Functional renormalisation group for turbulence

Turbulence is a complex nonlinear and multi-scale phenomenon. Although the fundamental underlying Navier-Stokes equations have been known for two centuries, it remains extremely challenging to extract from them statistical properties of turbulence. Therefore, practical purpose, sustained effort has devoted obtaining some effective description turbulence, that we may call turbulence modelling, or theory In this respect, Renormalisation Group (RG) appears as tool choice, since precisely designed provide theories by performing in systematic way average over fluctuations. However, suitable framework RG, allowing particular non-perturbative approximations, missing, which thwarted long RG applications. This provided modern formulation called functional renormalisation group. The use FRG rooted important progress theoretical understanding homogeneous isotropic major one rigorous derivation, equations, an analytical expression any Eulerian multi-point multi-time correlation function, exact limit large wavenumbers. We propose {\it JFM Perspectives} survey method basic introduction emphasise how field-theoretical allows systematically profoundly exploit symmetries. then show enables describe forced at scale, was not accessible perturbative means. expound derivation spatio-temporal behaviour $n$-point functions, largely illustrate these results through analysis data experiments direct numerical simulations.