On the Boussinesq hypothesis for a stochastic Proudman-Taylor model

Franco Flandoli; Dejun Luo

doi:10.1137/23m1587944

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arXiv · 2304.11798

On the Boussinesq hypothesis for a stochastic Proudman-Taylor model

Franco Flandoli·Dejun Luo

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Abstract

We introduce a stochastic version of Proudman-Taylor model, a 2D-3C fluid approximation of the 3D Navier-Stokes equations, with the small-scale turbulence modeled by a transport-stretching noise. For this model we may rigorously take a scaling limit leading to a deterministic model with additional viscosity on large scales. In certain choice of noises without mirror symmetry, we identify an AKA effect. This is the first example with a 3D structure and a stretching noise term.

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Franco Flandoli, Dejun Luo. 2023-04-24. On the Boussinesq hypothesis for a stochastic Proudman-Taylor model. https://doi.org/10.1137/23m1587944

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