Scaling of near-wall streamwise turbulence intensity: from a viewpoint of attached eddy model

Scaling of near-wall streamwise turbulence intensity has been one of the debating topics at least for the past two decades. There has been emerging evidence that the peak near-wall streamwise turbulence intensity may deviate from the logarithmic scaling with Re_τ predicted by extending the classical attached eddy model to the near-wall region. Recently, a new theory has been proposed by Chen & Sreenivasan (2021, J. Fluid Mech., 908, R3) based on a physical argument on near-wall dissipation deficit in the invisid limit, but two different and mutually independent Navier-Stokes-based models have repeatedly predicted that the near-wall peak streamwise turbulence intensity is proportional to inverse of log Re_τ (Monkewitz & Nagib, J. Fluid Mech., Skouloudis & Hwang, 2021, Phys. Rev. Fluids, 6:034602). In this talk, I will present a new theory obtained by extending the spectrum-based attached eddy model of Perry, Henbest & Chong (1986, J. Fluid Mech. 165:163-199) to the near-wall region with incorporation of viscous wall effect lack in the classcial theory, and show that if the near-wall peak intensity is bounded, it is propoportional to inverse of log Re_τ in the inviscid limit, favouring the predictions by the Navier-Stokes-based models. The relevent evidence from both experimental data and a Navier-Stokes-based model will be presented to support the theory.