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We smear quenched lattice QCD ensembles with lattice volume $32^3\times 8$ byusing Wilson flow. Six ensembles at temperature near the critical temperature$T_c$ corresponding to the critical inverse coupling $\beta_c=6.06173(49)$ areused to investigate the localization of topological charge density. If theeffective smearing radius of Wilson flow is large enough, the density, size andpeak of Harrington-Shepard (HS) caloron-like topological lumps of ensembles arestable when $\beta\leq 6.050$, but start to change significantly when$\beta\geq6.055$. The inverse participation ratio (IPR) of topological chargedensity shows similar results, it begins to increase when $\beta\geq 6.055$ andis stable when $\beta\leq 6.050$. The pseudoscalar glueball mass is extractedfrom the topological charge density correlator (TCDC) of ensembles at$T=1.19T_c,~\textrm{and }1.36T_c$, the masses are $1.915(98)\textrm{ GeV}$ and$1.829(123)\textrm{ GeV}$ respectively, they are consistent with results fromconventional methods.

Localization of topological charge density near $T_c$ in quenched QCD with Wilson flow