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)(GAMMA) which allows the scaling solutions in the inertial range of spatial scales. The pdf decays as exponential of some power of GAMMA3/A2, where A is the minimal area inside the loop.