Turbulence, String Theory and Ising Model

Abstract

We advance the vortex cell approach to turbulence \cite{TSVS} by elaborating the Clebsch field dynamics on the surface of vortex cells. We argue that resulting statistical system can be described as 3D Ising model interacting with Compactified Bosonic String on the Riemann surface describing phase boundary. The cells come out as $\sigma=1$ phase of the Ising model in strong magnetic field. At large circulation around large loop the dominant Ising configuration correspond to minimal volume cells covering the area inside the loop, which naturally leads to the Area law and exponential PDF tails.