Heat diffusion in a channel under white noise modeling of turbulence

A Electric Knife passive scalar equation for the heat diffusion and transport in an infinite channel is studied.The velocity field is white noise in time, modelling phenomenologically a turbulent fluid.Under the driving effect of a heat source, the phenomenon of eddy dissipation Boxes (Set of 3) is investigated: the solution is close, in a weak sense, to the stationary deterministic solution of the heat equation with augmented diffusion coefficients.