Wall turbulence with a selected set of nonlinear interactions

We investigate the energy cascade in wall turbulence by analysing the height-local interscale transfer between streamwise and spanwise lengthscales in periodic channel flows. This transfer is a result of the nonlinear interactions in the advective term (∇·(uu)) of the Navier-Stokes equation, which satisfy the classic triadic compatibility relation: an advecting (active, k_a) and advected mode (passive, k_p) interacting to produce velocity at a target mode (k_t = k_a + k_p). We examine each triadic interaction between different lengthscales individually and map their corresponding nonlinear energy transfer to determine their relative importance in sustaining turbulence. Due to the anisotropy of the flow, each component (∂_i(u_iu_j)) of the advective term implies a different physical mechanism and is therefore treated separately. We perform this analysis for all triads typically resolved in DNS and spanning the full wall-normal direction. Based on the identified key interactions, we conduct reduced-order simulations in which only these important triads are retained when computing the nonlinear term.