1 Table of Contents: “... Phenomenological theories -- 1 The closure problem of turbulence -- 2 Karman-Howarth equations in Fourier space...”

2 Table of Contents: “... -- 4 The stochastic models -- 5 Phenomenology of the closures -- 6 Numerical resolution of the closure...”

3 Table of Contents: “... of the closures -- 6 Numerical resolution of the closure equations -- 7 The enstrophy divergence and energy...”

4 “... developments using mathematical spectral methods (two-point closures like the EDQNM theory), direct-numerical...”