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We consider the vorticity form of the 2D Euler equations which is perturbedby a suitable transport type noise and has white noise initial condition. It isshown that, under certain conditions, this equation converges to the 2DNavier-Stokes equation driven by the space-time white noise.

Convergence of transport noise to Ornstein-Uhlenbeck for 2D Euler equations under the enstrophy measure