On scale invariance and Ward identities in statistical hydrodynamics

(Received 16 April 1991, accepted 3 June 1991)

Abstract
Considering the incompressible viscid fluid driven by random force f(t,r), we have found out the existence of such nontrivial correlators, that the characteristic functional of alluded stochastic process has the symmetry features, as if no random force is present. Based on this fact, two sets of Ward identities related with the scale invariance of Navier-Stokes equations are constructed. These identities are important for renormalization in functional-integral approach to hydrodynamical turbulence. Besides, they impose some restriction on turbulence spectra. The particular case of degenerating turbulence with energy spectrum is also under consideration.