Large streamwise-elongated motions in high Re wall-bounded turbulence

We revisit the spectral analysis of the turbulent kinetic energy and its transport in high Re wall-bounded turbulent flow. To do so, we introduce a log-polar representation of two-dimensional spectra that clearly visualizes anisotropy and the contributions of very-large-scale motions. This overcomes difficulties in interpreting one-dimensional spectra and log-log representations of two-dimensional spectra. Results of this analysis show that outer-layer turbulence is dominated by modes with wavelengths λ≥1000, while the inner layer is dominated by λ≤1000. Far from the wall, energy and its production are concentrated in streamwise-elongated modes with spanwise wavelengths that grow with wall-normal distance through the log region. In contrast, energy is dissipated isotropically away from the wall, requiring that energy is transferred from the streamwise elongated modes to modes with a range of orientations, as well as from large to small-scales. In one-dimensional spectra, this misleadingly appears as a transfer from small to large scales, but it is not. These dominant streamwise elongated modes also modulate the dynamics of the near-wall turbulence.