The influence of energy-containing scales on the distribution of spectral energy transfers

We present computations of individual mode-to-mode energy transfers from direct numerical simulations of homogeneous isotropic turbulence. Unlike previous approaches based on shell-filtered velocity fields, this method distinguishes between the energy exchanged by each pair of modes within a triad. We introduce a potential function based on the energy content of the modes involved, and show that it predicts the distribution of intense energy transfers in the vicinity of the sampling mode considered. By performing simulations with forcing applied at intermediate wavenumbers, we demonstrate that the region of most intense transfers is determined by the spectral location of the energy-containing scales rather than by the local or non-local character of the triad. Direct energy exchanges with the energy-containing range are suppressed by geometric constraints from the divergence-free condition, but persist as residuals when the sampling mode is close to the energy-containing scales. The comparison with an estimator derived from eddy-damped quasi-normal Markovian theory shows good agreement and recovers the forward, scale-local nature of energy transfer consistent with the cascade picture.