  This review summarizes the coherent structures (CS) based on two-point
correlations and their applications, with a focus on the interpretation of
statistic CS and their characteristics. We review studies on this topic, which
have attracted attention in recent years, highlighting improvements,
expansions, and promising future directions for two-point statistics of CS in
turbulent flow. The CS is one of typical structures of turbulent flow,
transporting energy from large-scale to small-scale structures. To investigate
the CS in turbulent flow, a large amount of two-point correlation techniques
for CS identification and visualization have been, and are currently being,
intensively studied by researchers. Two-point correlations with examples and
comparisons between different methods are briefly reviewed at first. Some of
the uses of correlations in both Eulerian and Lagrangian frames of reference to
obtain their properties at consecutive spatial locations and time events are
surveyed. Two-point correlations, involving space-time correlations, two-point
spatial correlations, and cross correlations, as essential to theories and
models of turbulence and for the analyses of experimental and numerical
turbulence data are then discussed. The velocity-vorticity correlation
structure (VVCS) as one of the statistical CS based on two-point correlations
is reiterated in detail. Finally, we summarize the current understanding of
two-point correlations of turbulence and conclude with future issues for this
field.
