  Global topological charge decorrelates very slowly or even freezes in fine
lattice simulations. On the other hand, its local fluctuations are expected to
survive and lead to the correct physical results as long as the volume is large
enough. We investigate this issue on recently generated configurations
including dynamical domain-wall fermions at lattice spacings a = 0.08 fm and
finer. We utilize the Yang-Mills gradient flow to define the topological charge
density operator and calculate its long-distance correlation, through which we
propose a new method for extracting the topological susceptibility in a
sub-volume. This method takes care of the finite volume correction, which
reduces the bias caused by the global topological charge. Our lattice data
clearly show a shorter auto-correlation time than that of the naive definition
using the whole lattice, and are less sensitive to the global topological
history. Numerical results show a clear sea-quark mass dependence, which agrees
well with the prediction of chiral perturbation theory.
