Statistical Fluid Mechanics and Statistical Mechanics of Fluid Turbulence

2 Statistical mechanics of a moving fluid

Fully developed turbulence and statistical mechanics

2014 This paper gives a self contained review of some recent progress of the statistical theory of fully developed turbulence. The emphasis is on both analogies and differences with Hamiltonian statistical mechanics, in particular critical phenomena. The method of spectral equations, which plays to a certain extent the role of a mean field theory, is discussed in detail. It is here viewed as a ...

Fluid mechanics, turbulent flow and turbulence modeling

This course material is used in two courses in the International Master’s programmeAppliedMechanics at Chalmers. The two courses are TME225 Mechanics of fluids (Chapters 1-10), and MTF270 Turbulence Modeling (Chapters 11-27). MSc students who follow these courses are supposed to have taken one basic course in fluid mechanics. The lecture notes are also used in the three-day course Unsteady Simu...

Defect turbulence and generalized statistical mechanics

We present experimental evidence that the motion of point defects in thermal convection patterns in an inclined fluid layer is well described by Tsallis statistics with an entropic index q ≈ 1.5. The dynamical properties of the defects (anomalous diffusion, shape of velocity distributions, power-law decay of correlations) are in good agreement with typical predictions of nonextensive models, ov...

Generalized statistical mechanics and fully developed turbulence

The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating fr...