  We study the time evolution of velocity and pressure gradients in isotropic
turbulence, by quantifying their decorrelation time scales as one follows fluid
particles in the flow. The Lagrangian analysis uses data in a public database
generated using direct numerical simulation of the Naiver-Stokes equations, at
a Reynolds number 430. It is confirmed that when averaging over the entire
domain, correlation functions decay on timescales on the order of the mean
Kolmogorov turnover time scale, computed from the globally averaged rate of
dissipation and viscosity. However, when performing the analysis in different
subregions of the flow, turbulence intermittency leads to large spatial
variability in the decay time scales. Remarkably, excellent collapse of the
auto-correlation functions is recovered when using the `local Kolmogorov
time-scale' defined using the locally averaged, rather than the global,
dissipation-rate. This provides new evidence for the validity of Kolmogorov's
Refined Similarity Hypothesis, but from a Lagrangian viewpoint that provides a
natural frame to describe the dynamical time evolution of turbulence.
