Turbulence appears in many ways, independently of the system that supports its manifestations. In all cases, it can be seen that:

a) Its manifestations are irreversible, in the sense that one cannot repeat them (no two von Kárman vortex streets are exactly equal, for instance);

b) There is not an unique cause, or system of causes to explain it, as there is not an exhaustive explanation of its occurrence (notwithstanding the case for the Navier-Stokes equation to be numerically solved);

c) Although its onset may be predicted (using the concept of the Reynolds number, for instance), one can not predict the precise manner of its full development (vortex dynamics has plenty of room for determinism to fail, as soon as one tries to write equations for the trajectory of a single vortex);

These three conditions fulfil what Jean-Luc Marion [De Surcroît, Paris, PUF, 2001] proposes for a phenomenon to be called a **saturated phenomenon**: one in which intuition is given in a way that definitely exceeds what the available concept is ever able to predict and show. Therefore, the question:

Is the manifestation of turbulence a saturated phenomenon?

  • I might recommend looking at Serres, in particular Birth of Physics, in which he explores turbulence pretty extensively... :)
    – Joseph Weissman
    Jul 27 '13 at 3:31
  • Thank you for your suggestion, Joseph Weissman. I will try to read something about it, on the web, and then, perhaps to buy it Aug 14 '13 at 14:20

Turbulence is very sensitive to initial conditions, and, in this sense, is chaotic. But I do not agree that is not deterministic. Direct Numerical Simulation (DNS) allows one to simulate the production of vortices without using simplifying sub-models.

Such predictions might fail to perfectly match an experiment, because they are sensitive to initial conditions (they are chaotic), but they are still deterministic.

Now I am not familiar with the concept of "saturated phenomenon", but it looks quite close to the definition of a chaotic phenomenon.

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