In hydrodynamics coherent structures have been a catch word, which like turbulence, has no precise widely accepted definition. In fact, the "definitions" used by some of the originators of the idea are almost opaque.
Herein, a coherent structure in a fluid or a plasma will be defined as a
deformable domain with a boundary, where the topological features of the
interior is constant over the domain.
For example, in a fluid there may exist domains of streamline flow, without
vorticity and such that the Pfaff dimension is 1. Embedded in such a streamline
flow can be a bounded region in which the Pfaff dimension is 2, and the domain
of coherent (topological) structure contains vorticity.
Similarly, there can exist deformable domains of Pfaff dimension 3 within a streamline flow (say that has vorticity and is of Pfaff dimension 2). Such coherent structures sometimes are described as chaotic domains.
It is this author's contention that irreversible turbulent processes are domains
of Pfaff dimension 4.