ABSTRACT
Turbulence is a general term used for describing the erratic motions displayed by nonlinear systems that are driven far from their equilibrium position and thus display complicated motions involving different time and length scales. Without other precision, the term generally refers to hydrodynamic turbulence, as the main field of research has been directed toward irregular motions of fluids and the solutions of Navier–Stokes equations. During the twentieth century, theoretical developments showed important breakthroughs thanks to the qualitative ideas of Richardson and the quantitative arguments of Kolmogorov that culminated in the so-called K41 theory [25,30,31]. This statistical approach, although giving successful predictions, still faces an irreducible obstacle due to the lack of closure in the infinite hierarchy of moment equations.
