  The phenomenon of dissipation enhancement by transport noise is shown for
stochastic 2D Navier-Stokes equations in velocity form. In the 3D case,
suppression of blow-up is proved for stochastic Navier-Stokes equations in
vorticity form; in particular, quantitative estimate allows us to choose the
parameters of noise, uniformly in initial vorticity bounded in $L^2$-norm, so
that global solutions exist with a large probability sufficiently close to 1.
