The mesolayer of attached eddies in wall-bounded turbulent flows

Abstract

It has recently been reported that the outer peak in the secondorder statistics of the streamwise velocity depends on the Reynolds number. Starting from this puzzling observation, here I propose that the streamwise velocity component of each of the energy-containing motions in the form of Towsnend’s attached eddies exhibit innerscaling nature in the region close to the wall (see figure 1). Some compelling evidence on this proposition has been presented with a careful inspection of scaling of velocity spectra from direct numerical simulations and a linear analysis with an eddy viscosity. It is shown that this behavior can emerge due to inhomogeneous turbulent dissipation in the wall-normal direction, and also enables one to explain the Reynolds-number-dependent behavior of the outer peak as well as the near-wall penetration of the large-scale outer structures in a consistent manner. Extension of this concept to Townsend’s attached eddy hypothesis further reveals that the selfsimilarity in the streamwise velocity of the attached eddies would be theoretically broken in the region close to the wall.