Random systems,turbulence and disordering fields

The statistical theory of random processes is cast into a Lagrangian form. The formalism requires the existence of an arbitrarily weak random stirring force, playing the role of a disordering field. In scale invariant systems the coupling strength of the weak stirring force can be scaled out and it disappears from the theory. The formalism is applied to the turbulent flow of an incompressible fluid; in particular, we derive the Feynman rules by means of which the distribution of fluctuations around an average flow can be determined. The formalism is further illustrated on the example of a stationary fluid flow between parallel planes: an approximate formula for the correlation function of vorticities is obtained, which is expected to be valid at large Reynolds numbers.