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 $D=0.58$m 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, $C_{\epsilon }$, develops in the outer wake, coinciding with a ring of enhanced turbulence intermittency at both small ($\ell \le \lambda$) and large ($\ell \ge D$) scales, where $\lambda$ is the Taylor microscale. In the blade-tip region, $C_{\epsilon }$ scales with $\sqrt{R{e}_D}/R{e}_{\lambda }$, where $R{e}_D$ is a global Reynolds number and $R{e}_{\lambda }$ a local turbulent Reynolds number based on $\lambda$-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, $C_{\epsilon }$ 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 $C_{\epsilon }$ 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.