Quantitative mixing and dissipation enhancement property of Ornstein–Uhlenbeck flow

Pappalettera, Umberto

doi:10.1080/03605302.2022.2122835

Cited by 5 publications

(2 citation statements)

References 28 publications

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“…The first example is the advection of a passive tracer in a 1-D periodic domain by an Ornstein–Uhlenbeck process: perhaps the simplest class of problems amenable to detailed analysis. See Pappalettera (2022) for a mathematical treatment of this problem without source terms. The second example further builds intuition for the statistical significance of the conditionally averaging procedure by examining a three-velocity state approximation to an Ornstein–Uhlenbeck in an abstract -dimensional setting and a concrete two-dimensional (2-D) setting.…”

Section: Examplesmentioning

confidence: 99%

Statistical non-locality of dynamically coherent structures

2023

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We analyse a class of stochastic advection problems by conditionally averaging the passive tracer equation with respect to a given flow state. In doing so, we obtain expressions for the turbulent diffusivity as a function of the flow statistics spectrum. When flow statistics are given by a continuous-time Markov process with a finite state space, calculations are amenable to analytic treatment. When the flow statistics are more complex, we show how to approximate turbulent fluxes as hierarchies of finite state space continuous-time Markov processes. The ensemble average turbulent flux is expressed as a linear operator that acts on the ensemble average of the tracer. We recover the classical estimate of turbulent flux as a diffusivity tensor, the components of which are the integrated autocorrelation of the velocity field in the limit that the operator becomes local in space and time.

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Section: Examplesmentioning

confidence: 99%

Statistical non-locality of dynamically coherent structures

2023

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“…There are some motivations for the analysis of Eq. ( 4) based on the idea to extend to SPDE the remarkable principle of Wong-Zakai [20], see for example [2,3,14,15,18,19,16]. Assuming that the external source q and the initial temperature θ 0 are deterministic, under suitable mild assumptions the deterministic function…”

Section: Introductionmentioning

confidence: 99%

The Dissipation Properties of Transport Noise

Flandoli

Luongo

2022

Mathematics of Planet Earth

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The aim of this work is to present, in a compact way, the latest results about the dissipation properties of transport noise in fluid mechanics. Starting from the reasons why transport noise is natural in a passive scalar equation for the heat diffusion and transport, several results about enhanced dissipation due to the noise are presented. Rigorous statements are matched with numerical experiments in order to understand that the sufficient conditions stated are not yet optimal but give a first useful indication.

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Transport Noise in the Heat Equation

Flandoli

Luongo

2023

Lecture Notes in Mathematics

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Quantitative mixing and dissipation enhancement property of Ornstein–Uhlenbeck flow

Cited by 5 publications

References 28 publications

Statistical non-locality of dynamically coherent structures

Statistical non-locality of dynamically coherent structures

The Dissipation Properties of Transport Noise

Transport Noise in the Heat Equation

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