Sensitivity and feedback of wind-farm induced gravity waves

Area of Science:

• Atmospheric science
• Renewable energy engineering
• Fluid dynamics

Background:

• Wind farms cause boundary layer displacement, potentially generating atmospheric gravity waves.
• These waves can interact with the free atmosphere and the boundary layer interface.
• Gravity waves may influence wind farm energy extraction through induced pressure fields.

Purpose of the Study:

• Assess sensitivity of gravity-wave excitation to dimensionless groups.
• Investigate feedback of gravity-wave induced pressure fields on energy extraction.
• Analyze effects of atmospheric state and wind farm configuration on gravity waves.

Main Methods:

• Developed a fast boundary-layer model with a three-layer atmospheric representation.
• Coupled the model with an analytical wake model for turbine interactions.
• Validated the model using large-eddy simulations and investigated sensitivity analyses.

Main Results:

• Inversion layers create shallow-water flow dynamics, with the Froude number being critical.
• Gravity-wave excitation peaks at a Froude number of one.
• Maximum feedback on energy extraction occurs slightly below a Froude number of one.
• Surface friction and internal gravity waves reduce flow perturbation and power loss.
• Power loss increases with wind farm size and turbine height.
• Gravity-wave effects are minimal for very wide/long farms, peaking at a width-to-depth ratio of ~3/2.

Conclusions:

• The Froude number is a key parameter in wind-farm induced gravity-wave generation.
• Wind farm configuration significantly impacts gravity-wave effects and energy loss.
• Understanding these interactions is crucial for optimizing large-scale wind farm design and operation.