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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
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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

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JFM Papers
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Journal of Fluid Mechanics , Volume 981 , 25 February 2024 , A28
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© The Author(s), 2024. Published by Cambridge University Press

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