We introduce a stochastic version of the 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.

Publication:

SIAM Journal on Mathematical Analysis, Vol. 56, Iss. 3 (2024)

http://dx.doi.org/10.1137/23M1587944

Author:

Franco Flandoli

Scuola Normale Superiore of Pisa, 56124 Pisa, Italy.

Dejun Luo

Key Laboratory of RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.

Email: luodj@amss.ac.cn