  The random forced Navier-Stokes equation can be obtained as a variational
problem of a proper action. In virtue of incompressibility, the integration
over transverse components of the fields allows to cast the action in the form
of a large deviation functional. Since the hydrodynamic operator is nonlinear,
the functional integral yielding the statistics of fluctuations can be
practically computed by linearizing around a physical solution of the
hydrodynamic equation. We show that this procedure yields the dimensional
scaling predicted by K41 theory at the lowest perturbative order, where the
perturbation parameter is the inverse Reynolds number. This result is valid
over a finite spatio-temporal domain, where the physical solution can be
considered as stationary.
