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Reconstruction of turbulent flow fields from lidar measurements using large-eddy simulation

Published online by Cambridge University Press:  13 November 2020

Pieter Bauweraerts  and
Johan Meyers Open the ORCID record for Johan Meyers [Opens in a new window]
Pieter Bauweraerts
Affiliation:
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300A, B3001Leuven, Belgium
Johan Meyers*
Affiliation:
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300A, B3001Leuven, Belgium
*
†Email address for correspondence: johan.meyers@kuleuven.be
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Abstract

We investigate the reconstruction of a turbulent flow field in the atmospheric boundary layer from a time series of lidar measurements, using large-eddy simulations (LES) and a four-dimensional variational data assimilation algorithm. This leads to an optimisation problem in which the error between measurements and simulations is minimised over an observation time horizon. We also consider reconstruction based on a Taylor's frozen turbulence (TFT) model as a point of comparison. To evaluate the approach, we construct a series of virtual lidar measurements from a fine-grid LES of a pressure-driven boundary layer. The reconstruction uses LES on a coarser mesh and smaller domain, and results are compared to the fine-grid reference. Two lidar scanning modes are considered: a classical plan-position-indicator mode, which swipes the lidar beam in a horizontal plane, and a three-dimensional pattern that is based on a Lissajous curve. We find that normalised errors lie between $15\,\%$ and $25\,\%$ (error variance normalised by background variance) in the scanning region, and increase to $100\,\%$ over a distance that is comparable to the correlation length scale outside this scanning region. Moreover, LES outperforms TFT by 30 %–70 % depending on scanning mode and location.

JFM classification

Turbulent Flows: Turbulent boundary layers Geophysical and Geological Flows: Atmospheric flows Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , A17
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Adrian, R. J. 1979 Conditional eddies in isotropic turbulence. Phys. Fluids 22 (11), 2065–2070.CrossRefGoogle Scholar
Adrian, R. J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure: homogeneous shear flow. J. Fluid Mech. 190, 531–559.CrossRefGoogle Scholar
Aitken, M. L., Banta, R. M., Pichugina, Y. L. & Lundquist, J. K. 2014 Quantifying wind turbine wake characteristics from scanning remote sensor data. J. Atmos. Ocean. Technol. 31 (4), 765–787.CrossRefGoogle Scholar
Banakh, V. A., Bodaruev, V. V. & Smalikho, I. N. 1997 Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data. Atmos. Ocean. Opt. 10, 957–965.Google Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Bewley, T. R., Moin, P. & Temam, R. 2001 DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 447, 179–225.CrossRefGoogle Scholar
Borraccino, A., Schlipf, D., Haizmann, F. & Wagner, R. 2017 Wind field reconstruction from nacelle-mounted lidars short range measurements. Wind Energy Sci. Disc. 2, 269–283.CrossRefGoogle Scholar
Borzi, A. & Schulz, V. 2011 Computational Optimization of Systems Governed by Partial Differential Equations. SIAM.CrossRefGoogle Scholar
Bos, R., Giyanani, A. & Bierbooms, W. 2016 Assessing the severity of wind gusts with lidar. Remote Sens. 8 (9), 758.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Byrd, R. H., Lu, P., Nocedal, J. & Zhu, C. 1995 A limited memory algorithm for bound constrained optimization. J. Sci. Comput. 16 (5), 1190–1208.Google Scholar
Chai, T. & Lin, C.-L. 2003 Estimation of turbulent viscosity and diffusivity in adjoint recovery of atmospheric boundary layer flow structures. Multiscale Model. Simul. 1 (2), 196–220.CrossRefGoogle Scholar
Chai, T., Lin, C.-L. & Newsom, R. K. 2004 Retrieval of microscale flow structures from high-resolution Doppler lidar data using an adjoint model. J. Atmos. Sci. 61 (13), 1500–1520.2.0.CO;2>CrossRefGoogle Scholar
Courtier, P., Andersson, E., Heckley, W., Vasiljevic, D., Hamrud, M., Hollingsworth, A., Rabier, F., Fisher, M. & Pailleux, J. 1998 The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: formulation. Q. J. R. Meteorol. Soc. 124 (550), 1783–1807.Google Scholar
Dimitrov, N. & Natarajan, A. 2017 Application of simulated lidar scanning patterns to constrained Gaussian turbulence fields for load validation. Wind Energy 20 (1), 79–95.CrossRefGoogle Scholar
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), 397–416.CrossRefGoogle Scholar
Frehlich, R., Hannon, S. M. & Henderson, S. W. 1998 Coherent Doppler lidar measurements of wind field statistics. Boundary-Layer Meteorol. 86 (2), 233–256.CrossRefGoogle Scholar
Gal-Chen, T., Xu, M. & Eberhard, W. L. 1992 Estimations of atmospheric boundary layer fluxes and other turbulence parameters from Doppler lidar data. J. Geophys. Res. 97 (D17), 18409–18423.CrossRefGoogle Scholar
Goit, J. P. & Meyers, J. 2015 Optimal control of energy extraction in wind-farm boundary layers. J. Fluid Mech. 768, 5–50.CrossRefGoogle Scholar
Haben, S. A., Lawless, A. S. & Nichols, N. K. 2011 Conditioning and preconditioning of the variational data assimilation problem. Comput. Fluids 46 (1), 252–256.CrossRefGoogle Scholar
Hager, W. W. 2000 Runge–Kutta methods in optimal control and the transformed adjoint system. Numer. Math. 87 (2), 247–282.CrossRefGoogle Scholar
Iungo, G. V., Wu, Y.-T. & Porté-Agel, F. 2013 Field measurements of wind turbine wakes with lidars. J. Atmos. Ocean. Technol. 30 (2), 274–287.CrossRefGoogle Scholar
Jang, S. S., Joseph, B. & Mukai, H. 1986 Comparison of two approaches to on-line parameter and state estimation of nonlinear systems. Ind. Engng Chem. Res. 25 (3), 809–814.Google Scholar
Jazwinski, A. H. 2007 Stochastic Processes and Filtering Theory. Courier Corporation.Google Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Käsler, Y., Rahm, S., Simmet, R. & Kühn, M. 2010 Wake measurements of a multi-MW wind turbine with coherent long-range pulsed Doppler wind lidar. J. Atmos. Ocean. Technol. 27 (9), 1529–1532.CrossRefGoogle Scholar
Krishnamurthy, R., Choukulkar, A., Calhoun, R., Fine, J., Oliver, A. & Barr, K. S. 2013 Coherent Doppler lidar for wind farm characterization. Wind Energy 16 (2), 189–206.CrossRefGoogle Scholar
Le Dimet, F.-X. & Talagrand, O. 1986 Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus 38 (2), 97–110.CrossRefGoogle Scholar
Lewis, J. M. & Derber, J. C. 1985 The use of adjoint equations to solve a variational adjustment problem with advective constraints. Tellus 37 (4), 309–322.CrossRefGoogle Scholar
Li, J. 2015 A note on the Karhunen–Loève expansions for infinite-dimensional Bayesian inverse problems. Stat. Probab. Lett. 106, 1–4.CrossRefGoogle Scholar
Lin, C.-L., Chai, T. & Sun, J. 2001 Retrieval of flow structures in a convective boundary layer using an adjoint model: identical twin experiments. J. Atmos. Sci. 58 (13), 1767–1783.2.0.CO;2>CrossRefGoogle Scholar
Lorenc, A. C. 1981 A global three-dimensional multivariate statistical interpolation scheme. Mon. Weath. Rev. 109 (4), 701–721.2.0.CO;2>CrossRefGoogle Scholar
Lorenc, A. C. 1986 Analysis methods for numerical weather prediction. Q. J. R. Meteorol. Soc. 112 (474), 1177–1194.CrossRefGoogle Scholar
Lundquist, J. K., Churchfield, M. J., Lee, S. & Clifton, A. 2015 Quantifying error of lidar and sodar Doppler beam swinging measurements of wind turbine wakes using computational fluid dynamics. Atmos. Meas. Tech. 8, 907–920.CrossRefGoogle Scholar
Mason, P. J. & Thomson, D. J. 1992 Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech. 242, 51–78.CrossRefGoogle Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719.CrossRefGoogle Scholar
Menut, L., Flamant, C., Pelon, J. & Flamant, P. H. 1999 Urban boundary-layer height determination from lidar measurements over the Paris area. Appl. Opt. 38 (6), 945–954.CrossRefGoogle ScholarPubMed
Meyers, J. 2011 Error-landscape assessment of large-eddy simulations: a review of the methodology. J. Sci. Comput. 49 (1), 65–77.CrossRefGoogle Scholar
Meyers, J. & Sagaut, P. 2007 Evaluation of Smagorinsky variants in large-eddy simulations of wall-resolved plane channel flows. Phys. Fluids 19, 095105.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Moeng, C.-H. 1984 A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41 (13), 2052–2062.2.0.CO;2>CrossRefGoogle Scholar
Moré, J. J. & Thuente, D. J. 1994 Line search algorithms with guaranteed sufficient decrease. ACM Trans. Math. Softw. 20 (3), 286–307.CrossRefGoogle Scholar
Munters, W., Meneveau, C. & Meyers, J. 2016 Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows. Phys. Fluids 28 (2), 025112.CrossRefGoogle Scholar
Newsom, R. K. & Banta, R. M. 2004 Assimilating coherent Doppler lidar measurements into a model of the atmospheric boundary layer. Part I: algorithm development and sensitivity to measurement error. J. Atmos. Ocean. Technol. 21 (9), 1328–1345.2.0.CO;2>CrossRefGoogle Scholar
Newsom, R. K., Ligon, D., Calhoun, R., Heap, R., Cregan, E. & Princevac, M. 2005 Retrieval of microscale wind and temperature fields from single-and dual-Doppler lidar data. J. Appl. Meteorol. 44 (9), 1324–1345.CrossRefGoogle Scholar
Nocedal, J. & Wright, S. J. 2006 Numerical Optimization. Springer Science & Business Media.Google Scholar
Peña, A. & Hasager, C. B. 2011 Remote sensing for wind energy. Risø National Laboratory for Sustainable Energy Tech. Rep. 3184(EN). Technical University of Denmark.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Raach, S., Schlipf, D., Haizmann, F. & Cheng, P. W. 2014 Three dimensional dynamic model based wind field reconstruction from lidar data. J. Phys.: Conf. Ser. 524, 012005.Google Scholar
Rao, C. V. & Rawlings, J. B. 2002 Constrained process monitoring: moving-horizon approach. AIChE J. 48 (1), 97–109.CrossRefGoogle Scholar
Rhodes, M. E. & Lundquist, J. K. 2013 The effect of wind-turbine wakes on summertime US Midwest atmospheric wind profiles as observed with ground-based Doppler lidar. Boundary-Layer Meteorol. 149 (1), 85–103.CrossRefGoogle Scholar
Schlipf, D., Schlipf, D. J. & Kühn, M. 2013 Nonlinear model predictive control of wind turbines using lidar. Wind Energy 16 (7), 1107–1129.CrossRefGoogle Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to $\delta ^+\approx 2000$. Phys. Fluids 26 (10), 105109.CrossRefGoogle Scholar
Simley, E., Pao, L., Frehlich, R., Jonkman, B. & Kelley, N. 2011 Analysis of wind speed measurements using continuous wave lidar for wind turbine control. In 49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, p. 263. AIAA.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. I. Coherent structures. Q. Appl. Maths 45 (3), 561–571.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weath. Rev. 91 (3), 99–164.2.3.CO;2>CrossRefGoogle Scholar
Squire, D. T., Morrill-Winter, C., Hutchins, N., Schultz, M. P., Klewicki, J. C. & Marusic, I. 2016 Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers. J. Fluid Mech. 795, 210–240.CrossRefGoogle Scholar
Stuart, A. M. 2010 Inverse problems: a Bayesian perspective. Acta Numerica 19, 451–559.CrossRefGoogle Scholar
Talagrand, O. & Courtier, P. 1987 Variational assimilation of meteorological observations with the adjoint vorticity equation. I: theory. Q. J. R. Meteorol. Soc. 113 (478), 1311–1328.CrossRefGoogle Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164 (919), 476–490.Google Scholar
Townsend, A. A. 1980 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Tröltzsch, F. 2010 Optimal Control of Partial Differential Equations: Theory, Methods, and Applications, vol. 112. American Mathematical Society.Google Scholar
Trémolet, Y. 2006 Accounting for an imperfect model in 4D-Var. Q. J. R. Meteorol. Soc. 132 (621), 2483–2504.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.CrossRefGoogle Scholar
Wakimoto, R. M. & McElroy, J. L. 1986 Lidar observation of elevated pollution layers over Los Angeles. J. Clim. Appl. Meteorol. 25 (11), 1583–1599.2.0.CO;2>CrossRefGoogle Scholar
Xia, Q., Lin, C.-L., Calhoun, R. & Newsom, R. K. 2008 Retrieval of urban boundary layer structures from Doppler lidar data. Part I: accuracy assessment. J. Atmos. Sci. 65 (1), 3–20.CrossRefGoogle Scholar