| 27 Aug 2026
The TANDEM wake model: coupled turbulence and deficit momentum modeling in stratified atmospheric boundary layers
Abstract. Engineering wake models are essential tools for estimating aerodynamic interactions between wind turbines. All utility-scale wind turbines operate in the atmospheric boundary layer (ABL), where Coriolis forces and stratification shape the structure and dynamics of wake evolution, but these effects are often neglected or highly simplified in engineering wake models. We propose the TANDEM (\tandem) framework in which the wake deficit is computed by co-evolving a parabolized equation for the streamwise momentum deficit jointly with a parabolized equation for the wake-added turbulence kinetic energy (TKE) using a one-equation eddy viscosity closure. The eddy viscosity formulation uses a generalized mixing length, which interpolates Monin–Obukhov similarity theory in the surface layer and a dynamics-dependent wake mixing length above the surface layer. The TANDEM wake model is coupled with an initial condition from the Unified Momentum Model, which generalizes classical theory to turbine yaw misalignment and high thrust coefficients. Single-turbine wake predictions using the TANDEM wake model capture the skewed wake shape and enhanced wake recovery in veered conditions that are coarsely parameterized or neglected by existing analytical models, when compared with large-eddy simulations (LES). Across neutrally and stably stratified ABLs, the TANDEM model predicts normalized downstream power production of a single turbine with a mean absolute error (MAE) of 4.3 %, compared with 6.5 % for a skewed Gaussian model or 21 % for an axisymmetric Gaussian model. In a four-turbine wind farm, the TANDEM model provides the lowest predictive error of farm power among the tested models across full- and partial-wake conditions. Further, normalized turbine power predictions in a 25-turbine wake steering case study are 4.7 % for the TANDEM model, compared with 8.8 % for an analytical vortex sheet model and 11 % for a Gaussian wake model. Continued work on coupling array-scale effects with turbine-scale wake evolution is recommended to improve TANDEM model predictions in moderate to large wind farms. Nonetheless, we see the TANDEM framework as a promising scaffold to build a new class of wake models for improved wake predictions in ABL flows.
This manuscript presents the TANDEM engineering wake model, which couples wake momentum and wake-added turbulence through a parabolized formulation and introduces a generalized near-wake treatment. The model is evaluated against LES for single wakes under varying inflow conditions, small turbine arrays, a wind-farm control case, and a deeper 10-row array. There is substantial technical work here, and the manuscript contains potentially useful developments for engineering wake modeling. My principal concern is that the manuscript tends to present TANDEM as a broadly physics-based, generalizable wind-farm wake model, whereas the results show that important parts of the formulation remain dependent on LES calibration and that the model has significant limitations for cumulative and deep-array wakes.
The first issue is the extent to which the model can be regarded as predictive rather than postdictively calibrated. Several important model quantities are obtained from particular LES cases. These include the far-wake constant Cν, the stability-related parameter Cw, the dissipation length scale ℓϵ, and the near-wake parameter α, while other quantities are inherited from earlier calibrated models. The authors state, for example, that TANDEM captures the enhanced wake recovery associated with increasing wind veer through its resolved physics, without veer-specific calibration. That is an interesting result, but the wording should be more careful. The model does not contain a parameter fitted specifically as a function of veer, but the turbulence closure and several associated constants have nevertheless been obtained from LES. The extent to which the observed performance reflects genuine predictive generalization, rather than the transferability of a calibrated closure, needs to be demonstrated more rigorously.
Related to this, the paper would benefit from a clearer separation between the datasets or cases used for model development and those used strictly for validation. At present, a number of parameters are derived from LES, and the resulting model is then evaluated primarily against LES generated within the same overall modeling framework. The authors should state explicitly which cases were used to determine each model parameter and which cases constitute genuinely independent tests. This is essential if claims of generality are to be supported.
A more serious issue appears in the deep-array calculations. The 10-row case shows that TANDEM does not correctly reproduce the cumulative evolution of the wake-added turbulence and associated wake recovery. The manuscript attributes this to excessive dissipation of the modeled wake-added turbulence, which reduces Δk, the mixing length, the eddy viscosity, and ultimately the wake-recovery rate. This is not a minor deficiency. Cumulative wake behavior is one of the central problems that an engineering wind-farm flow model must address. The authors themselves conclude that a two-equation closure, such as k−ϵ or k−ω, may be necessary to capture the asymptotic behavior more accurately. If an additional turbulence transport equation is ultimately required, then the present one-equation closure should be presented more explicitly as an intermediate model rather than as a generally applicable solution.
The neglect of array-scale atmospheric-boundary-layer feedback is equally important. The manuscript states that array-level effects are completely neglected in the current framework and suggests future coupling to a top-down ABL model. It goes further, stating that it is unclear whether the present approach can model wind-farm wakes without additional dynamics. This qualification is important, but it sits uneasily with some of the broader claims made elsewhere in the manuscript.
The scope of the conclusions should be narrowed considerably. The results support the conclusion that TANDEM improves the prediction of certain single-wake features and short-array interactions relative to several simpler engineering models. They do not yet support a general claim that TANDEM provides a complete engineering model for wind-farm flow. The single-wake results are among the strongest parts of the paper. In veered inflow, TANDEM reproduces the skewed wake structure much more convincingly than the Gaussian and vortex models, which respectively fail to represent the skewing or substantially overpredict it. The model also introduces a response of the wake-recovery rate to veer that is absent from the simpler analytical models. These are worthwhile results and should perhaps form a more central part of the paper's contribution. The multi-turbine results also show promise. In the wind-farm control tests, the TANDEM and k−ℓ formulations generally yield lower turbine-power errors than some simpler engineering wake models. However, these results should be interpreted alongside the later failure in the deep array, rather than presented in isolation as evidence of general model superiority.
I also think the manuscript needs a clearer accounting of model complexity. TANDEM is repeatedly compared against considerably simpler analytical wake models. Improved agreement with LES is not surprising when additional transported quantities, turbulence physics, near-wake treatments, and calibrated closure parameters are introduced. The relevant question is whether the improvement is sufficient to justify the increased model complexity and whether the model remains computationally efficient enough for its intended engineering applications. This tradeoff should be quantified.
The treatment of the near wake should also be discussed more critically. The model introduces a generalized near-wake length that depends on the thrust coefficient, inflow turbulence intensity, and wind veer, along with a prescribed near-wake mixing length. Because this treatment is important for coupling the near and far wakes, the authors should provide clearer evidence that its form remains robust beyond the calibration cases.
Finally, I suggest that the authors reconsider some of the language used throughout the manuscript. Terms such as "physics-based," "generalizes well," and similar statements should be reserved for cases where the evidence clearly supports them. The model contains important physical structure, but it also contains empirical closure and calibration and overstates the demonstrated range of applicability. The LES calibration and validation strategy needs to be clarified, the limitations revealed by the deep-array case need to be treated as central rather than peripheral, and the claims concerning general wind-farm applicability need to be narrowed.