Heat diffusion in a channel under white noise modeling of turbulence

Franco Flandoli; Eliseo Luongo; Franco Flandoli; Eliseo Luongo

doi:10.3934/mine.2022034

Mathematics in Engineering

2022, Volume 4, Issue 4: 1-21. doi: 10.3934/mine.2022034

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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

Received: 02 June 2021 Accepted: 01 September 2021 Published: 24 September 2021

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.
- turbulence,
- eddy diffusion,
- vortex patch,
- transport noise,
- Dirichlet boundary condition
Citation: Franco Flandoli, Eliseo Luongo. Heat diffusion in a channel under white noise modeling of turbulence[J]. Mathematics in Engineering, 2022, 4(4): 1-21. doi: 10.3934/mine.2022034

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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.

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