Energy transfer between scales and position in a turbulent recirculation bubble

The energy transfer among the different scales of the turbulent structures is analysed by means of the generalised Kolmogorov equation (GKE). The equation is applied to a turbulent channel with the addition of a bump which creates a strong shear layer and separation bubble. The GKE can provide an intricate description of the energy scale-by-scale budget in both physical and separation space, through the identification of the regions of production and dissipation of energy. Conventional one-point statistics do not allow any analysis across scales. The GKE statistics show that the turbulent structures follow two paths: they are trapped by the recirculation bubble, deformed and dissipated or they are convected downstream by the shear layer and elongated in the streamwise direction. These paths correspond to the direct and inverse energy cascades, respectively. The main feature of this complex flow is that the energy dynamics depends, in a non-trivial way, on both the physical position and separation scales, and does not follow the classical energy path occurring in homogeneous isotropic turbulence.