Analysis of the energy budget in turbulent channel flow using orthogonal wavelets

The spatial and scale statistics of turbulence kinetic energy are examined in turbulent channel flow at Re_τ = 300 using the orthonormal wavelet transform. The behaviour of the production, viscous and transfer terms is examined in terms of their variation with both space and scale. All terms are numerically large at wavenumbers at which a −5/3 slope is apparent in the velocity spectra, and they all exhibit significant spatial variability as evidenced by large flatnesses which increase with decreasing scale size. The flatness of terms involving transfer are particularly large. Attention focusses primarily on the sublayer and local-equilibrium regions: in the former, scale-to-scale flux is large and negative and consistent with conventional “backscatter” in Fourier space. In the linear sublayer, the flux is positive, consistent with Couette-like vortex stretching. The present work paves the way for close scrutiny of those components of the subgrid-scale stress that contribute most to the subgrid energy flux in large-eddy simulation of near-wall turbulent flows.