A generalization of Yaglom's equation which accounts for the large-scale forcing in heated decaying turbulence

In most real or numerically simulated turbulent flows, the energy dissipated at small scales is equal to that injected at very large scales, which are anisotropic. Despite this injection-scale anisotropy, one generally expects the inertial-range scales to be locally isotropic. For moderate Reynolds numbers, the isotropic relations between second-order and third-order moments for temperature (Yaglom's equation) or velocity increments (Kolmogorov's equation) are not respected, reflecting a non-negligible correlation between the scales responsible for the injection, the transfer and the dissipation of energy. In order to shed some light on the influence of the large scales on inertial-range properties, a generalization of Yaglom's equation is deduced and tested, in heated grid turbulence (R-lambda = 66). In this case, the main phenomenon responsible for the non-universal inertial-range behaviour is the non-stationarity of the second-order moments, acting as a negative production term.