Turbulence dynamics in separated flows: the generalised Kolmogorov equation for inhomogeneous anisotropic conditions

The generalised Kolmogorov equation is used to describe the scale-by-scale turbulence dynamics in the shear layer and in the separation bubble generated by a bulge at one of the walls in a turbulent channel flow. The second-order structure function, which is the basis of such an equation, is used as a proxy to define a scale-energy content, that is an interpretation of the energy associated with a given scale. Production and dissipation regions and the flux interchange between them, in both physical and separation space, are identified. Results show how the generalised Kolmogorov equation, a five-dimensional equation in our anisotropic and strongly inhomogeneous flow, can describe the turbulent flow behaviour and related energy mechanisms. Such complex statistical observables are linked to a visual inspection of instantaneous turbulent structures detected by means of the Q-criterion. Part of these turbulent structures are trapped in the recirculation where they undergo a pseudo-cyclic process of disruption and reformation. The rest are convected downstream, grow and tend to larger streamwise scales in an inverse cascade. The classical picture of homogeneous isotropic turbulence in which energy is fed at large scales and transferred to dissipate at small scales does not simply apply to this flow where the energy dynamics strongly depends on position, orientation and length scale.