Wake Effect Modeling

The core computation of wake models is the velocity deficit—the reduction in free-stream wind speed behind a rotor. Momentum is extracted by the upstream turbine, creating a slower, turbulent wake that expands as it travels downstream.

• Jensen/Park model: Assumes a linearly expanding wake with a uniform velocity deficit profile; computationally fast but neglects near-wake details
• Gaussian wake model: Represents the velocity deficit as a self-similar Gaussian distribution, better capturing the gradual recovery at wake edges
• Conservation of momentum is applied across control volumes to ensure mass and energy balance

The velocity deficit at a downstream turbine location directly determines its available power, as power scales with the cube of wind speed.

Wakes are not merely slower wind; they contain elevated turbulence intensity that imposes unsteady aerodynamic loads on downstream turbines. Models must quantify this added turbulence to predict fatigue damage accumulation.

• Frandsen turbulence model: Computes added turbulence as a function of thrust coefficient and downstream distance, widely implemented in the IEC 61400-1 standard for turbine design
• Crespo-Hernández model: Provides empirical fits for maximum added turbulence in the near and far wake regions based on wind tunnel and field data
• Elevated turbulence increases equivalent fatigue loads on blades, drivetrain, and tower, shortening component lifetimes if not accounted for in siting

Accurate turbulence modeling is essential for bankable energy yield assessments and structural integrity verification.

Wakes do not propagate in a straight line; they meander laterally and vertically due to large-scale atmospheric turbulence. This stochastic movement smears the time-averaged velocity deficit and intermittently exposes downstream turbines to higher wind speeds.

• Dynamic wake meandering (DWM) model: Treats the wake as a passive tracer transported by large turbulent eddies, solving a stochastic differential equation for wake centerline position
• Meandering explains why instantaneous power fluctuations at downstream turbines can be larger than steady-state models predict
• The DWM framework couples with aeroelastic codes like HAWC2 or OpenFAST to compute time-resolved loads

Ignoring meandering leads to underestimation of extreme loads and overestimation of wake losses in some atmospheric conditions.

In a wind farm with multiple rows, a downstream turbine may sit in the superposition of several wakes. Wake combination models define how individual velocity deficits merge into a combined effect.

• Linear superposition: Sums velocity deficits from all upstream turbines; simple but can produce unphysical negative velocities in dense arrays
• Quadratic superposition: Sums the squares of velocity deficits, then takes the square root; more conservative and physically plausible
• Energy balance method: Combines wakes by conserving kinetic energy flux, providing a middle ground between linear and quadratic approaches
• Dominant wake method: Considers only the most influential upstream wake, reducing computational cost for large arrays

The choice of superposition method significantly impacts predicted farm output and optimal layout design.

For the highest fidelity, wake effects are resolved using large-eddy simulation (LES)—a computational fluid dynamics approach that explicitly resolves the energy-containing turbulent eddies while modeling sub-grid scales.

• LES captures tip vortices, helical wake instability, and the full turbulent mixing process that engineering models parameterize
• Actuator line method: Represents each turbine blade as a rotating line of body forces, avoiding the computational cost of resolving blade boundary layers
• Coupled with atmospheric boundary layer inflow, LES predicts farm-wide blockage effects and deep-array efficiency
• Used primarily for research, model validation, and high-stakes offshore project optimization rather than routine layout design

LES provides the ground truth against which faster engineering models are calibrated.

Wake models traditionally focus on downstream effects, but turbines also induce upstream blockage—a pressure field that decelerates flow ahead of the rotor. At the farm scale, this creates a global blockage effect reducing incident wind speed across the entire array.

• Blockage is caused by the induction zone, where streamlines diverge upstream of the rotor plane
• Two-scale momentum theory: Separates turbine-scale induction from farm-scale atmospheric response
• Global blockage can reduce farm-level wind speed by 1–3% before any wake losses are accounted for
• Emerging models couple wake parameterizations with mesoscale weather models to capture farm-atmosphere interaction

Accounting for blockage is increasingly important for gigawatt-scale offshore clusters where the cumulative atmospheric perturbation is significant.

The foundational analytical model representing a wind turbine rotor as a permeable disk that extracts kinetic energy from the flow, creating a pressure drop. This theory defines the axial induction factor and establishes the theoretical maximum power extraction, known as the Betz limit. In wake modeling, it provides the initial velocity deficit boundary condition for far-wake calculations, linking the turbine's thrust coefficient directly to the magnitude of downstream momentum loss.

A metric quantifying the ratio of wind speed standard deviation to the mean wind speed, expressed as a percentage. In wake modeling, added turbulence intensity is a critical output because it drives fatigue loads on downstream turbines. Wake-added turbulence is modeled as a function of the ambient turbulence and the thrust coefficient. High ambient turbulence accelerates wake recovery through enhanced mixing but increases structural stress on rotors operating in the disturbed flow.

A large-scale, low-frequency lateral oscillation of the wake deficit caused by atmospheric boundary layer eddies larger than the rotor diameter. This dynamic phenomenon is not captured by steady-state models. Dynamic wake meandering models transport the velocity deficit as a passive scalar advected by the turbulent background flow, significantly improving the prediction of instantaneous power fluctuations and fatigue loading at downstream turbines compared to static wake superposition.

A widely used engineering wake model that assumes a top-hat velocity deficit profile expanding linearly with downstream distance. The model relies on a single empirical parameter: the wake decay constant, which varies with ambient turbulence. While computationally efficient for large-scale wind farm layout optimization, its simplicity fails to capture the realistic Gaussian-like radial profile of the velocity deficit, often leading to underprediction of power in the near-wake region.

An analytical model that assumes a self-similar Gaussian radial profile for the velocity deficit, providing a more physically accurate representation than the top-hat Jensen model. The wake width expands based on a turbulence-dependent diffusion coefficient. Variants like the Bastankhah and Porté-Agel model use mass and momentum conservation to derive the velocity deficit, offering improved accuracy for yawed inflow conditions and near-wake predictions critical for active wake control strategies.

A high-fidelity computational fluid dynamics technique that resolves the energy-containing large turbulent eddies while modeling sub-grid scale dissipation. In wake modeling, LES with actuator line models captures tip vortices, helical wake structures, and turbulent mixing with high spatial and temporal resolution. This method serves as the benchmark for developing and validating lower-fidelity engineering models, particularly for studying complex terrain effects and wind farm blockage.