Heat diffusion in a channel under white noise modeling of turbulence

Abstract

A 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 is investigated: the solution is close, in a weak sense, to the stationary deterministic solution of the heat equation with augmented diffusion coefficients.

Keywords

• turbulence
• eddy diffusion
• vortex patch
• transport noise
• dirichlet boundary condition