the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 May 2026
A generalised Gaussian wake model based on extended actuator disc theory
Abstract. Engineering wake models have been widely used for wind farm design and optimization due to low computational cost. Recent work suggests that the key to improving the wake models lies in the prediction of the transition point between the 'near-wake' and 'far-wake' regions. This study proposes an analytical model for this transition point based on a relationship between the wake-centreline pressure gradient and the divergence of Reynolds shear stresses. Using this relationship together with an extended actuator disc analysis for a turbine in a laterally confined flow, the proposed model also predicts the initial wake profile at the start of the far-wake region for any practical inflow turbulence conditions and local blockage ratios. In addition, a new Gaussian far-wake model considering the local blockage effect is formulated to form a complete engineering wake model. The model is validated against a series of Reynolds-averaged Navier-Stokes (RANS) simulations of an actuator disc over a wide range of inflow turbulence intensities, thrust coefficients and local blockage ratios. The model predictions are in good agreement with the simulation results.
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RC1: 'Comment on wes-2026-76', Anonymous Referee #1, 28 May 2026
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2026-76/wes-2026-76-RC1-supplement.pdfCitation: https://doi.org/
10.5194/wes-2026-76-RC1 -
RC2: 'Comment on wes-2026-76', Anonymous Referee #2, 02 Jun 2026
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2026-76/wes-2026-76-RC2-supplement.pdf
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RC3: 'Comment on wes-2026-76', Anonymous Referee #3, 09 Jun 2026
This work introduces an engineering model for the prediction of the wake deficit downstream of wind turbines. The predictions are validated via RANS simulations employing the k-epsilon model. Similarly to previous works, the current analytical approach adopts an eddy viscosity hypothesis to simplify the streamwise momentum equation. The particularly novel aspect of the current work is the introduction of a criterion for the ‘near wake’ distance beyond which the velocity profile assumes a Gaussian shape, and where far wake models are applicable. The criterion is interesting – however, it raises several questions.
First, there is some is some inconsistency regarding the physical definition of the near wake distance. In line 195 it is stated that the near wake ends when R-dp/dx is maximum (R being the divergence of the Reynolds stresses). However, in line 250 the start of the far wake (and therefore the end of the near wake) is stated to occur when the pressure gradient is negligible. Which of the two is correct and how are these connected to the initial motivation behind finding the near wake distance, i.e., the location beyond which the velocity profile becomes Gaussian?
Second, the authors state that the location of maximum R-dp/dx approximately coincides with the location where the streamwise integral of R is equal to R. This latter condition is then used to inform the near wake model. However, this condition is given without proof and no physical reasoning is also included. It seems to be solely based on the results of the k-epsilon simulations which, indeed, in most cases (apart from the very low ambient turbulence ones) show an approximate coincidence of the two criteria. However, this justification is insufficient: The k-epsilon model is notoriously inaccurate in the near, non-self-similar wake region and therefore data from experiments or more elaborate simulations would be needed to provide backing to the claim of the authors. Moreover, a thorough discussion with respect to the physical significance of this condition would have to be included.
Third, there seems to be an inconsistency in the application of the boundary condition of equation 24. The expression [R equal to integral of R] is a heuristic condition and does not a-priori signify the end of the near wake region (see previous paragraph). Still, the authors derive a boundary condition for this expression from the fact that at extremely high turbulent mixing this condition should occur at the plate as, on physical terms, one would expect that then, the wake would transition to its ‘far wake regime’ immediately. The implicit assumption here is that the above condition actually reflects the end of the near wake (even though no proof was provided), not only for the cases tested by the authors (low or intermediate turbulence) but also for extremely high turbulence. It is noteworthy to mention that the validity of the condition becomes especially dubious at such high turbulence conditions, as these would occur at very high thrust coefficients, where vortex shedding would arise, or extremely high ambient turbulence values, which would overwhelm the turbulence of the wake. The flow physics here are significantly different from the ones considered by the authors, and therefore one cannot extrapolate their k-epsilon results there.
A minor point is that the manuscript would benefit from a thorough review of past works on wake models, as in late years there have been several works that discuss points also considered in the current manuscript, namely the transition of the near to far wake dynamics, and the effect of the near wake pressure gradient.
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Citation: https://doi.org/10.5194/wes-2026-76-RC3
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