Turbulent energy distribution in scales and energy transfers in non-homogeneous turbulence*

Wakes produced by bluff bodies give rise to intense turbulence whose dynamics cannot be described by the classical Richardson-Kolmogorov cascade; this is not only due to mean flow gradients, responsible for turbulence production, but also due to coherence and inhomogeneity in the turbulence fluctuations. We address this latter aspect of wake turbulence through asymptotic matching of the second order structure function and subsequently examining its governing equation (the Kármán-Howarth-Monin-Hill - KHMH - equation) at inner (small) and outer (large) scales. Through direct numerical simulation of turbulent wakes generated by pairs of prisms, we find that the second order structure functions display clear 2/3 power laws and are self-similar both in terms of inner and outer scales, provided the coherence is not too strong. This is in spite of the non-equilibrium and non-homogeneous nature of the cascade, which gives rise to power law dependencies of the normalised dissipation on the local Reynolds number and which is clearly manifest in the fact that all terms involved in the KHMH equation are active. These terms are found to be self-similar only in terms of inner scales, which is in fact the sole requirement in predicting 2/3 power laws in non-homogeneous turbulence.