LOOP EQUATION AND AREA LAW IN TURBULENCE

This is an extended version of the preprint,⁴ based on the lectures given at Cargese Summer School and Chernogolovka Summer School in 1993. The incompressible fluid dynamics is reformulated as dynamics of closed loops C in coordinate space. We derive explicit functional equation for the pdf of the circulation P_C (Γ) which allows the scaling solutions in the inertial range of spatial scales. The pdf decays as exponential of some power of Γ³/A², where A is the minimal area inside the loop.