  A definition of K41 scaling law for suitable families of measures is given
and investigated. First, a number of necessary conditions are proved. They
imply the absence of scaling laws for 2D stochastic Navier-Stokes equations and
for the stochastic Stokes (linear) problem in any dimension, while they imply a
lower bound on the mean vortex stretching in 3D. Second, for 3D stochastic
Navier-Stokes equations necessary and sufficient conditions for K41 are proved,
translating the problem into bounds for energy and enstrophy of high and low
modes respectively. The validity of such conditions in 3D remains open.
Finally, a stochastic vortex model with such properties is presented.
