Energy transfer in turbulent channel flows and implications for resolvent modelling

We analyse the inter-scale transfer of energy for two types plane Poiseuille flow: P4U exact coherent state Park and Graham (2015) turbulent flow in a minimal channel. For both flows, dominant energy-producing modes are streamwise-constant streaks with spanwise spacing approximately 100 wall units. Since viscous dissipation these scales is not sufficient to balance production, nonlinear terms redistribute excess other scales. Spanwise-constant (that is, Tollmien-Schlichting-like zero wavenumber), particular, account significant amount net gain from terms. compare predictions resolvent analysis we show that it does model well. Nevertheless, find transferred can be predicted reasonably well by Cess eddy viscosity profile. As such, an effective explains good most energetic streaks. It also improves as basis structures whose streamwise lengths greater than their widths counteracting non-normality operator. Eddy respect conservative nature which must sum over all less effective, consequently, receive