Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-22T09:54:19.173Z Has data issue: false hasContentIssue false
  • English
  • Français

Large-eddy simulation-based reconstruction of turbulence in a neutral boundary layer using spectral-tensor regularization

Published online by Cambridge University Press:  27 February 2024

Ahmed Alreweny Open the ORCID record for Ahmed Alreweny [Opens in a new window] ,
Stefan Vandewalle Open the ORCID record for Stefan Vandewalle [Opens in a new window]  and
Johan Meyers Open the ORCID record for Johan Meyers [Opens in a new window]
Ahmed Alreweny*
Affiliation:
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300A, B3001 Leuven, Belgium
Stefan Vandewalle
Affiliation:
Department of Computer Science, KU Leuven, Celestijnenlaan 200A, B3001 Leuven, Belgium
Johan Meyers
Affiliation:
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300A, B3001 Leuven, Belgium
*
†Email address for correspondence: ahmed.alreweny@kuleuven.be
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose an efficient method to reconstruct the turbulent flow field in a neutrally stratified atmospheric boundary layer using large-eddy simulation (LES) and a series of lidar measurements. The reconstruction is formulated as a strong four-dimensional variational data assimilation problem, which involves optimizing two competing terms that contribute in the objective functional. The first term is a likelihood term, while the second contains the initial background distribution of turbulent velocity fluctuations and works as a regularization term. However, computing and storing the full background covariance tensor in turbulent flows is time consuming and resource intensive. In the current work, we investigate the possibility of replacing the complex background tensor by simple analytical approximations based on spectral tensors such as the Hunt–Graham–Wilson (HGW) model (Boundary-Layer Meteorol., vol. 85, 1997, pp. 35–52) or the Mann model (J. Fluid Mech., vol. 273, 1994, pp. 141–168). Afterwards, the problem is solved using a quasi-Newton algorithm and preconditioned to enhance the convergence rate. We test the method using virtual lidar measurements collected on a fine reference LES. Results show a super-linear convergence rate of the optimization algorithm to a local minimum and very good agreement between virtual lidar measurements and reconstruction in the scanning region. Furthermore, we demonstrate that incorporating the Saffman energy spectrum ($E(k) \sim k^2$ where E is the energy spectrum and k is the magnitude of the wavenumber vector) at low wavenumbers into the Mann spectral tensor yields a longer streamwise correlation length, resulting in reduced reconstruction error when compared with the Batchelor spectrum ($E(k) \sim k^4$). Finally, we observe that using the HGW model or Mann model with a Saffman spectrum yields similar results.

JFM classification

Turbulent Flows: Turbulent boundary layers Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Homogeneous turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 981 , 25 February 2024 , A28
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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
Alcayaga, L., Larsen, G.C., Kelly, M. & Mann, J. 2020 Large-scale coherent structures in the atmosphere over a flat terrain. J. Phys.: Conf. Ser. 1618, 062030.Google Scholar
Bannister, R.N. 2017 A review of operational methods of variational and ensemble-variational data assimilation. Q. J. R. Meteorol. Soc. 143 (703), 607–633.CrossRefGoogle Scholar
Bauweraerts, P. & Meyers, J. 2020 Reconstruction of turbulent flow fields from lidar measurements using large-eddy simulation. J. Fluid Mech. 906, A17.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), 1–18.CrossRefGoogle Scholar
Byrd, R.H., Lu, P., Nocedal, J. & Zhu, C. 1995 A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16 (5), 1190–1208.CrossRefGoogle 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
Chen, Y., Guo, F., Schlipf, D. & Cheng, P.W. 2022 Four-dimensional wind field generation for the aeroelastic simulation of wind turbines with lidars. Wind Energy Sci. 7 (2), 539–558.CrossRefGoogle Scholar
Chougule, A., Mann, J., Kelly, M. & Larsen, G.C. 2018 Simplification and validation of a spectral-tensor model for turbulence including atmospheric stability. Boundary-Layer Meteorol. 167, 371–397.CrossRefGoogle Scholar
Davidson, P.A. 2010 On the decay of Saffman turbulence subject to rotation, stratification or an imposed magnetic field. J. Fluid Mech. 663, 268–292.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
Gilling, L. 2009 TuGen: synthetic turbulence generator, manual and user's guide. DCE Tech. Rep. 76. Department of Civil Engineering, Aalborg University.Google 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
Guo, F., Mann, J., Peña, A., Schlipf, D. & Cheng, P.W. 2022 The space-time structure of turbulence for lidar-assisted wind turbine control. Renew. Energy 195, 293–310.CrossRefGoogle Scholar
Gustafsson, N., et al. 2018 Survey of data assimilation methods for convective-scale numerical weather prediction at operational centres. Q. J. R. Meteorol. Soc. 144 (713), 1218–1256.CrossRefGoogle Scholar
Holmes, P., Lumley, J.L. & Berkooz, G. 1996 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.CrossRefGoogle Scholar
Hunt, J.C.R. & Graham, J.M.R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 84 (2), 209–235.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.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
Kaimal, J.C., Wyngaard, J.C., Izumi, Y. & Coté, O.R. 1972 Spectral characteristics of surface-layer turbulence. Q. J. R. Meteorol. Soc. 98 (417), 563–589.Google 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
Kristensen, L., Lenschow, D.H., Kirkegaard, P. & Courtney, M. 1989 The spectral velocity tensor for homogeneous boundary-layer turbulence. Boundary-Layer Meteorol. 47 (1–4), 149–193.CrossRefGoogle Scholar
Le Dimet, F.-X., Navon, I.M. & Ştefănescu, R. 2017 Variational data assimilation: optimization and optimal control. In Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications, vol. III, pp. 1–53. Springer International Publishing.CrossRefGoogle Scholar
Lee, M.J. & Hunt, J.C.R. 1989 The structure of sheared turbulence near a plane boundary. In Proceedings of the 7th Symposium on Turbulent Shear Flows, vol. 1, pp. 8.1.1–8.1.6. Springer.Google Scholar
Lin, C.L., Chai, T. & Sun, J. 2001 Retrieval of flow structures in a convective boundary layer using an adjoint model: indentical twin experiments. J. Atmos. Sci. 58 (13), 1767–1783.2.0.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
Mann, J. 1994 The spatial structure of neutral atmospheric surface-layer turbulence. J. Fluid Mech. 273, 141–168.CrossRefGoogle Scholar
Mann, J. 1998 Wind field simulation. Prob. Engng Mech. 13 (4), 269–282.CrossRefGoogle Scholar
Marusic, I. & Heuer, W.D.C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99, 114504.CrossRefGoogle ScholarPubMed
Mason, P.J. & Thomson, D.J. 1992 Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech. 242 (28), 51–78.CrossRefGoogle Scholar
Meyers, J. & Sagaut, P. 2007 Evaluation of Smagorinsky variants in large-eddy simulations of wall-resolved plane channel flows. Phys. Fluids 19 (9), 095105.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), 1324–1344.CrossRefGoogle Scholar
Nguyen, C.V. & Soulhac, L. 2021 Data assimilation methods for urban air quality at the local scale. Atmos. Environ. 253, 118366.CrossRefGoogle Scholar
Nocedal, J. & Wright, S.J. 2006 Numerical Optimization, 2nd edn. Springer.Google Scholar
Peltier, L.J., Wyngaard, J.C., Khanna, S. & Brasseur, J.G. 1996 Spectra in the unstable surface layer. J. Atmos. Sci. 53 (1), 49–61.2.0.CO;2>CrossRefGoogle Scholar
Peña, A., et al. 2013 Remote sensing for wind energy. Tech. Rep. DTU Wind Energy-E-Report-0029(EN). DTU Wind Energy, Technical University of Denmark.Google Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Sabale, A.K. & Gopal, N.K.V. 2019 Nonlinear aeroelastic analysis of large wind turbines under turbulent wind conditions. AIAA J. 57 (10), 4416–4432.CrossRefGoogle Scholar
Saffman, P.G. 1967 The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27 (3), 581–593.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
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
Stuart, A.M. 2010 Inverse problems: a Bayesian perspective. Acta Numerica 19, 451–559.Google Scholar
Stull, R.B. 1988 An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers.CrossRefGoogle Scholar
Sun, J., Flicker, D.W. & Lilly, D.K. 1991 Recovery of three-dimensional wind and temperature fields from simulated single-Doppler radar data. J. Atmos. Sci. 48 (6), 876–890.2.0.CO;2>CrossRefGoogle Scholar
Wilson, D.K. 1997 A three-dimensional correlation/spectral model for turbulent velocities in a convective boundary layer. Boundary-Layer Meteorol. 85 (1), 35–52.CrossRefGoogle Scholar
Wilson, D.K 1998 Anisotropic turbulence models for acoustic propagation through the neutral atmospheric surface layer. Tech. Rep. ARL-TR-1519. US Army Research Laboratory.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