models. We assess models of varying fidelity for the IEA 22 MW turbine, comparing single- and two-turbine cases against LES. All reproduced qualitative trends for power and if applicable loads, but quantitative agreement varied and in general the error increased with increasing yaw angle.
Mads Baungaard, Takafumi Nishino, and Maarten Paul van der Laan
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-50, https://doi.org/10.5194/wes-2025-50, 2025
Manuscript not accepted for further review
Short summary
Short summary
A systematic comparison between 2D and 3D Reynolds-averaged Navier-Stokes simulations of wind farm flows have been conducted. It is found that the 2D simulations are, at least, two orders of magnitude computationally cheaper than their corresponding 3D simulations, while the predicted farm power is within -30 % to 15 % for all cases considered. The large computational speed-ups and sensible results makes 2D simulations a promising option in the low- to mid-fidelity range.
Mark Kelly
Wind Energ. Sci., 10, 535–558, https://doi.org/10.5194/wes-10-535-2025, https://doi.org/10.5194/wes-10-535-2025, 2025
Short summary
Short summary
Industrial standards for wind turbine design are based on 10 min statistics of wind speed at turbine hub height, treating fluctuations as turbulence. But recent work shows that the effect of strong transients is described by flow acceleration. We devise a method to measure the acceleration that turbines encounter; the extremes offshore defy 10 min averages due to various phenomena beyond turbulence. These findings are translated into a recipe supporting statistical design.
Maarten Paul van der Laan, Mark Kelly, Mads Baungaard, Antariksh Dicholkar, and Emily Louise Hodgson
Wind Energ. Sci., 9, 1985–2000, https://doi.org/10.5194/wes-9-1985-2024, https://doi.org/10.5194/wes-9-1985-2024, 2024
Short summary
Short summary
Wind turbines are increasing in size and operate more frequently above the atmospheric surface layer, which requires improved inflow models for numerical simulations of turbine interaction. In this work, a novel steady-state model of the atmospheric boundary layer (ABL) is introduced. Numerical wind turbine flow simulations subjected to shallow and tall ABLs are conducted, and the proposed model shows improved performance compared to other state-of-the-art steady-state models.
Maarten Paul van der Laan, Oscar García-Santiago, Mark Kelly, Alexander Meyer Forsting, Camille Dubreuil-Boisclair, Knut Sponheim Seim, Marc Imberger, Alfredo Peña, Niels Nørmark Sørensen, and Pierre-Elouan Réthoré
Wind Energ. Sci., 8, 819–848, https://doi.org/10.5194/wes-8-819-2023, https://doi.org/10.5194/wes-8-819-2023, 2023
Short summary
Short summary
Offshore wind farms are more commonly installed in wind farm clusters, where wind farm interaction can lead to energy losses. In this work, an efficient numerical method is presented that can be used to estimate these energy losses. The novel method is verified with higher-fidelity numerical models and validated with measurements of an existing wind farm cluster.
Maarten Paul van der Laan, Mads Baungaard, and Mark Kelly
Wind Energ. Sci., 8, 247–254, https://doi.org/10.5194/wes-8-247-2023, https://doi.org/10.5194/wes-8-247-2023, 2023
Short summary
Short summary
Understanding wind turbine wake recovery is important to mitigate energy losses in wind farms. Wake recovery is often assumed or explained to be dependent on the first-order derivative of velocity. In this work we show that wind turbine wakes recover mainly due to the second-order derivative of the velocity, which transport momentum from the freestream towards the wake center. The wake recovery mechanisms and results of a high-fidelity numerical simulation are illustrated using a simple model.
Mads Baungaard, Stefan Wallin, Maarten Paul van der Laan, and Mark Kelly
Wind Energ. Sci., 7, 1975–2002, https://doi.org/10.5194/wes-7-1975-2022, https://doi.org/10.5194/wes-7-1975-2022, 2022
Short summary
Short summary
Wind turbine wakes in the neutral atmospheric surface layer are simulated with Reynolds-averaged Navier–Stokes (RANS) using an explicit algebraic Reynolds stress model. Contrary to standard two-equation turbulence models, it can predict turbulence anisotropy and complex physical phenomena like secondary motions. For the cases considered, it improves Reynolds stress, turbulence intensity, and velocity deficit predictions, although a more top-hat-shaped profile is observed for the latter.
Tuhfe Göçmen, Filippo Campagnolo, Thomas Duc, Irene Eguinoa, Søren Juhl Andersen, Vlaho Petrović, Lejla Imširović, Robert Braunbehrens, Jaime Liew, Mads Baungaard, Maarten Paul van der Laan, Guowei Qian, Maria Aparicio-Sanchez, Rubén González-Lope, Vinit V. Dighe, Marcus Becker, Maarten J. van den Broek, Jan-Willem van Wingerden, Adam Stock, Matthew Cole, Renzo Ruisi, Ervin Bossanyi, Niklas Requate, Simon Strnad, Jonas Schmidt, Lukas Vollmer, Ishaan Sood, and Johan Meyers
Wind Energ. Sci., 7, 1791–1825, https://doi.org/10.5194/wes-7-1791-2022, https://doi.org/10.5194/wes-7-1791-2022, 2022
Short summary
Short summary
The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of wind farm flow control benefits. Here we present the first part of the benchmark results for three blind tests with large-scale rotors and 11 participating models in total, via direct power comparisons at the turbines as well as the observed or estimated power gain at the wind farm level under wake steering control strategy.
Jana Fischereit, Kurt Schaldemose Hansen, Xiaoli Guo Larsén, Maarten Paul van der Laan, Pierre-Elouan Réthoré, and Juan Pablo Murcia Leon
Wind Energ. Sci., 7, 1069–1091, https://doi.org/10.5194/wes-7-1069-2022, https://doi.org/10.5194/wes-7-1069-2022, 2022
Short summary
Short summary
Wind turbines extract kinetic energy from the flow to create electricity. This induces a wake of reduced wind speed downstream of a turbine and consequently downstream of a wind farm. Different types of numerical models have been developed to calculate this effect. In this study, we compared models of different complexity, together with measurements over two wind farms. We found that higher-fidelity models perform better and the considered rapid models cannot fully capture the wake effect.
Mads Baungaard, Maarten Paul van der Laan, and Mark Kelly
Wind Energ. Sci., 7, 783–800, https://doi.org/10.5194/wes-7-783-2022, https://doi.org/10.5194/wes-7-783-2022, 2022
Short summary
Short summary
Wind turbine wakes are dependent on the atmospheric conditions, and it is therefore important to be able to simulate in various different atmospheric conditions. This paper concerns the specific case of an unstable atmospheric surface layer, which is the lower part of the typical daytime atmospheric boundary layer. A simple flow model is suggested and tested for a range of single-wake scenarios, and it shows promising results for velocity deficit predictions.
Mark Kelly, Søren Juhl Andersen, and Ásta Hannesdóttir
Wind Energ. Sci., 6, 1227–1245, https://doi.org/10.5194/wes-6-1227-2021, https://doi.org/10.5194/wes-6-1227-2021, 2021
Short summary
Short summary
Via 11 years of measurements, we made a representative ensemble of wind ramps in terms of acceleration, mean speed, and shear. Constrained turbulence and large-eddy simulations were coupled to an aeroelastic model for each ensemble member. Ramp acceleration was found to dominate the maxima of thrust-associated loads, with a ramp-induced increase of 45 %–50 % plus ~ 3 % per 0.1 m/s2 of bulk ramp acceleration magnitude. The LES indicates that the ramps (and such loads) persist through the farm.
Maarten Paul van der Laan, Mark Kelly, and Mads Baungaard
Wind Energ. Sci., 6, 777–790, https://doi.org/10.5194/wes-6-777-2021, https://doi.org/10.5194/wes-6-777-2021, 2021
Short summary
Short summary
Wind farms operate in the atmospheric boundary layer, and their performance is strongly dependent on the atmospheric conditions. We propose a simple model of the atmospheric boundary layer that can be used as an inflow model for wind farm simulations for isolating a number of atmospheric effects – namely, the change in wind direction with height and atmospheric boundary layer depth. In addition, the simple model is shown to be consistent with two similarity theories.
Cited articles
Abkar, M., Sørensen, J. N., and Porté-Agel, F.: An Analytical Model for the
Effect of Vertical Wind Veer on Wind Turbine Wakes, Energies, 11, 1838,
https://doi.org/10.3390/en11071838, 2018. a
Abramowitz, M. and Stegun, I. A.: Handbook of Mathematical Functions with
Formulas, Graphs, and Mathematical Tables, in: 9th Edn., Dover, New York, ISBN 0-486-61272-4, 1972. a
Beljaars, A. C. M. and Bosveld, F. C.: Cabauw data for the validation of land
surface parametrization schemes, J. Climate, 10, 1172–1193, 1997. a
Berg, J., Mann, J., and Patton, E. G.: Lidar-Observed Stress Vectors and Veer
in the Atmospheric Boundary Layer, J. Atmos. Ocean. Tech., 30, 1961–1969, https://doi.org/10.1175/JTECH-D-12-00266.1, 2013. a, b
Blackadar, A. K.: The vertical distribution of wind and turbulent exchange in a neutral atmosphere, J. Geophys. Res., 67, 3095–3102, 1962. a
Blackadar, A. K. and Tennekes, H.: Asymptotic similarity in neutral barotrophic planetary boundary layers, J. Atmos. Sci., 25, 1015–1020, 1968. a
Bohren, C. F. and Albrecht, B. A.: Atmospheric Thermodynamics, Oxford
University Press, New York, ISBN 0-19-509904-4, 1998. a
Brown, A. R., Beljaars, A. C., Hersbach, H., Hollingsworth, A., Miller, M., and Vasiljevic, D.: Wind turning across the marine atmospheric boundary layer, Q. J. Roy. Meteorol. Soc., 131, 1233–1250, https://doi.org/10.1256/qj.04.163, 2005. a
Brugger, P., Fuertes, F. C., Vahidzadeh, M., Markfort, C. D., and Porté-Agel,
F.: Characterization of Wind Turbine Wakes with Nacelle-Mounted Doppler
LiDARs and Model Validation in the Presence of Wind Veer, Remote Sens., 11,
2247, https://doi.org/10.3390/rs11192247, 2019. a
Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: Flux-profile
relationships in the atmospheric surface layer, J. Atmos. Sci., 28, 181–189, 1971. a
Carl, D. M., Tarbell, T. C., and Panofsky, H. A.: Profiles of Wind and
Temperature from Towers over Homogeneous Terrain, J. Atmos. Sci., 30,
788–794, 1973. a
Choukulkar, A., Pichugina, Y., Clack, C. T., Calhoun, R., Banta, R., Brewer,
A., and Hardesty, M.: A new formulation for rotor equivalent wind speed for
wind resource assessment and wind power forecasting, Wind Energy, 19,
1439–1452, https://doi.org/10.1002/we.1929, 2016. a
Clack, C. T., Alexander, A., Choukulkar, A., and MacDonald, A. E.: Demonstrating the effect of vertical and directional shear for resource
mapping of wind power, Wind Energy, 19, 1687–1697, https://doi.org/10.1002/we.1944,
2016.
a
Clark, M. R.: Investigating cold-frontal gradients in surface parameters using operationally-available minute-resolution data, Meteorol. Appl., 20, 405–416, https://doi.org/10.1002/met.1298, 2013. a
Clarke, R. H.: Note on baroclinicity and the inverse behaviour of surface
stress and wind turning in the boundary layer, Contrib. Atmos. Phys., 48, 46–50, 1975. a
Cronin, M. F., Gentemann, C. L., Edson, J., Ueki, I., Bourassa, M., Brown, S., Clayson, C. A., Fairall, C. W., Farrar, J. T., Gille, S. T., Gulev, S.,
Josey, S. A., Kato, S., Katsumata, M., Kent, E., Krug, M., Minnett, P. J.,
Parfitt, R., Pinker, R. T., Stackhouse, P. W., Swart, S., Tomita, H.,
Vandemark, D., Weller, A. R., Yoneyama, K., Yu, L., and Zhang, D.: Air-Sea
Fluxes With a Focus on Heat and Momentum, Front. Mar. Sci., 6, 430, https://doi.org/10.3389/fmars.2019.00430, 2019. a
Derbyshire, S. H.: Nieuwstadt's stable boundary layer revisited, Q. J. Roy. Meteorol. Soc., 116, 127–158, https://doi.org/10.1002/qj.49711649106, 1990. a
Dimitrov, N., Kelly, M. C., Vignaroli, A., and Berg, J.: From wind to loads: wind turbine site-specific load estimation with surrogate models trained on high-fidelity load databases, Wind Energ. Sci., 3, 767–790, https://doi.org/10.5194/wes-3-767-2018, 2018. a
Ekman, V.: On the influence of the Earth's rotation on ocean currents, Math.
Astron. Phys., 2, 1–52, 1905. a
Ellison, T. H.: Atmospheric Turbulence, in: Surveys in mechanics: A collection of surveys of the present position of research in some branches of mechanics, written in commemoration of the 70th birthday of G. I. Taylor, edited by: Batchelor, G. and Davies, R., Cambridge University Press, p. 475, 1956. a
Floors, R., Pena, A., and Gryning, S.-E.: The effect of baroclinity on the wind in the Planetary boundary layer, Q. J. Roy. Meteorol. Soc., 141,
619–30, 2015. a
Foster, R. and Levy, G.: The Contribution of Organized Roll Vortices to the
Surface Wind Vector in Baroclinic Conditions, J. Atmos. Sci., 55, 1466–1472,
https://doi.org/10.1175/1520-0469(1998)055<1466:TCOORV>2.0.CO;2, 1998. a
Gao, L., Li, B., and Hong, J.: Effect of wind veer on wind turbine power
generation, Phys.f Fluids, 33, 015101, https://doi.org/10.1063/5.0033826, 2021. a
Geernaert, G.: Measurements of the Angle Between the Wind Vector and Wind
Stress Vector in the Surface-Layer Over the North-Sea, J. Geophys. Res.-Oceans, 93, 8215–8220, https://doi.org/10.1029/JC093iC07p08215, 1988. a
Ghannam, K. and Bou-Zeid, E.: Baroclinicity and directional shear explain
departures from the logarithmic wind profile, Q. J. Roy. Meteorol. Soc., 147, 443–464, https://doi.org/10.1002/qj.3927, 2021. a
Hatlee, S. C. and Wyngaard, J. C.: Improved Subfilter-scale Models from the
HATS Field Data, J. Atmos. Sci., 64, 1694–1705, 2007. a
Horst, T. W.: The footprint for estimation of atmosphere-surface exchange
fluxes by profile techniques, Bound.-Lay. Meteorol., 90, 171–188, 1999. a
Hoxit, L. R.: Planetary Boundary Layer Winds in Baroclinic Conditions, J.
Atmos. Sci., 31, 1003–1020, 1974. a
Hulsman, P., Sucameli, C., Petrović, V., Rott, A., Gerds, A., and Kühn, M.:
Turbine power loss during yaw-misaligned free field tests at different
atmospheric conditions, J. Phys.: Conf. Ser., 2265, 032074, https://doi.org/10.1088/1742-6596/2265/3/032074, 2022. a
Kelly, M.: Estimation of local turbulence intensity via mesoscale stability and winds, with microscale shear and terrain, Tech. Rep. DTU Wind Energy E-0213, Wind Energy Dept., Risø Lab/Campus, Danish Tech. Univ. (DTU),
Roskilde, Denmark, https://doi.org/10.11581/DTU.00000262, 2020. a, b
Kelly, M. and Jørgensen, H. E.: Statistical characterization of roughness
uncertainty and impact on wind resource estimation, Wind Energ. Sci., 2,
189–209, https://doi.org/10.5194/wes-2-189-2017, 2017. a
Kelly, M., Troen, I., and Jørgensen, H. E.: Weibull-k revisited:
“tall” profiles and height variation of wind statistics, Bound.-Lay. Meteorol., 152, 107–124, 2014b. a
Kelly, M., Cersosimo, R. A., and Berg, J.: A universal wind profile for the
inversion-capped neutral atmospheric boundary layer, Q. J. Roy. Meteorol. Soc., 145, 982–992, https://doi.org/10.1002/qj.3472, 2019a. a, b
Kelly, M., Kersting, G., Mazoyer, P., Yang, C., Fillols, F. H., Clark, S., and Matos, J. C.: Uncertainty in vertical extrapolation of measured wind speed via shear, Tech. Rep. DTU Wind Energy E-0195(EN), Wind Energy Dept., Risø Lab/Campus, Danish Tech. Univ. (DTU), Roskilde, Denmark,
https://doi.org/10.11581/dtu.00000261, 2019b. a
Krishna, K.: The planetary-boundary-layer model of Ellison (1956) – A
retrospect, Bound.-Lay. Meteorol., 19, 293–301, 1980. a
Li, D.: The O'KEYPS Equation and 60 Years Beyond, Bound.-Lay. Meteorol., 179, 19–42, https://doi.org/10.1007/s10546-020-00585-y, 2021. a
Lindvall, J. and Svensson, G.: Wind turning in the atmospheric boundary layer
over land, Q. J. Roy. Meteorol. Soc., 145, 3074–3088, https://doi.org/10.1002/qj.3605, 2019. a
Liu, L., Gadde, S. N., and Stevens, R. J.: Geostrophic drag law for
conventionally neutral atmospheric boundary layers revisited, Q. J. Roy. Meteorol. Soc., 147, 847–857, https://doi.org/10.1002/qj.3949, 2021. a
Markowski, P. and Richardson, Y.: On the Classification of Vertical Wind Shear as Directional Shear versus Speed Shear, Weather Forecast., 21, 242–247, 2006. a
Mikhail, A.: Height extrapolation of wind data, Solar Energ. Eng., 107,
10–14, 1985. a
Moeng, C.-H. and Wyngaard, J. C.: Evaluation of Turbulent Transport and
Dissipation Closures in Second-Order Modeling, J. Atmos. Sci., 46, 2311–2330, 1989. a
Murphy, P., Lundquist, J. K., and Fleming, P.: How wind speed shear and
directional veer affect the power production of a megawatt-scale operational
wind turbine, Wind Energ. Sci., 5, 1169–1190,
https://doi.org/10.5194/wes-5-1169-2020, 2020. a
Narasimhan, G., Gayme, D. F., and Meneveau, C.: Effects of wind veer on a yawed wind turbine wake in atmospheric boundary layer flow, ARXIV [preprint],
https://doi.org/10.48550/ARXIV.2210.09525, 2022. a
Nieuwstadt, F. T. M.: The Turbulent Structure of the Stable, Nocturnal Boundary Layer, J. Atmos. Sci. 41, 2202–2216, 1984. a
Panofsky, H. and Dutton, J.: Atmospheric Turbulence, Wiley, ISBN 978-0-471-05714-7, 1984. a
Peña, A.: Østerild: A natural laboratory for atmospheric turbulence,
J. Renew. Sustain. Energ., 11, 063302, https://doi.org/10.1063/1.5121486, 2019. a, b
Peña, A., Floors, R. R., Sathe, A., Gryning, S.-E., Wagner, R., Courtney,
M., Larsén, X. G., Hahmann, A. N., and Hasager, C. B.: Ten Years of
Boundary-Layer and Wind-Power Meteorology at Høvsøre, Denmark,
Bound.-Lay. Meteorol., 158, 1–26, https://doi.org/10.1007/s10546-015-0079-8, 2016. a
Pope, S. B.: Turbulent Flows, Cambridge University Press, ISBN 978-0-521-59886-6, 2000. a
Robertson, A. N., Shaler, K., Sethuraman, L., and Jonkman, J.: Sensitivity
analysis of the effect of wind characteristics and turbine properties on wind
turbine loads, Wind Energ. Sci., 4, 479–513,
https://doi.org/10.5194/wes-4-479-2019, 2019. a
Rossby, C. G. and Montgomery, R. B.: The Layer of Frictional Influence in Wind and Ocean Currents, Pap. Phys. Oceanogr. Meteorol., 3, 1–101, 1935. a
Rotta, J.: Statistical theory of non-homogeneous turbulence (“Statistiche
Theorie nichthomogener Turbulenz”), Z. Physik, 129, 547–572, 1951. a
Santos, P., Peña, A., and Mann, J.: Departure from Flux-Gradient Relation
in the Planetary Boundary Layer, Atmosphere, 12, 672, https://doi.org/10.3390/atmos12060672, 2021. a
Shu, Z., Li, Q., He, Y., and Chan, P. W.: Investigation of marine wind veer
characteristics using wind lidar measurements, Atmosphere, 11, 1178,
https://doi.org/10.3390/atmos11111178, 2020. a
Sogachev, A. and Kelly, M.: On Displacement Height, from Classical to Practical Formulation: Stress, Turbulent Transport and Vorticity Considerations, Bound.-Lay. Meteorol., 158, 361–381, https://doi.org/10.1007/s10546-015-0093-x, 2016. a
Sørensen, N. N.: General Purpose Flow Solver Applied to Flow over Hills, PhD thesis Risø-R-864(EN), Risø National Laboratory, Roskilde, Denmark, ISBN 87-550-2079-8, 1995. a
Sørensen, N. N., Bechmann, A., Johansen, J., Myllerup, L., Botha, P.,
Vinther, S., and Nielsen, B.: Identification of severe wind conditions using
a Reynolds-averaged Navier-Stokes solver, J. Phys.: Conf. Ser., 75, 012053, https://doi.org/10.1088/1742-6596/75/1/012053, 2007. a
Svensson, G. and Holtslag, A. A. M.: Analysis of Model Results for the Turning of the Wind and Related Momentum Fluxes in the Stable Boundary Layer,
Bound.-Lay. Meteorol., 132, 261–277, 2009. a
Triviño, C.: Validation of Vertical Wind Shear Methods, Zenodo [presentation], https://doi.org/10.5281/zenodo.5549897, 2017. a
van der Laan, M. P. and Sørensen, N. N.: A 1D version of EllipSys,
Technical Report DTU Wind Energy E-0141 (EN), Danish Technical
University, Roskilde, Denmark, ISBN 978-87-93549-08-1, 2017. a
van der Laan, M. P., Kelly, M., Floors, R., and Peña, A.: Rossby number
similarity of an atmospheric RANS model using limited-length-scale
turbulence closures extended to unstable stratification, Wind Energ. Sci., 5, 355–374, https://doi.org/10.5194/wes-5-355-2020, 2020. a, b, c, d, e, f, g, h, i, j, k, l, m, n
Wyngaard, J. C.: Toward numerical modeling in the `Terra Incognita', J.
Atmos. Sci., 61, 1816–1826, 2004. a
Zilitinkevich, S. S. and Esau, I. N.: On integral measures of the neutral
barotrophic planetary boundary layer, Bound.-Lay. Meteorol., 104, 371–379,
2002. a
Zilitinkevich, S. S. and Esau, I. N.: Resistance and heat-transfer laws for
stable and neutral planetary boundary layers: old theory advanced and
re-evaluated, Q. J. Roy. Meteorol. Soc., 131, 1863–1892, 2005. a
Short summary
The turning of the wind with height, which is known as veer, can affect wind turbine performance. Thus far meteorology has only given idealized descriptions of veer, which has not yet been related in a way readily usable for wind energy. Here we derive equations for veer in terms of meteorological quantities and provide practically usable forms in terms of measurable shear (change in wind speed with height). Flow simulations and measurements at turbine heights support these developments.
The turning of the wind with height, which is known as veer, can affect wind turbine...
Altmetrics
Final-revised paper
Preprint