Predictions on Two-dimensional Turbulence by Conformal Field Theory

Abstract

A generalized theory of two-dimensional isotropic turbulence is developed based on conformal symmetry. A number of minimal models of conformal turbulence are solved under an extended constraint including both the enstrophy cascade by Kraichnan and the discontinuity of vorticity by Saffman. There are an infinite number of solutions which fall into two different categories. An explicit relation is derived in one of the categories between the central charge of Virasoro algebra, the lowest anomalous dimension and the power of the energy spectrum. Some statistical properties such as energy spectrum, skewness, flatness and Casimir invariants are predicted and compared with numerical simulation by the pseudospectral method.