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Turbulence as a near-equilibrium process. (English) Zbl 0838.76034

Deift, Percy (ed.) et al., Dynamical systems and probabilistic methods in partial differential equations. 1994 summer seminar on dynamical systems and probabilistic methods for nonlinear waves, June 20-July 1, 1994, MSRI, Berkeley, CA, USA. Providence, RI: American Mathematical Society. Lect. Appl. Math. 31, 235-249 (1996).
Summary: The small-scale structure of fully developed homogeneous turbulence in an incompressible flow is described as a perturbation of an ensemble of vortices in thermal equilibrium. A cartoon model that illustrates how an equilibrium spectrum can coexist with an energy cascade is displayed. Analytical and numerical results that explain why the vortex model is reasonable are summarized; an important role is played by a generalization of the Kosterlitz-Thouless analysis of vortex phase transitions.
For the entire collection see [Zbl 0831.00019].

MSC:

76F99 Turbulence
82B35 Irreversible thermodynamics, including Onsager-Machlup theory
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
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