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.