Near-wall turbulent fluctuations in the absence of wide outer motions

Abstract

AbstractNumerical experiments that remove turbulent motions wider than ${ \lambda }_{z}^{+ } \simeq 100$ are carried out up to ${\mathit{Re}}_{\tau } = 660$ in a turbulent channel. The artificial removal of the wide outer turbulence is conducted with spanwise minimal computational domains and an explicit filter that effectively removes spanwise uniform eddies. The mean velocity profile of the remaining motions shows very good agreement with that of the full simulation below ${y}^{+ } \simeq 40$, and the near-wall peaks of the streamwise velocity fluctuation scale very well in the inner units and remain almost constant at all the Reynolds numbers considered. The self-sustaining motions narrower than ${ \lambda }_{z}^{+ } \simeq 100$ generate smaller turbulent skin friction than full turbulent motions, and their contribution to turbulent skin friction gradually decays with the Reynolds number. This finding suggests that the role of the removed outer structures becomes increasingly important with the Reynolds number; thus one should aim to control the large scales for turbulent drag reduction at high Reynolds numbers. In the near-wall region, the streamwise and spanwise velocity fluctuations of the motions of ${ \lambda }_{z}^{+ } \leq 100$ reveal significant lack of energy at long streamwise lengths compared to those of the full simulation. In contrast, the losses of the wall-normal velocity and the Reynolds stress are not as large as those of these two variables. This implies that the streamwise and spanwise velocities of the removed motions penetrate deep into the near-wall region, while the wall-normal velocity and the Reynolds stress do not.