Eddy heat exchange at the boundary under white noise turbulence

TL;DR

This paper proves the existence of an eddy heat diffusion coefficient in a turbulent fluid model with boundary effects, demonstrating enhanced diffusion despite the eddy coefficient vanishing at the boundary.

Contribution

It introduces a mathematical proof of eddy heat diffusion in a boundary-influenced turbulent flow model, addressing boundary vanishing effects.

Findings

Existence of eddy heat diffusion coefficient proven.

Enhanced diffusion occurs despite boundary effects.

Eddy coefficient approaches zero at the boundary.

Abstract

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.