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Research Article | Open Access

Heat diffusion in a channel under white noise modeling of turbulence

Franco Flandoli( ), Eliseo Luongo
Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy
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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

turbulenceeddy diffusionvortex patchtransport noiseDirichlet boundary condition

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Mathematics in Engineering
Volume 4 Issue 4,
August 2022
Pages 1-21
DOI: 10.3934/mine.2022034

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Cite this article:
Flandoli F, Luongo E. Heat diffusion in a channel under white noise modeling of turbulence. Mathematics in Engineering, 2022, 4(4): 1-21. https://doi.org/10.3934/mine.2022034

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Received: 02 June 2021
Accepted: 01 September 2021
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)