3.6 Topological Analysis, Coherent Events, and Related Dynamics

As already mentioned, it has been known since the direct observations by Siggia (1981) that coherent structures exist in isotropic turbulence. ^[**]

It must be noticed that the term coherent structures can be fuzzy. In the following, we follow only the conventional use, provisionally avoiding the question of temporal coherence are they known to preserve themselves temporally? of these structures. Only considering instantaneous spatial coherence, these structures may be grouped into two classes: vortex tubes (also referred to as worms or vortex filaments) and vortex sheets. The former are identified as elongated, tubelike vortices mainly subjected to an axial strain, whereas the latter are related to vorticity sheets that experience a plain strain.

The existence of these events raises several important questions for both the analysis of isotropic turbulence study and the general turbulence theory:

1. How do we define these events, or, more precisely, how do we define them unequivocally?

2. What is the dynamics of these events: How are they generated? What is their life cycle? Do they exhibit some universal features?

3. What is their role in isotropic turbulence dynamics? How are they related to well-known features such as the kinetic-energy cascade, the turbulent kinetic-energy dissipation, and the internal intermittency?

Recent results dealing with these issues are subsequently surveyed. But let us emphasize here that, despite the impressive amount of efforts devoted to the analysis of isotropic turbulence, a global complete theory for...