2001/05/18 by Darryl D. Holm, DARRYL D. HOLM · 2 citations
Engineering · Physics and Astronomy · #Autocorrelation #Combustion and flame dynamics #Compressibility #Dissipation #Fluid Dynamics and Turbulent Flows #Isotropy #K-omega turbulence model #Kinetic energy #Particle Dynamics in Fluid Flows #Scaling #Turbulence #Turbulence kinetic energy #nlin.CD
paper · pdf · doi:10.1017/s002211200200160x
11 pages, no figures. Includes an important remark by G. L. Eyink in the conclusions
arxiv created 2001/05/18 · openalex publication_date 2002/09/24 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Lagrangian averaged Navier–Stokes–alpha (LANS-α) model of turbulence is found to possess a Kármán–Howarth (KH) theorem for the dynamics of its second-order autocorrelation functions in homogeneous isotropic turbulence. This KH result implies that alpha-filtering in the LANS-α model of turbulence does not affect the exact Navier–Stokes relation between second and third moments at separation distances large compared to the model's length scale α. Moreover, at separations r that are smaller than α, the KH scaling between energy dissipation rate and longitudinal third-order autocorrelation changes to match the scaling found in two-dimensional incompressible flow. This is consistent with the corresponding change in scaling of the kinetic energy spectrum from k −5/3 for larger scales with k α < 1, which switches to k −3 for smaller scales with k α > 1, as discovered in Foias, Holm & Titi (2001).