Inter-scale energy transfer in turbulent channels

Abstract We investigate the energy cascade in wall-bounded turbulence by analysing the inter-scale transfer between wall-parallel lengthscales in periodic channels. This transfer originates from the nonlinear interactions in the advective term of the Navier-Stokes equations, which satisfy the classical triadic compatibility relations. Each triadic interaction is examined individually, and the corresponding nonlinear energy transfers are mapped to assess their relative importance in sustaining turbulence. Motivated by the anisotropy of the flow, we interpret each of the nine contributions to the advection term arising from the different combinations of the streamwise, spanwise and wall-normal velocities as carrying distinct physical information, and therefore analyse them separately. Time-averaged maps of the energy transfer across all lengthscales and wall-normal positions for a channel flow at Re τ ≈ 180 are used to explore the mechanisms underlying the cascade process. As a proof of concept, reduced-order simulations are performed by retaining only the interactions identified as responsible for significant energy transfer based on our framework. Turbulent dynamics are successfully reproduced when 30% or more of the total interactions are included, while noticeable deviations emerge in the near-wall region when this proportion is further reduced.