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 anisotropic kinetic alpha (AKA) effect. This is the first example with a 3D structure and a stretching noise term.

On the Boussinesq hypothesis for a stochastic Proudman–Taylor model

FLANDOLI, FRANCO;LUO, DEJUN
2024

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 anisotropic kinetic alpha (AKA) effect. This is the first example with a 3D structure and a stretching noise term.
2024
Settore MAT/06 - Probabilita' e Statistica Matematica
Boussinesq hypothesis; Proudman-Taylor model; turbulence; scaling limit; AKA effect
   Noise in Fluids
   NoisyFluid
   European Commission
   101053472
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/137622
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