Eddy heat exchange at the boundary under white noise turbulence

: We prove the existence of an eddy heat diffusion coefficient coming from an idealized model of turbulent fluid. A difficulty lies in the presence of a boundary, with also turbulent mixing and the eddy diffusion coefficient going to zero at the boundary. Nevertheless, enhanced diffusion takes place. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.