The spatial organization of wind turbine wakes

Wind turbine wakes play a central role in determining wind farm performance, yet their spatial organization remains only partially understood. Here, we apply a spatially localized multifractal analysis to quantify the strength of dependencies (local roughness) and extreme velocity fluctuations (local intermittency) in turbine wakes, and relate these properties to established metrics in wind energy research. Using two-dimensional nacelle-mounted LiDAR plan-position-indicator scans, we extract scale-invariant features that enable systematic comparisons across the wake without requiring time-resolved data. Designed to robustly handle irregular sampling, our analysis yields four main findings: i.) Four distinct wake zones are identified, each exhibiting unique patterns of roughness and intermittency. ii.) Coherent, strongly correlated patches emerge 2 to 5 rotor diameters D downstream, with intermittency strengthening periodically at multiple D positions and along the wake-free-flow interface. iii.) The classical “intermittency ring” is consequently redefined as a set of localized “intermittency bubbles”, iv.) which interact dynamically with the ambient atmosphere through an inverse energy cascade, transferring energy from small to large scales. These findings, supported by concurrent cup anemometer observations under free-inflow conditions, demonstrate that local multifractal analysis provides a robust and cost-effective diagnostic framework for wake characterization and wake-model validation, with direct relevance for wind-farm design and control.

💡 Research Summary

This paper investigates the spatial organization of wind‑turbine wakes using a novel, spatially localized multifractal (LMF) analysis applied to nacelle‑mounted LiDAR plan‑position‑indicator (PPI) scans. The authors collected two‑dimensional line‑of‑sight velocity fields downstream of a utility‑scale turbine (rotor diameter D = 115.7 m) under stable nocturnal boundary‑layer conditions. Traditional wind‑energy metrics—velocity deficit (VD) and turbulence intensity (TI)—are first computed on a regular 15 m grid for comparison, but these first‑order statistics provide only a smooth, monotonic picture of wake recovery.

The LMF framework extends conventional analysis by estimating two log‑cumulants, C₁ and C₂, across spatial scales r = 55–170 m (0.47–1.47 D). From these, the authors derive local roughness (c₁) and local intermittency (c₂) exponents. c₁ quantifies the strength of spatial correlations (higher values indicate long‑range dependence), while c₂ measures deviation from Gaussian behavior (more negative values imply stronger small‑scale intermittency). Both exponents are mapped onto the same grid as the classical metrics, enabling direct visual and statistical comparison.

Key findings:

1. Four distinct wake zones are identified based on joint behavior of c₁ and c₂ along the wake centreline.

   • Near‑wake (0–2 D): c₁ rises from ~0.25 to >0.5, while c₂ becomes increasingly negative, marking the end of the near‑wake when c₁ crosses 0.5 and c₂ reaches its first minimum.
   • Mid‑wake (≈2–6 D): c₁ remains in the 0.5–1.0 range, indicating strong long‑range correlations; c₂ exhibits a full intermittency cycle with pronounced minima near 2.4 D, 4.2 D, and sometimes 6 D, suggesting periodic reinforcement of extreme fluctuations.
   • Transition zone (≈6–10 D): c₁ drops below 0.5, the flow becomes “rougher,” and c₂ can become positive—a rare outcome in multifractal analysis—signalling an inverse cascade where energy transfers from small to larger scales.
   • Far‑wake (>10 D): c₁ turns negative, indicating noise‑like, uncorrelated behaviour; c₂ returns to negative values but with reduced magnitude.

2. Coherent patches and “intermittency bubbles.” The high‑c₁ patches between 2 D and 5 D downstream correspond to strongly correlated regions, while the intermittent “bubbles” (negative c₂) appear not only along the wake‑free‑flow interface (the classic “intermittency ring”) but also periodically inside the wake core. This redefines the ring as a set of localized bubbles.

3. Inverse energy cascade. The occasional positive c₂ region suggests that extreme fluctuations become more likely at larger scales, consistent with an upscale transfer of energy. The authors link this to vortex‑thinning mechanisms of tip vortices, where small‑scale kinetic energy is depleted and transferred upward in scale.

4. Validation with cup‑anemometer data. Simultaneous cup‑anemometer measurements under free‑inflow conditions show high correlation with the LiDAR‑derived c₂ fields, confirming that the LMF approach captures genuine physical intermittency despite the lack of time‑resolved LiDAR data.

Methodologically, the LMF analysis is robust to irregular sampling; the coefficient of determination across 222 scans is R² ≈ 0.84 for c₁ and 0.80 for c₂. The scaling regime (55–170 m) is chosen where clear power‑law behavior is observed, ensuring reliable exponent estimation.

Implications: By providing spatially resolved maps of roughness and intermittency, the LMF framework offers a cost‑effective diagnostic tool for wake characterization, model validation, and wind‑farm layout optimization. It reveals multiscale, non‑Gaussian dynamics that are invisible to conventional VD/TI metrics, thereby enriching our physical understanding of wake recovery, meandering, and energy transfer processes.

In summary, the study demonstrates that localized multifractal analysis can uncover hidden structures within turbine wakes, redefine classic concepts such as the intermittency ring, and supply actionable insights for both scientific research and practical wind‑energy engineering.