Spectra of energy transport in turbulent channel flows for moderate Reynolds numbers

Abstract

To reveal the scale dependence of the transport of turbulent kinetic energy in a channel flow, the constituents of a spectral energy budget equation are evaluated using direct numerical simulations. At each height in the buffer and overlap layers, the upward turbulent transport provides energy to the fluctuations at small scales, but removes it from those at large scales. Energy removed from the large scales in the overlap layer is carried upward to the centre of the channel and also downward to the vicinity of the wall. The downward energy fluxes at the large scales result in the well-known anomaly of turbulence intensity and the constituents of the budget equation near the wall. In the overlap layer the cospectrum of the spatial turbulent transport is scaled well by the mixing length. It shows that the structure of fluctuations involved in turbulent transport is self-similar in this layer, supporting the classical assumption. The cospectra of pressure–strain correlations are also evaluated. They are not scaled by the wall unit near the wall, but no symptom of the influence of large-scale structures is observed in the cospectra, at least for the present range of Reynolds numbers. Above the buffer layer the cospectra of the pressure–strain correlations are almost isotropic, and their relevant length scale is given by the mixing length in the overlap layer. The pressure–strain correlations are therefore rather local quantities.