Advertisement

Boundary-Layer Meteorology

, Volume 171, Issue 2, pp 191–212 | Cite as

Turbulence Characteristics of Wind-Speed Fluctuations in the Presence of Open Cells: A Case Study

  • Xiaoli G. LarsénEmail author
  • Søren E. Larsen
  • Erik L. Petersen
  • Torben K. Mikkelsen
Research Article

Abstract

Open cellular structures are frequently observed accompanying cold fronts over the North Sea. Through a two-day case study, measurements from two sites that are 100 km apart, and both covered by open cells, show that the turbulence is characterized by (1) considerable energy in the spectral gap region; (2) similar large-scale wind variation from surface to 100 m. These observations challenge existing algorithms for calculating parameters relevant to wind energy, including the turbulence intensity. We suggest that, in the presence of open cells, the stability effect is more related to the large-scale process, while the conventional parameter, the surface-layer Obukhov length, is less suitable. This issue is also revealed by the comparison of measurements with an unstable-boundary-layer spectral model. A mesoscale spectral model \(A a_1 f^{-2/3}\) is proposed to include the stability effect, when combined with a boundary-layer turbulence model for neutral conditions. The stability effect is introduced to this mesoscale model in a simple manner through calibration, with the coefficient A obtained from regression using standard 10-min time series (from measurements or numerical modelling). The combined model successfully reproduces the power spectrum of wind-speed fluctuations for the two-day open-cell event.

Keywords

Turbulence models Mesoscale spectral model Open cells 

Notes

Acknowledgements

The first author acknowledges the support from PSO X-WiWa project (PSO-12020, including the access to data at site M8 from Ørsted) and the ForskEL/EUDP OffshoreWake project (PSO-12521) and the CCA project from the Wind Energy Department. We thank particularly one anonymous reviewer for many detailed suggestions that have significantly helped improve this paper. We thank researcher Neil Davis from DTU Wind Energy for the help with language.

References

  1. Atkinson BW, Zhang JW (1996) Mesoscale shallow convection in the atmosphere. Rev Geophys 4:403–431CrossRefGoogle Scholar
  2. Bakan S, Schwarz E (1992) Cellular convection over the north-eastern atlantic. Int J Climatol 12:353–367CrossRefGoogle Scholar
  3. Brummer B, Rump B, Kruspe G (1992) A cold air outbreak near spitsbergen in spring time: boundary layer modification and cloud development. Boundary-Layer Meteorol 61:13–46CrossRefGoogle Scholar
  4. Busack B, Bakan S, Luthardt H (1985) Surface conditions during mesoscale cellular convection. Bull Am Meteorol Soc 54:4–10Google Scholar
  5. Businger JA, Wyngaard JC, Izumi Y, Bradley E (1971) Flux-profile relationships in the atmospheric surface layer. J Atmos Sci 28:181–189CrossRefGoogle Scholar
  6. Cheynet E, Jakobseb JB, Reuder J (2018) Velocity spectra and coherence estimates in the marine atmospheric boundary layer. Boundary-Layer Meteorol 169:429.  https://doi.org/10.1007/s10546-018-0382-2 CrossRefGoogle Scholar
  7. Courtney M, Troen I (1990) Wind speed spectrum for one year of continuous 8 hz measurements. In: Nineth symposium on turbulence and diffusion, American Metrorol Society, pp 301–304Google Scholar
  8. Etling D, Brown RA (1993) Roll vortices in the planetary boundary layer: a review. Boundary-Layer Meteorol 65:215–248CrossRefGoogle Scholar
  9. Floors R, Lea G, Peña A, Karagali I, Ahsbahs T (2016) Report on RUNE’s coastal experiment and first inter-comparisons between measurements systems. Wind Energy Department, Roskilde. Tech Rep DTU Wind Energy-E-Report-0115 (EN). http://orbit.dtu.dk/files/127277148/final.pdf
  10. Gage K, Nastrom G (1985) On the spectrum of atmospheric velocity fluctuations seen by MST/ST radar and their interpretation. Radio Sci 20:1339–1347CrossRefGoogle Scholar
  11. Gage K, Nastrom G (1986) Theoretical interpretation of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft during GASP. J Atmos Sci 43:729–740CrossRefGoogle Scholar
  12. Heggem T, Lende R, Løvseth J (1998) Analysis of long time series of coastal wind. J Atmos Sci 55:2907–2917CrossRefGoogle Scholar
  13. Högström U, Hunt J, Smedman AS (2002) Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorol 103:101–124CrossRefGoogle Scholar
  14. Højstrup J (1982) Velocity spectra in the unstable boundary layer. J Atmos Sci 39:2239–2248CrossRefGoogle Scholar
  15. Kaimal J, Finnigan J (1994) Atmospheric boundary layer flows. Oxford University Press, New York, p 289Google Scholar
  16. Kaimal J, Wyngaard J, Izumi Y, Coté O (1972) Spectral characteristics of surface-layer turbulence. Q J R Meteorol Soc 98:563–589CrossRefGoogle Scholar
  17. Kaimal J, Wyngaard J, Haugen J, Coté O, Izumi Y, Caughey S, Readings CJ (1976) Turbulence structure in the convective boundary layer. J Atmos Sci 33:2152–2169CrossRefGoogle Scholar
  18. Kim K, Adrian R (1999) Very large-scale motion in the outer layer. Phys Fluids 11:417–422CrossRefGoogle Scholar
  19. Larsen SE (1986) Hotwire measurements of atmospheric turbulence near the ground. Tech Rep Risø-R-233, Risø National Laboratory, Roskilde. ISBN 87-550-0056-8Google Scholar
  20. Larsen SE, Højstrup J, Olsen H (1985) Parameterization of the low frequency part of spectra of horizontal velocity component in the stable surface boundary layer. In: Proceeings of the models of turbulence and diffusion in stably stratified regions of the natural environment. Clarendon Press, pp 181–204Google Scholar
  21. Larsén XG, Vincent CL, Larsen SE (2013) Spectral structure of the mesoscale winds over the water. Q J R Meteorol Soc 139:685–700.  https://doi.org/10.1002/qj.2003 CrossRefGoogle Scholar
  22. Larsén XG, Larsen SE, Petersen EL (2016) Full-scale spectrum of boundary-layer winds. Boundary-Layer Meteorol 159:349–371CrossRefGoogle Scholar
  23. Larsén XG, Bolaños R, Du J, Kelly M, Koefoed-Hansen H, Larsen S, Karagali I, Badger M, Hahmann A, Imberger M, Sørensen JT, Jackson S, Volker P, Petersen O, Jenkins A, Graham A (2017a) Final report for X-WiWa project: extreme winds and waves for offshore turbines. Report DTU Wind Energy E-0154. ISBN: 978-87-93549-22-7. http://orbit.dtu.dk/files/139272513/FinalReport_PSO12020_XWiWa_20171031.pdf or Final Project Report on http://www.xwiwa.dk/main-results
  24. Larsén XG, Du J, Bolaños R, Larsen SE (2017b) On the impact of wind on the development of wave field during storm Britta. Ocean Dyn 67(11):1407–1427.  https://doi.org/10.1007/s10236-017-1100-1 CrossRefGoogle Scholar
  25. Larsén XG, Petersen EL, Larsen SE (2018) Variation of boundary-layer wind spectra with height. Q J R Meteorol Soc. 1–13  https://doi.org/10.1002/qj.3301
  26. LeMone M (1976) Modulation of turbulence energy by longitudinal rolls in an unstable planetary boundary layer. J Atmos Sci 33:1308–1320CrossRefGoogle Scholar
  27. Lilly D, Petersen E (1983) Aircraft measurements of atmospheric kinetic energy spectra. Tellus 35A:379–382CrossRefGoogle Scholar
  28. Lindborg E (1999) Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J Fluid Mech 388:259–288CrossRefGoogle Scholar
  29. Mann J (1994) The spatial structure of neutral atmospheric surface-layer turbulence. J Fluid Mech 273:141–168CrossRefGoogle Scholar
  30. Mehrens AR, Hahmann AN, Larsén XG, von Bremen L (2016) Correlation and coherence of mesoscale wind speeds over the sea. Q J R Meteorol Soc 142:3186–3194CrossRefGoogle Scholar
  31. Mikkelsen T, Larsen SE, Jørgensen HE, Astrup P, Larsén XG (2017) Scaling of turbulence spectra measured in strong shear flow near the earth surface. Phys Scr 92(124):002Google Scholar
  32. Nilsson E, Rutgersson A, Smedman AS, Sullivan P (2012) Convective boundary-layer structure in the presence of wind-following swell. Q J R Meteorol Soc 138:1476–1489.  https://doi.org/10.1002/qj.1898 CrossRefGoogle Scholar
  33. Peña A, Floors R, Wagner R, Courtney M, Gryning SE, Salthe A, Larsén XG, Hahmann AN, Hasager C (2016) Ten years of boundary-layer and wind-power meteorology at Høvsøre, Denmark. Boundary-Layer Meteorol 158:1–26CrossRefGoogle Scholar
  34. Petersen EL (1975) On the kinetic energy spectrum of the atmospheric motions in the planetary boundary layer. Tech Rep RISØ285, Risø National Laboratory, Roskilde. http://www.risoe.dk/rispubl/reports_INIS/RISO285.pdf
  35. Smedman AS (1991) Occurrence of roll circulation in a shallow boundary layer. Boundary-Layer Meteorol 51:343–358CrossRefGoogle Scholar
  36. Smedman AS, Bergström H, Högström U (1995) Spectra, variance and length scales in a marine stable boundary layer dominated by a low level jet. Boundary-Layer Meteorol 76:211–232CrossRefGoogle Scholar
  37. Smedman-Högström AS, Högström U (1974) Spectral gap in surface-layer measurements. J Atmos Sci 32:660–672Google Scholar
  38. Sørensen P, Hansen A, Rosas P (2002) Wind models for simulation of power fluctuations from wind farms. J Wind Eng Ind Aerodyn 90:1381–1402CrossRefGoogle Scholar
  39. Sørensen P, Cutululis NA, Vigueras-Rodríguez A, Madsen H, Pinson P, Jensen LE, Hjerrild J, Donovan M (2008) Modelling of power fluctuations from large offshore wind farms. Wind Energy 11:29–43CrossRefGoogle Scholar
  40. Tchen C, Larsen S, Pécseli H, Mikkelsen T (1985) Large-scale spectral structure with a gap in the stably stratified atmosphere. Phys Scr 31:616–620CrossRefGoogle Scholar
  41. Van der Hoven I (1957) Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour. J Meteorol 14:160–164CrossRefGoogle Scholar
  42. Vincent CL (2010) Mesoscale wind fluctuations over danish waters. Risø-PhD; No 70(EN), PhD thesis. ISBN 978-87-550-3864-6Google Scholar
  43. Vincent CL, Larsén XG, Larsen SE, Sørensen P (2013) Cross-spectra over the sea from observations and mesoscale modelling. Boundary-Layer Meteorol 146:297–318CrossRefGoogle Scholar
  44. Vinnichenko NK (1970) The kinetic energy spectrum in the free atmosphere—1 second to 5 years. Tellus 22:158–166CrossRefGoogle Scholar
  45. Wu L, Hristov T, Rutgersson A (2018) Vertical profiles of wave-coherent momentum flux and velocity variances in the marine atmospheric boundary layer. J Phys Ocean.  https://doi.org/10.1175/JPO-D-17-0052.1

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Wind Energy DepartmentRisø Campus of the Danish Technical UniversityRoskildeDenmark

Personalised recommendations