Vendredi 6 mars 2026 à 14h00, salle des séminaires IRPHE
Abstract: Turbulent wakes are inherently non-homogeneous, yet they are often studied using the Kolmogorov equilibrium paradigm [1], specifically designed for stationary and homogeneous turbulence. In particular, the equilibrium scaling of the dissipation rate set the basis for the so-called Townsend & George similarity predictions for the mean wake expansion and recovery. Over recent years however, convincing evidence has been accumulating which suggests that a different dissipation scaling exists [2, 3] in various turbulent flows which yield another set of similarity predictions [4]. In the context of wind farm flows [5], the axisymmetric swirling wake of a wind turbine surrogate is analysed using this non-equilibrium framework [6]. Assuming that swirl dominates the near wake [7], the similarity analysis is revisited and a new scaling law for the mean swirl decay is found. Using a combination of Particle Image Velocimetry (PIV) and Hot-Wire Anemometry (HWA), we show that the swirling motion is a key component of the near wake, controlling the mean flow deficit properties and the onset of self-similarity. The measurements collected in the swirling wake support the new scaling law proposed in this work and increases the number of situations where non-equilibrium turbulence applies. This stresses the motivation to revisit turbulent wakes (and other flows) with a theory which does not rely on the strong assumption of homogeneity. Recent advances in non-homogeneous turbulence theory [8, 9] have provided the community with predictions (and evidence) regarding the behaviour and structure of non-homogeneous turbulent flows with homogeneous physics. In particular, Beaumard et al. [9] have shown that more terms than just the inter-scale transfer rate are active in the so-called Karman-Howarth-Monin-Hill (KHMH) equation and may be proportional to the dissipation rate. By analysing the turbulent wakes PIV data of two side-by-side square prisms performed in Chen et al. [3], we compute some of the available terms and show that turbulent diffusion persists down to the small scales and counteracts the inter-scale energy transfer rate of horizontal turbulent kinetic energy over a range of scales [10]. This turbulent diffusion-cascade interaction suggests that the average inter-scale transfer rate can be significantly faster than the turbulence dissipation rate, which is allowed by the counter-acting non-zero average inter-space transport, with their sum scaling proportionally to the dissipation rate over a wide range of scales. These two contributions raise new questions regarding how our understanding and modeling of turbulent wakes may be improved with new theoretical tools.
[1] A. N. Kolmogorov. The local structure of turbulence in incompressible viscous fluid for very large reynolds number. Cr Acad. Sci. USSR, 30:301, 1941.
[2] J. C. Vassilicos. Dissipation in turbulent flows. Annual review of fluid mechanics, 47(1):95–114, 2015.
[3] J. G. Chen, C. Cuvier, J-M. Foucaut, Y. Ostovan, and J. C. Vassilicos. A turbulence dissipation inhomogeneity scaling in the wake of two side-by-side square prisms. Journal of Fluid Mechanics, 924:A4, 2021.
[4] T. Dairay, M. Obligado, and J. C. Vassilicos. Non-equilibrium scaling laws in axisymmetric turbulent wakes. Journal of Fluid Mechanics, 781:166–195, 2015.
[5] F. Port´e-Agel, M. Bastankhah, and S. Shamsoddin. Wind-turbine and wind-farm flows: a review. Boundary-layer meteorology, 174(1):1–59, 2020.
[6] E. Fuentes Noriega and N. Mazellier. Scaling analysis of the swirling wake of a porous disc: application to wind turbines. Journal of Fluid Mechanics, 1003:A34, 2025.
[7] Elizabeth H Camp and Ra´ul Bayo´an Cal. Mean kinetic energy transport and event classification in a model wind turbine array versus an array of porous disks: Energy budget and octant analysis. Physical Review Fluids, 1(4):044404, 2016.
[8] J. G. Chen and J. C. Vassilicos. Scalings of scale-by-scale turbulence energy in non-homogeneous turbulence. Journal of Fluid Mechanics, 938:A7, 2022.
[9] P. Beaumard, P. Bragan¸ca, CC Cuvier, K. Steiros, and J. C. Vassilicos. Scale-by-scale nonequilibrium with kolmogorov-like scalings in non-homogeneous stationary turbulence. Journal of Fluid Mechanics, 984:A35, 2024.
[10] E. Fuentes Noriega and J. C. Vassilicos. Turbulent diffusion–cascade interaction. Journal of Fluid Mechanics, 1028:A3, 2026.
Ernesto Fuentes Noriega, Postdoctoral fellow, Laboratoire de Mécanique des Fluides de Lille