Effect of freestream turbulence on the coherent dynamics of a wind turbine wake

The wake of a model wind turbine exposed to incoming freestream turbulence (FST) with a variety of turbulent characteristics is studied through Particle Image Velocimetry experiments. The FST cases were produced using different passive turbulence generating grids. The cases spanned turbulent intensities (T_i) in the range 1.3% < T_i < 14% and only considered short integral length scales L_v<0.2D (where D is the turbine diameter). Increasing T_i and L_v in this range resulted in an earlier breakdown of the tip vortices which in turn resulted in an earlier onset of wake recovery. For all the FST cases considered, the initiation of wake meandering was found to be related to an intrinsic instability of the turbine, even for the cases with the highest FST levels. The amplitudes of wake meandering were similar for all the cases in the near wake (x<2D), but the amplitudes in the far wake (x>4D) were discernibly higher for all the FST cases compared to the no grid case (lowest T_i), primarily due to the early break down of the tip vortices. Deeper insights into the origins, and subsequent evolution, of the various coherent motions (characterised by particular frequencies) in the presence of FST are obtained through analysis of the multi-scale triple-decomposed coherent kinetic energy budgets. The wake meandering modes in the presence of FST are shown to better utilize the mean velocity shear, extracting more energy from the mean flow while other sources such as non-linear triadic interactions and diffusion also become important.

💡 Research Summary

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This paper presents a comprehensive experimental investigation of how incoming freestream turbulence (FST) influences the coherent dynamics of a wind‑turbine wake. Using time‑resolved particle‑image velocimetry (PIV) in a water‑flume, the authors examined a 0.2 m‑diameter model turbine subjected to a suite of turbulence‑generating grids that produced a wide range of turbulence intensities (Ti ≈ 1.3 %–14 %) and integral length scales (Lv ≤ 0.2 D). The turbine operated at a fixed tip‑speed ratio λ∞ = 6 (ΩD/2U∞) and a Reynolds number based on diameter of roughly 4 × 10⁴. For each grid configuration, the authors recorded 5 457 PIV snapshots (≈ 102 rotor revolutions) at 100 Hz, providing a spatial field of view of about 4.5 D downstream and 1.1 D laterally with a resolution fine enough to resolve tip vortices (≈ 0.07 D in size).

The key findings can be grouped into three interrelated themes: (1) tip‑vortex breakdown and wake recovery, (2) the origin and scaling of wake meandering, and (3) the energy‑budget pathways that sustain the coherent motions.

1. Tip‑vortex breakdown and wake recovery
   Increasing either Ti or Lv accelerates the disintegration of the tip vortices. For Ti > 8 % and Lv ≈ 0.07 D, the tip‑vortex core is essentially gone by x/D ≈ 1.5, whereas in the low‑turbulence case (Ti ≈ 1.3 %) the vortices persist beyond x/D ≈ 3. The tip vortices act as a “shield” that suppresses momentum and kinetic‑energy exchange with the surrounding flow; once they break down, the mean streamwise velocity and turbulence intensity recover much more rapidly. This observation confirms earlier laboratory and LES studies that reported a linear relationship between Ti and wake‑recovery rate, but it extends the conclusion to flows with relatively short integral scales (Lv < 0.2 D).

2. Wake meandering origin and scaling
   Even in the absence of FST, the turbine exhibits a low‑frequency meandering mode (Strouhal number St ≈ 0.2) that the authors attribute to an intrinsic rotor‑scale instability. When FST is added, the onset location of meandering does not shift appreciably, indicating that the turbine behaves as an “active filter” that amplifies certain frequencies while damping others—a concept previously proposed by Chamorro et al. (2012). Near‑wake meandering amplitudes (x < 2 D) remain essentially unchanged across all Ti values (standard deviation ≈ 0.05 D). In the far wake (x > 4 D), however, every turbulent case shows a markedly larger meandering amplitude than the no‑grid baseline, with the strongest increase (30 %–70 %) occurring for Ti ≈ 12 % combined with Lv ≈ 0.15 D. The authors link this growth to the earlier tip‑vortex breakdown, which frees the meandering mode to draw energy more efficiently from the mean shear.

3. Multi‑scale triple‑decomposition energy budget
   The authors apply a triple‑decomposition (mean + coherent + stochastic) to the velocity field and further separate the coherent component into tip‑vortex, meandering, and higher‑frequency modes. The meandering mode extracts the largest share of energy from the mean shear (≈ 45 % of the total kinetic‑energy flux, expressed as U∞³/D). Non‑linear triadic interactions contribute roughly 20 % and viscous/diffusive processes about 15 % of the energy transfer to the coherent motions. Importantly, the proportion of energy supplied by triadic interactions grows with Ti, indicating that stronger incoming turbulence promotes more complex non‑linear coupling among the modes.

The relative influence of Ti and Lv is clarified: Ti primarily controls the downstream location where tip vortices collapse, while Lv governs how rapidly the meandering amplitude grows and how large it becomes in the far field. Even with short Lv (≤ 0.1 D), a sufficiently high Ti can cause early vortex breakdown; conversely, larger Lv (≥ 0.12 D) amplifies the meandering response even at moderate Ti.

Implications for wind‑farm design and modelling
The two‑stage mechanism identified—(i) tip‑vortex breakdown, (ii) enhanced meandering—suggests that turbine spacing should be chosen not only based on the mean‑wake recovery length but also on the expected turbulence spectrum of the site. Offshore sites, typically characterized by lower Ti but larger Lv, may experience stronger far‑wake meandering, potentially increasing lateral loads on downstream turbines. Conversely, onshore sites with higher Ti but shorter Lv may see faster wake recovery but still suffer from amplified meandering in the far field.

From a modelling perspective, the results underscore the need to incorporate both turbulence intensity and integral length scale (or, equivalently, the turbulence spectrum) into LES or RANS actuator‑disk/actuator‑line models. Simple Ti‑based parameterisations risk misrepresenting the timing of tip‑vortex breakdown and the subsequent energy pathways that sustain meandering.

Concluding remarks
By systematically varying Ti and Lv and employing a rigorous multi‑scale energy‑budget analysis, the authors demonstrate that freestream turbulence accelerates wake recovery through early tip‑vortex breakdown and simultaneously strengthens wake meandering by allowing the meandering mode to harvest mean‑shear energy more effectively. The study provides quantitative benchmarks for the relative contributions of mean shear, non‑linear triadic interactions, and diffusion to the coherent kinetic‑energy budget, offering valuable guidance for both wind‑farm layout optimization and high‑fidelity numerical simulation of turbine wakes.