Abstract
We develop a model that predicts all two-point correlations in high Reynolds number turbulent flow, in both space and time. This is accomplished by combining the design philosophies behind two existing models, the Mann spectral velocity tensor, in which isotropic turbulence is distorted according to rapid distortion theory, and Kristensen’s longitudinal coherence model, in which eddies are simultaneously advected by larger eddies as well as decaying. The model is compared with data from both observations and large-eddy simulations and is found to predict spatial correlations comparable to the Mann spectral tensor and temporal coherence better than any known model. Within the developed framework, Lagrangian two-point correlations in space and time are also predicted, and the predictions are compared with measurements of isotropic turbulence. The required input to the models, which are formulated as spectral velocity tensors, can be estimated from measured spectra or be derived from the rate of dissipation of turbulent kinetic energy, the friction velocity and the mean shear of the flow. The developed models can, for example, be used in wind-turbine engineering, in applications such as lidar-assisted feed forward control and wind-turbine wake modelling.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Batchelor GK (1953) The theory of homogeneous turbulence. Cambridge University Press, Cambridge, UK, pp 28–33
Berg J, Mann J, Patton EG (2013) Lidar-observed stress vectors and veer in the atmospheric boundary layer. J Atmos OceanTechnol 30(9):1961–1969. doi:10.1175/JTECH-D-12-00266.1
Bossanyi E, Savini B, Iribas M, Hau M, Fischer B, Schlipf D, van Engelen T, Rossetti M, Carcangiu CE (2012) Advanced controller research for multi-MW wind turbines in the UPWIND project. Wind Energy 15(1):119–145. doi:10.1002/we.523
Bossanyi E (2013) Un-freezing the turbulence: application to LiDAR-assisted wind turbine control. IET Renew Power Gener 7(4):321–329
Chougule AS (2013) Influence of atmospheric stability on the spatial structure of turbulence. DTU Wind Energy PhD-0028 (EN)
Chougule A, Mann J, Segalini A, Dellwik E (2014) Spectral tensor parameters for wind turbine load modeling from forested and agricultural landscapes. Wind Energy 18(3):469–481. doi:10.1002/we.1709
de Maré M, Mann J (2014) Validation of the Mann spectral tensor for offshore wind conditions at different atmospheric stabilities. J Phys Conf Ser 524(1):12,106
Fung JCH, Hunt JCR, Malik NA, Perkins RJ (1992) Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes. J Fluid Mech 236:281–318. doi:10.1017/S0022112092001423
Hanazaki H, Hunt JCR (2004) Structure of unsteady stably stratified turbulence with mean shear. J Fluid Mech 507:1–42. doi:10.1017/S0022112004007888
Hunt JCR, Wray AA, Buell JC (1987) Big whorls carry little whorls. In: Proceedings of the 1987 Summer Program,CTR-S87 NASA Centre for Turbulence Research
Kaneda Y, Ishida T (2000) Suppression of vertical diffusion in strongly stratified turbulence. J Fluid Mech 402:311–327
Kolmogorov AN (1968) Local structure of turbulence in an incompressible viscous fluid at very high Reynolds numbers. Soviet Physics Uspekhi 10(6):734
Kristensen L (1979) On longitudinal spectral coherence. Boundary-Layer Meteorol 16(2):145–153. doi:10.1007/BF02350508
Larsen GC, Madsen HA, Thomsen K, Larsen TJ (2008) Wake meandering: a pragmatic approach. Wind Energy 11(4):377–395. doi:10.1002/we.267
Mann J (1994) The spatial structure of neutral atmospheric surface-layer turbulence. J Fluid Mech 273:141–168. doi:10.1017/S0022112094001886
Mikkelsen T, Angelou N, Hansen K, Sjöholm M, Harris M, Slinger C, Hadley P, Scullion R, Ellis G, Vives G (2013) A spinner-integrated wind lidar for enhanced wind turbine control. Wind Energy 16(4):625–643. doi:10.1002/we.1564
Moffatt K (1967) Interaction of turbulence with strong wind shear. In: Yaglom AM, Tatarski VI (eds) Atmosphere turbulence and radio wave propagationAtmosphere turbulence and radio wave propagation. Nauka, Moscow, pp 139–156
Ott S, Mann J (2005) An experimental test of Corrsin’s conjecture and some related ideas. New J Phys 7(1):142
Pao LY, Johnson KE (2011) Control of wind turbines. IEEE Control Syst 31(2):44–62
Peña A, Gryning SE, Mann J (2010) On the length-scale of the wind profile. Q J R Meteorol Soc 136(653):2119–2131. doi:10.1002/qj.714
Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge, UK, pp 219–223
Saffman PG (1963) An approximate calculation of the Lagrangian auto-correlation coefficient for stationary homogeneous turbulence. Appl Sci Res Sect A 11(3):245–255. doi:10.1007/BF03184983
Salhi a, Cambon C (2010) Stability of rotating stratified shear flow: an analytical study. Phys Rev E 81(2):026,302
Sathe A, Mann J (2013) A review of turbulence measurements using ground-based wind lidars. Atmos Meas Tech 6(11):3147–3167. doi:10.5194/amt-6-3147-2013
Schlipf D, Cheng PW, Mann J (2013) Model of the correlation between lidar systems and wind turbines for lidar-assisted control. J Atmos OceanTechnol 30:2233
Simley E, Pao LY, Frehlich R, Jonkman B, Kelley N (2014) Analysis of light detection and ranging wind speed measurements for wind turbine control. Wind Energy 17(3):413–433. doi:10.1002/we.1584
Sullivan PP, Patton EG (2011) The effect of mesh resolution on convective boundary layer statistics and structures generated by large-eddy simulation. J Atmos Sci 68(10):2395–2415. doi:10.1175/JAS-D-10-05010.1
Townsend AA (1976) The structure of turbulent shear flow, 2nd edn. Cambridge University Press, Cambridge, UK, pp 88–91
von Kármán T (1948) Progress in the statistical theory of turbulence. Proc Nail Acad Sci 34(11):530–539
Wilczek M, Stevens RJAM, Narita Y, Meneveau C (2014) A wavenumber-frequency spectral model for atmospheric boundary layers. J Phys Conf Ser 524(1):12,104
Wilczek M, Narita Y (2012) Wave-number-frequency spectrum for turbulence from a random sweeping hypothesis with mean flow. Phys Rev E 6(86):066,308
Wyngaard JC, Coté OR (1972) Cospectral similarity in the atmospheric surface layer. Q J R Meteorol Soc 98(417):590–603. doi:10.1002/qj.49709841708
Acknowledgments
This work has been made possible by funding from Forsknings- og Innovationsstyrelsen, DONG Energy A/S and the DSF Flow Center. The authors would like to thank Ned Patton at UCAR for generously making LES data available, and Gunner Larsen and Søren Ott for valuable suggestions and feedback.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
de Maré, M., Mann, J. On the Space-Time Structure of Sheared Turbulence. Boundary-Layer Meteorol 160, 453–474 (2016). https://doi.org/10.1007/s10546-016-0143-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10546-016-0143-z