  In this paper, we show that suitable transport noises produce anomalous
dissipation of energy of solutions to the 2D Navier-Stokes equations and
diffusion equations in all dimensions. The key ingredients are Meyers' type
estimates for SPDEs with transport noise which are combined with recent scaling
limits for such SPDEs. The former allow us to obtain, for the first time for
such type of scaling limits, convergence in a space of positive smoothness
uniformly in time. Compared to known results, one of the main novelties is that
anomalous dissipation might take place even in presence of a transport noise of
arbitrarily small intensity. Further, we discuss physical interpretations.
