<p>It is well known that the inadequate spatial resolution of hot-wire anemometry can lead to significant underestimation of measured quantities, such as the streamwise Reynolds stress, particularly at high Reynolds numbers. In this study, we propose a spatial resolution correction method based on a new scaling (the mean turbulent energy dissipation rate and the kinematic viscosity) introduced by Tang and Antonia (<CitationRef CitationID="CR53">2022</CitationRef>) for wall-bounded turbulent flows. This method is tested in a zero pressure gradient boundary layer at several Reynolds numbers (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4120_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$Re_{\tau}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>e</mi> <mi>τ</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> = 2284, 3475, 4045, 4162, and 14000), where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4120_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$Re_{\tau}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>e</mi> <mi>τ</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> is based on the friction velocity and the boundary layer thickness. By replacing the under-resolved small-scale portion of the energy spectra measured by hot-wires with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4120_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$Re_{\tau}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>e</mi> <mi>τ</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>-independent spectra obtained from direct numerical simulation (DNS) of wall-bounded turbulent flows, the proposed correction method provides reasonable estimates of the streamwise Reynolds stress in the near-wall region.</p>

Spatial resolution correction for hot-wire measurements based on the dissipative scaling in a zero pressure gradient boundary layer

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发表日期：

2025年10月5日

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D. Liu,
S. L. Tang,
R. A. Antonia

摘要

It is well known that the inadequate spatial resolution of hot-wire anemometry can lead to significant underestimation of measured quantities, such as the streamwise Reynolds stress, particularly at high Reynolds numbers. In this study, we propose a spatial resolution correction method based on a new scaling (the mean turbulent energy dissipation rate and the kinematic viscosity) introduced by Tang and Antonia (2022) for wall-bounded turbulent flows. This method is tested in a zero pressure gradient boundary layer at several Reynolds numbers ( $Re_{\tau}$ $R e_{τ}$ = 2284, 3475, 4045, 4162, and 14000), where $Re_{\tau}$ $R e_{τ}$ is based on the friction velocity and the boundary layer thickness. By replacing the under-resolved small-scale portion of the energy spectra measured by hot-wires with $Re_{\tau}$ $R e_{τ}$ -independent spectra obtained from direct numerical simulation (DNS) of wall-bounded turbulent flows, the proposed correction method provides reasonable estimates of the streamwise Reynolds stress in the near-wall region.