2007/12/31 by Laurent Chevillard, L. Chevillard, C. Meneveau +4 · 1 citation
Engineering · Environmental Science · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Plant Water Relations and Carbon Dynamics #physics.flu-dyn
paper · pdf · doi:10.1063/1.3005832
published as Phys. Fluids 20, 101504 (2008) · 16 pages, 10 figures, minor revisions, final version published in Phys. Fluids
openalex publication_date 2008/10/01 · arxiv created 2008/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Modeling the velocity gradient tensor A=∇u along Lagrangian trajectories in turbulent flow requires closures for the pressure Hessian and viscous Laplacian of A. Based on an Eulerian–Lagrangian change in variables and the so-called recent fluid deformation closure, such models were proposed recently [Chevillard and Meneveau, Phys. Rev. Lett. 97, 174501 (2006)]. The resulting stochastic model was shown to reproduce many geometric and anomalous scaling properties of turbulence. In this work, direct comparisons between model predictions and direct numerical simulation (DNS) data are presented. First, statistical properties of A are described using conditional averages of strain skewness, enstrophy production, energy transfer, and vorticity alignments, conditioned upon invariants of the velocity gradient. These conditionally averaged quantities are found to be described accurately by the stochastic model. More detailed comparisons that focus directly on the terms being modeled in the closures are also presented. Specifically, conditional statistics associated with the pressure Hessian and the viscous Laplacian are measured from the model and are compared with DNS. Good agreement is found in strain-dominated regions. However, some features of the pressure Hessian linked to rotation-dominated regions are not reproduced accurately by the model. Geometric properties such as vorticity alignment with respect to principal axes of the pressure Hessian are mostly predicted well. In particular, the model predicts that an eigenvector of the rate of strain will be also an eigenvector of the pressure Hessian, in accord with basic properties of the Euler equations. The analysis identifies under what conditions the Eulerian–Lagrangian change in variables with the recent fluid deformation closure works well, and in which flow regimes it requires further improvements.