2014/11/30 by Léonie Canet, Bertrand Delamotte, Nicolás Wschebor · 1 citation
Earth and Planetary Sciences · Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Classical mechanics #Climate variability and models #Direct numerical simulation #Fixed point #Fluid Dynamics and Turbulent Flows #Functional renormalization group #Geometry #Homogeneous isotropic turbulence #Homogeneous space #Intermittency #Isotropy #K-epsilon turbulence model #K-omega turbulence model #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Meteorological Phenomena and Simulations #Physics #Quantum mechanics #Renormalization group #Statistical physics #Turbulence #cond-mat.stat-mech #hep-th #nlin.CD
paper · pdf · doi:10.1103/physreve.93.063101
published as Phys. Rev. E 93, 063101 (2016) · 30 pages, 5 figures, published version, some discussions added
openalex publication_date 2016/06/02 · arxiv created 2016/06/06 · arxiv updated 2016/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the regime of fully developed homogeneous and isotropic turbulence of the Navier-Stokes (NS) equation in the presence of a stochastic forcing, using the nonperturbative (functional) renormalization group (NPRG). Within a simple approximation based on symmetries, we obtain the fixed-point solution of the NPRG flow equations that corresponds to fully developed turbulence both in d=2 and 3 dimensions. Deviations to the dimensional scalings (Kolmogorov in d=3 or Kraichnan-Batchelor in d=2) are found for the two-point functions. To further analyze these deviations, we derive exact flow equations in the large wave-number limit, and show that the fixed point does not entail the usual scale invariance, thereby identifying the mechanism for the emergence of intermittency within the NPRG framework. The purpose of this work is to provide a detailed basis for NPRG studies of NS turbulence; the determination of the ensuing intermittency exponents is left for future work.