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

1. 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 ?

2. Have the authors thought about addressing the more challenging issue of generating non-isotropic, non-homogeneous synthetic turbulence ?

3. 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 ?

4. 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 ?

5. Fig 1: how the ideal structure function is calculated ?

6. 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 ?

7. 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 ?

8. 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 ?

9. 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).

10. It would interesting to show the structure functions computed for the various domain size for both methods RPM and CBM.

Report

This paper discusses the generation of homogeneous, isotropic wind fields. The aim is to improve the quality of reconstructed fields by using knowledge of the correlation tensor. The paper is technically interesting and well written. It provides a useful overview of previous work, but the novelty of this work could be highlighted more effectively. 

Overall, I agree with the comments in the first report. 

My main criticism, which is left, concerns the discussion of the possible application of this work to wind energy systems, i.e. generating real wind fields. How can the IEC-wind field generators be improved? A comment on how to extend the proposed method to simulate full three-component wind fields would be helpful. 

Coming to real wind fields. Some remarks o the following questions would be of value: How can non-homogeneous situations be handled? A big problem will be non-stationarity. Which quantities should be measured in the field? I also question whether the increased accuracy shown is really valuable for real wind fields.  I would imagine that the intrinsic errors of the corrections  of wind field measurements are so high than the proposed increase in accuracy.  To discuss this frankly does not lower the quality of the work but is of interest for application.

Another question is whether the authors have any ideas about how to include higher-order correlations/statistics. For example, does the reconstructed wind field reproduce the well-known skewness scaling of ideal turbulence?

Despite my comments, I still find this work interesting, and it will be valuable for the wind energy community. In principle, therefore, I support publication.