1995/05/18 by Ph. Brax, Brax, Ph.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9505111
18 pages, Tex file, No figures
arxiv created 1995/05/18 · arxiv updated 2016/09/06
The long-time large-distance behaviour of free decaying two dimensional turbulence is studied. Stochastic solutions of the Navier-Stokes equation are explicitly shown to follow renormalisation group trajectories. It is proven that solutions of the Navier-Stokes equation asymptotically converge to fixed points which are conformal field theories. A particular fixed point is given by the free Gaussian field with a charge at infinity. The stream function is identified with a vertex operator. It happens that this solution also admits constant n-enstrophy fluxes in the asymptotic regime, therefore fulfilling all requirements to represent an asymptotic state of two-dimensional turbulence. The renormalisation basin of attraction of this fixed point consists of a charged Coulomb gas. This Coulomb gas gives an effective description of turbulence.