Dissipation scaling in wind turbine wakes exposed to free-stream turbulence
Abstract
The nature of the dissipation of turbulent kinetic energy (TKE) is investigated experimentally in the wake of a diameter D=0.58m wind turbine exposed to several ``flavours'' of high-Reynolds-number free-stream turbulence (FST). For low- and moderate-intensity FST, an annular region of elevated normalised dissipation, Cε, develops in the outer wake, coinciding with a ring of enhanced turbulence intermittency at both small (ℓ ≤ λ) and large (ℓ ≥ D) scales, where λ is the Taylor microscale. In the blade-tip region, Cε scales with √(ReD)/Reλ, where ReD is a global Reynolds number and Reλ a local turbulent Reynolds number based on λ-a scaling indicative of dissipation being out of equilibrium with the inter-scale flux of TKE in the inertial range of the energy cascade. This non-equilibrium regime is interpreted in light of the observed intermittency : large-scale intermittent events (i.e., low-wavenumber perturbations/``kicks''), driven by persistent tip-vortex and tip-shear-layer dynamics under low-intensity FST, require a finite time to cascade down to the dissipative scales, thereby introducing an imbalance between the inter-scale energy flux and dissipation. At the wake centreline, by contrast, Cε remains approximately constant with streamwise distance, reflecting either classical Kolmogorov-type equilibrium turbulence or balanced non-equilibrium turbulence, with intermittency confined to the small scales. Under high-intensity FST, large-scale intermittency is suppressed, consistent with the erosion of tip-vortex structures, and no comparable scaling for Cε could be identified using a single turbulent Reynolds number for these cases, where two similarly intense streams of turbulence, but of different origins, are adjacent to one another.
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BibTeX
@misc{bourhis2026dissipation,
title = {{Dissipation scaling in wind turbine wakes exposed to free-stream turbulence}},
author = {Martin Bourhis and Oliver R. H. Buxton},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03996},
eprint = {2609.03996},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03996},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dissipation scaling in wind turbine wakes exposed to free-stream turbulence
AU - Martin Bourhis
AU - Oliver R. H. Buxton
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03996
UR - https://arxiv.org/abs/2609.03996
AB - The nature of the dissipation of turbulent kinetic energy (TKE) is investigated experimentally in the wake of a diameter D=0.58m wind turbine exposed to several ``flavours'' of high-Reynolds-number free-stream turbulence (FST). For low- and moderate-intensity FST, an annular region of elevated normalised dissipation, C_ε, develops in the outer wake, coinciding with a ring of enhanced turbulence intermittency at both small (ℓ ≤ λ) and large (ℓ ≥ D) scales, where λ is the Taylor microscale. In the blade-tip region, C_ε scales with √(Re_D)/Re_λ, where Re_D is a global Reynolds number and Re_λ a local turbulent Reynolds number based on λ-a scaling indicative of dissipation being out of equilibrium with the inter-scale flux of TKE in the inertial range of the energy cascade. This non-equilibrium regime is interpreted in light of the observed intermittency : large-scale intermittent events (i.e., low-wavenumber perturbations/``kicks''), driven by persistent tip-vortex and tip-shear-layer dynamics under low-intensity FST, require a finite time to cascade down to the dissipative scales, thereby introducing an imbalance between the inter-scale energy flux and dissipation. At the wake centreline, by contrast, C_ε remains approximately constant with streamwise distance, reflecting either classical Kolmogorov-type equilibrium turbulence or balanced non-equilibrium turbulence, with intermittency confined to the small scales. Under high-intensity FST, large-scale intermittency is suppressed, consistent with the erosion of tip-vortex structures, and no comparable scaling for C_ε could be identified using a single turbulent Reynolds number for these cases, where two similarly intense streams of turbulence, but of different origins, are adjacent to one another.
ER -