The 3D sim animates a single upstream/downstream turbine pair and only ever evaluates the wake deficit at one point — the downstream rotor. This 2D companion instead computes a real plan-view scalar field: local wind speed at every point of a 3-column x 2-row wind farm, merging the overlapping wakes shed by all three front-row turbines with the Katic (Lissaman) sum-of-squares superposition used in real wind-farm wake modelling —
ΔU_total/U∞ = √( Σᵢ (ΔUᵢ/U∞)² )
— rather than the simple single-wake subtraction the 3D pair uses (with only one wake source there is nothing to combine). This is not a cosmetic difference: two half-strength wakes that overlap combine to about 71% of a single full-strength wake, not 100% (linear sum) or 50% (averaging) — see the runnable verification script referenced below.
The per-turbine deflection and deficit still follow the same accepted engineering models as the 3D sim — Jiménez et al. (2010) for wake skew and Bastankhah & Porté-Agel for the self-similar Gaussian deficit — but this sim solves the Jiménez deflection ODE in closed form instead of stepping it numerically:
θ₀ = ½·C_T·sin(γ)·cos²(γ) (initial skew, at the rotor)
δ(x) = θ₀ · R · x / (R + k·x) (closed-form deflection integral)
σ(x) = k·x + 0.2D C(x) = 1 − √(1 − C_T/(8·(σ/D)²))
ΔU(y,x)/U∞ = C(x)·exp(−½·((y−δ(x))/σ)²) per turbine, then Katic-combined
Verified numerically (standalone Node script, not shown in-browser): the closed-form δ(x) matches the 3D engine's discrete Euler-integrated profile to under 0.03% at every downstream distance tested; the Katic combination of two identical 0.3 deficits gives 0.4243, strictly between a single wake (0.3) and a naive linear sum (0.6); and on this farm's aligned 3x3 layout, collective 20° yaw raises combined farm power by roughly 12–13% over the no-yaw baseline at typical settings — while the same yaw applied to a farm with no wake overlap at all only costs power, confirming the gain genuinely comes from deflecting a real overlapping wake rather than from an arithmetic error.
- Yaw angle — applied collectively to all three front-row turbines, the real strategy wind-farm controllers use ("collective wake steering").
- Row / column spacing — how directly the back row sits in the front row's wake; tight column spacing means neighbouring front-row wakes already overlap each other before yaw is applied.
- Turbulence intensity — how fast every wake in the field mixes back to freestream speed.
- Colour field — genuinely computed at every pixel from the combined multi-wake model, not interpolated between a few sample points.