Offshore wind wake - 2D farm map

Jensen wake model

Behind a rotor of diameter D with thrust coefficient C_T the wind speed recovers as u = U₀[1 − (1 − √(1 − C_T)) (D/(D + 2kx))²] inside a wake cone of radius D/2 + kx. The decay constant k is about 0.04 offshore (low turbulence) and 0.075 on land. Where a rotor is only partly in a wake, the deficit is weighted by the overlap area of the two circles. Several wakes combine quadratically (Katic): δ_tot = √(∑δ_i²), and each turbine's own thrust depends on the speed it actually receives.

Power

P = ½ ρ A C_p u³ between cut-in (3 m/s) and rated speed, then flat at the rated 6 MW until cut-out at 25 m/s. Because power goes with u³, a 20 % slower wind costs about half the output of a turbine that is below rated speed, but a turbine above rated speed barely notices a mild wake.

Honest simplifications: a top-hat wake (no Gaussian profile, no wake meandering, no added turbulence in the wake), constant k, a generic 150 m / 6 MW turbine with fixed C_p and C_T curves, flat sea, neutral atmosphere, no blockage or coastal effects. The 2D map is a teaching model, not a yield assessment.

• Press Rotate wind direction and watch the efficiency marker travel along the rose: the dips are rows of turbines lined up with the wind.
• Compare Aligned 6x6 grid with Wide spacing, 10D and Staggered rows.
• Press Rated-wind day: above rated speed the wake loss almost vanishes.