the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Nov 2025
Generating high fidelity wind fields from the wind speed correlation tensor
Abstract. In this publication a new method to generate stochastic representations of homogeneous and isotropic wind fields is presented. In contrast to the typically employed algorithm, the new approach is based on the wind speed correlation tensor. This allows simulating a homogeneous and isotropic turbulent wind field with very high accuracy. In this publication, a deviation of the obtained dataset's structure function from the theoretical one of at least one order of magnitude lower than the commonly used method is achieved. Furthermore, a compensation method to decrease this error even further is proposed. Moreover, being a generic method, it can be used to simulate other Gaussian phenomena (e.g., temperature or index of refraction fluctuations) on various spatial domains and grid shapes.
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Status: open (until 21 Dec 2025)
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RC1: 'Comment on wes-2025-221', Anonymous Referee #1, 03 Dec 2025
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AC1: 'Reply on RC1', Matteo Faccioni, 12 Dec 2025
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The authors would like to thank the reviewer for her/his time and effort. All the raised points were very helpful in pointing out the parts not clear, and in tracking down the remaining mishaps.
The answers to the review are attached as a .pdf file.
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AC1: 'Reply on RC1', Matteo Faccioni, 12 Dec 2025
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- 1
Review of lin
Generating high fidelity wind fields from the wind speed correlation tensor
Wind Energy Science
Summary
The proposed study presents a method for generating synthetic isotropic homogeneous turbulence (denoted the CBM method by the authors). It is based on the a priori knowledge of the two-point correlation tensor that is used to generate the corresponding velocity field first in Fourier space using a series of random number before going back to physical space via inverse Fourier transform. The performance of the proposed method is tested against a more standard method based on the a priori knowledge of the velocity spectrum (the so-called RPM method).
The manuscript is well organized and well written, quality of the English language is good overall. The authors present some interesting analysis and findings that might interest the community. However, some points need to be addressed before the paper can be considered for publication.
Comments
As pointed out by the authors, the CBM method they propose does not seem to be that new. The novelty they added to the previous correlation-based methods is not clear at all. Could the authors give the reader more details about that ?
Have the authors thought about addressing the more challenging issue of generating non-isotropic, non-homogeneous synthetic turbulence ?
L124: the authors point out the limitation of previous correlation based methods (Dietrich and
Newsam, 1997; Wood and Chan, 1994) due to the fact they “on the correlation matrix having a Toeplitz structure” To the reviewer’s limited knowledge, the Toeplitz structure of the correlation matrix is directly linked to the fact that one considers homogeneous (or stationary) directions, which is mandatory to be able to use Fourier transforms. As the authors have designed their method to generate isotropic homogeneous turbulence, their method has the same requirement: a correlation matrix with a Toeplitz structure. Could the authors comment on that please ?
L125: “This is not always the case in wind field generation problems.” could the authors give some example of cases were correlation matrices are not of Toeplitz type but which their method could handle anyway ?
Fig 1: how the ideal structure function is calculated ?
For the RPM, the authors prescribe a von Karman spectrum (I presume it is one-dimensional), whereas for the CBM, they prescribe the full 3D tensor B_pq. What is the impact of these difference ?
L156 and subsequent: the description and the origin of the problem related to PSD with negative values is not clear at all. Could the author elaborate on that ?
Could the authors show the spectra of the velocity field obtained using the CBM and compare it to the expected spectrum and that used with the RPM ?
Fig 5: could the author explain why the error of the RPM remains independent of the size of the spatial domain ? It seems to contradict the point they made in the last paragraph of page 4 (line 98) stating that the grid domain acts as a bandpass filter. One would expect the performance to increase as the bandwidth of the filter increases (with domain size).
It would interesting to show the structure functions computed for the various domain size for both methods RPM and CBM.