In this study, asymptotic scaling of near-wall streamwise turbulence intensity u′u′/u2 τ (uτ is the friction velocity) is theoretically explored. The three scalings previously proposed are first reviewed with their derivation and physical justification: 1) u′u′/u2 τ ∼ ln Reτ (Reτ is the friction velocity); 2) u′u′/u2 τ ∼ 1/U + ∞ (U + ∞ is the inner-scaled freestream velocity in boundary layer); 3) u′u′/u2 τ ∼ Re−1/4
τ . A new analysis is subsequently developed based on velocity spectrum, and two possible scenarios are identified based on the asymptotic behaviour of the outer-scaling part of the near-wall velocity spectrum. In the former case, the outer-scaling part of the spectrum is assumed to reach a non-zero constant as Reτ → ∞, and it results in the scaling of u′u′/u2 τ ∼ ln Reτ , both physically and theoretically consistent with the classical attached eddy model. In the latter case, a sufficiently rapid decay of the outer-scaling part of the spectrum with Reτ is assumed due to the effect
of viscosity, such that u′u′/u2 τ < ∞ for all Reτ . The following analysis yields u′u′/u2 τ ∼ 1/ ln Reτ , asymptotically consistent with the scaling of u′u′/u2 τ ∼ 1/U + ∞ . The scalings are further verified with the existing simulation and experimental data and those from a quasilinear approximation (Holford et al., 2024, J. Fluid Mech., In press; arXiv:2305.15043), the spectra of which all appear to favor
u′u′/u2 τ ∼ 1/ ln Reτ , although new datasets for Reτ & O(104 ) would be necessary to conclude this issue.