1997/04/30 by Siegfried Grossmann, Siegfried Großmann, Detlef Lohse +1 · 59 citations
Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Computer science #Fluid Dynamics and Turbulent Flows #Function (biology) #Geometry #Lambda #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Order (exchange) #Parametrization (atmospheric modeling) #Physics #Plant Water Relations and Carbon Dynamics #Quantum mechanics #Scaling #Self-similarity #Similarity (geometry) #Statistical physics #Structure function #Third order #Turbulence #Wind and Air Flow Studies #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physreve.56.5473
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 56(5), 5473-5478 (American Physical Society) · 12 pages, 7 eps-figures, replaces version from April 11th, 1997; paper now in press at Phys. Rev. E
arxiv created 1997/08/05 · openalex publication_date 1997/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
From Navier-Stokes turbulence numerical simulations we show that for the extended self-similarity (ESS) method it is essential to take the third order structure function taken with the modulus and called D3*(r), rather than the standard third order structure function D3(r) itself. If this is done, we find ESS towards scales larger than order \ensuremath∼10\ensuremathη, where \ensuremathη is the Kolmogorov scale. If D3(r) is used, there is no ESS. We also analyze ESS within the Batchelor parametrization of the second and third order longitudinal structure function and focus on the scaling of the transversal structure function. The Re-asymptotic inertial range scaling develops only beyond a Taylor-Reynolds number Re_\ensuremathλ\ensuremath\gtrsim500.