Intermittency and Structure(s) of and/in Turbulence

  • Arkady Tsinober


Intermittency specifically in genuine fluid turbulence is associated mostly with some aspects of its spatiotemporal structure. Hence, the close relation between the origin(s) and meaning of intermittency and structure of turbulence. Just like there is no general agreement on the origin and meaning of the former, there is no consensus regarding what are the origin(s) and what turbulence structure(s) really mean. At the present state of matters both issues are pretty speculative and an example of ‘ephemeral’ collection of such is given in this chapter. We have to admit at this stage that structure(s) is(are) just an inherent property of turbulence.

Structureless turbulence is meaningless. There is no turbulence without structure(s). Every part (just as the whole) of the turbulent field—including the so-called ‘structureless background’—possess structure. Structureless turbulence (or any of its part) contradicts both the experimental evidence and the Navier–Stokes equations. The claims for ‘structureless background’ is a reflection of our inability to ‘see’ more intricate aspects of turbulence structure: intricacy, complexity and ‘randomness’ are not synonymous for absence of structure.

What is definite is that turbulent flows have lots of structure(s). The term structure(s) is used here deliberately in order to emphasize the duality (or even multiplicity) of the meaning of the underlying problem. The first is about how turbulence ‘looks’. The second implies the existence of some entities. Objective treatment of both requires use of some statistical methods. It is thought that these methods alone may be insufficient to cope with the problem, but so far no satisfactory solution was found. One (but not the only) reason—as mentioned—is that it is not so clear what one is looking for: the objects seem to be still elusive. For example, there is still a non-negligible set of people in the community that are in a great doubt that the concept of coherent structure is much different from the Emperors’s new Clothes.

An example of acute difficulties described in this chapter is associated with high dimension of what is called structures so that simple single parameter thresholding is inappropriate to make on them statistics due to the painful question how really “similar” are all these if the individual members of such an ensemble are defined by one parameter only. The view that turbulence structure(s) is(are) simple in some sense and that turbulence can be represented as a collection of simple objects only seems to be a nice illusion which, unfortunately, has little to do with reality. It seems somewhat wishfully naive to expect that such a complicated phenomenon like turbulence can merely be described in terms of collections of only such ‘simple’ and weakly interacting object.


Coherent Structure Turbulence Structure Vortex Tube Inertial Range Large Reynolds Number 
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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Arkady Tsinober
    • 1
  1. 1.School of Mechanical EngineeringTel Aviv UniversityTel AvivIsrael

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