Anisotropy and energy flux in wall turbulence

A term-by-term wavelet decomposition of the equation for turbulence kinetic energy in turbulent channel flow is used to provide a dual space-scale description of the production and flux of energy. Wavelet filtering, analogous to that used in large-eddy simulation, is performed on the nonlinear term that constitutes the energy flux. Meneveauʹs term, pi_{{sg}}^{(m)}[{bm i}] is used to represent forward scatter and backscatter. This term is highly intermittent, much more so than the equivalent terms for production at the same scale. Virtually all of $pi_{{sg}}^{(m)}[{bm i}] appears in only two components that involve subgrid flux of streamwise momentum in the wall-normal and spanwise directions. An equivalent term that is the wavelet transform of the pressure-gradient term is shown to be several orders of magnitude smaller, consistent with its neglect in current subgrid modelling techniques. However, the mean-square pressure-gradient fluctuations (that reach a maximum in the range of wavenumbers in which the velocity spectra exhibit a [minus sign]5/3 slope) are responsible for the significant spatial intermittency observed in the energy flux.