Turbulence is an ubiquitous phenomenon in natural and industrial flows. Yet, calculating its statistical properties, and in particular what is generically called intermittency effects, that is violations of standard scale invariance, remains an unsolved issue. In this talk, I will focus on isotropic and homogeneous turbulence in three-dimensional incompressible flows. I will explain how one can derive an exact asymptotic (i.e. at large wave-numbers) expression for the full space-time dependent two-point correlation function of the turbulent flow, using a field-theoretic approach, based on Non-Perturbative (or Functional) Renormalisation Group. I will discuss its properties and show that it encompasses some intermittency effects.
These predictions are compared to results from direct numerical simulation of Navier-Stokes equations, showing a remarkable agreement. I will present some generalization to higher order correlation functions.
- Fully developed isotropic turbulence: Symmetries and exact identities
L. Canet, B. Delamotte, N. Wschebor, Phys. Rev. E 91 (2015) 053004 - Fully developed isotropic turbulence: Nonperturbative renormalization group formalism and fixed-point solution
L. Canet, B. Delamotte, N. Wschebor, Phys. Rev. E 93 (2016) 063101 - Spatiotemporal velocity-velocity correlation function in fully developed turbulence
L. Canet, V. Rossetto, N. Wschebor, G. Balarac, arXiv:1607.03098 (2016) - Phys. Rev. E 95 (2017) 023107.
