TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.5.212
TI  - Functional renormalisation group approach to shell models of turbulence
PY  - 2023/11/28
UR  - https://www.scipost.org/SciPostPhys.15.5.212
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 5
SP  - 212
A1  - Fontaine, Côme
AU  - Tarpin, Malo
AU  - Bouchet, Freddy
AU  - Canet, Léonie
AB  - Shell models are simplified models of hydrodynamic turbulence, retaining only some essential features of the original equations, such as the non-linearity, symmetries and quadratic invariants. Yet, they were shown to reproduce the most salient properties of developed turbulence, in particular universal statistics and multi-scaling. We set up the functional renormalisation group (FRG) formalism to study generic shell models. In particular, we formulate an inverse RG flow, which consists in integrating out fluctuation modes from the large scales (small wavenumbers) to the small scales (large wavenumbers), which is physically grounded and has long been advocated in the context of turbulence. Focusing on the Sabra shell model, we study the effect of both a large-scale forcing, and a power-law forcing exerted at all scales. We show that these two types of forcing yield different fixed points, and thus correspond to distinct universality classes, characterised by different scaling exponents. We find that the power-law forcing leads to dimensional (K41-like) scaling, while the large-scale forcing entails anomalous scaling.
ER  -

@Article{10.21468/SciPostPhys.15.5.212,
	title={{Functional renormalisation group approach to shell models of turbulence}},
	author={Côme Fontaine and Malo Tarpin and Freddy Bouchet and Léonie Canet},
	journal={SciPost Phys.},
	volume={15},
	pages={212},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.5.212},
	url={https://scipost.org/10.21468/SciPostPhys.15.5.212},
}