  We consider on the torus the scaling limit of stochastic 2D (inviscid) fluid
dynamical equations with transport noise to deterministic viscous equations.
Quantitative estimates on the convergence rates are provided by combining
analytic and probabilistic arguments, especially heat kernel properties and
maximal estimates for stochastic convolutions. Similar ideas are applied to the
stochastic 2D Keller-Segel model, yielding explicit choice of noise to ensure
that the blow-up probability is less than any given threshold. Our approach
also gives rise to some mixing property for stochastic linear transport
equations and dissipation enhancement in the viscous case.
