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In this study, asymptotic scaling of near-wall streamwise turbulenceintensity $\overline{u'u'}/u_\tau^2$ ($u_\tau$ is the friction velocity) istheoretically explored. The three scalings previously proposed are firstreviewed with their derivation and physical justification: 1)$\overline{u'u'}/u_\tau^2 \sim \ln Re_\tau$ ($Re_\tau$ is the frictionvelocity); 2) $\overline{u'u'}/u_\tau^2 \sim 1/U_\infty^+$ ($U_\infty^+$ is theinner-scaled freestream velocity in boundary layer); 3)$\overline{u'u'}/u_\tau^2 \sim Re_\tau^{-1/4}$. A new analysis is subsequentlydeveloped based on velocity spectrum, and two possible scenarios are identifiedbased on the asymptotic behaviour of the outer-scaling part of the near-wallvelocity spectrum. In the former case, the outer-scaling part of the spectrumis assumed to reach a non-zero constant as $Re_\tau \rightarrow \infty$, and itresults in the scaling of $\overline{u'u'}/u_\tau^2 \sim \ln Re_\tau$, bothphysically and theoretically consistent with the classical attached eddy model.In the latter case, a sufficiently rapid decay of the outer-scaling part of thespectrum with $Re_\tau$ is assumed due to the effect of viscosity, such that$\overline{u'u'}/u_\tau^2 < \infty$ for all $Re_\tau$. The following analysisyields $\overline{u'u'}/u_\tau^2 \sim 1/\ln Re_\tau$, asymptotically consistentwith the scaling of $\overline{u'u'}/u_\tau^2 \sim 1/U_\infty^+$. The scalingsare further verified with the existing simulation and experimental data andthose from a quasilinear approximation (Holford \emph{et al.}, 2023,\texttt{arXiv:2305.15043}), the spectra of which all appear to favour$\overline{u'u'}/u_\tau^2 \sim 1/\ln Re_\tau$, although new datasets for$Re_\tau \gtrsim O(10^4)$ would be necessary to conclude this issue.

Near-wall turbulence intensity as $Re_\tau \rightarrow \infty$