Scaling of the streamwise turbulence intensity in the context of inner-outer interactions in wall turbulence

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The classical view of wall-bounded turbulence considers a near-wall inner region where all velocity statistics are universally dependent on distance from the wall when scaled with friction velocity and the kinematic viscosity of the fluid. This is referred to as an inner scaling and leads to Prandtl's law of the wall. Data from numerical simulations and experiments over the past decade or so, however, have provided compelling evidence that statistics of the fluctuating streamwise velocity do not follow inner scaling in this near-wall region and an interaction of outer and logarithmic regions exists, resulting in a Reynolds number dependence. In this paper we briefly review some of these studies and discuss the Reynolds number dependence of the streamwise turbulence intensity near the wall in terms of an inner-outer interaction. An established model for such an interaction between near-wall and logarithmic region turbulence is considered that comprises two mechanisms: superposition and modulation. Here outer-region motions, of which a fraction is wall-attached, are superimposed onto the near-wall dynamics, and concurrently the near-wall motions are modulated by this superimposed signature. We discuss to what extent the superposition effect can relate changes in the inner-scaled near-wall peak value of streamwise turbulence intensity to logarithmic region turbulence resembling features of attached eddies.