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Within the model A in the Hohenberg's dynamical universality classification,we investigate the critical slowing down effects on the critical fluctuationsdriven by the expanding quark-gluon plasma, using a trajectory and cooling rateobtained from hydrodynamics. We numerically solved the Langevin dynamics of thenon-conserved order parameter field and find that, compared with commonly usedHubble-like expansion, the cooling rate of a realistic hydrodynamic system ispretty large and the associated critical slowing down effects strongly suppressthe higher-order cumulants of the order parameter field ({\it e.g.,} $C_4$).Furthermore, for an evolving system that approaches the critical point, suchcritical slowing down suppression overcomes the enhancement of the criticalfluctuations, which indicates that the largest fluctuations of the orderparameter field ({\it i.e.,} $C_2$) do not necessarily associate with theevolving trajectory closest to the critical point.

Dynamical critical fluctuations near the QCD critical point with hydrodynamic cooling rate