Correlation functions in fully developed turbulence

Turbulence is an ubiquitous phenomenon in fluid flows. Yet, calculating its statistical properties, and in particular what is generically called intermittency effects, remains an open issue. In this talk, I will focus on isotropic and homogeneous fully developed turbulence in incompressible flows. While much effort has been devoted to characterising equal-time properties of the turbulent state, less is known about its temporal behaviour. I will present some analytical results on the time dependence of generic multi-point correlation functions in the stationary turbulent state. These results are obtained from « first principles », i.e. starting from the forced Navier-Stokes equation, and using a field-theoretical approach (based on Functional and Non-Perturbative Renormalisation Group techniques). They are asymptotically exact in the limit of large wave-numbers. I will compare these predictions with available results from both direct numerical simulations and experiments.