Remarks on turbulence theory

AbstractSome recent work in turbulence theory is reviewed, with emphasis on methods related to renormalized perturbation theory. The topics discussed include: constants of motion and equilibrium statistical mechanics of the Euler equations; cascade phenomena in turbulence and intermittency in the small scales; renormalized perturbation expansions and renormalization of viscosity; the difficulty of distinguishing convection from distortion effects in turbulence dynamics, the need for Lagrangian description, and related difficulties in the quantum field theory of many-body systems; the direct-interaction approximation for turbulence; what can presently be computed from turbulence theory