  We develop the formulation of turbulence in terms of the functional integral
over the phase space configurations of the vortex cells. The phase space
consists of Clebsch coordinates at the surface of the vortex cells plus the
Lagrange coordinates of this surface plus the conformal metric. Using the
Hamiltonian dynamics we find an invariant probability distribution which
satisfies the Liouville equation. The violations of the time reversal
invariance come from certain topological terms in effective energy of our
Gibbs-like distribution. We study the topological aspects of the statistics and
use the string theory methods to estimate intermittency.
