2016/09/30 by G. A. Gerolymos, I. Vallet
Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Anisotropy #Dissipation #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometry #Heat transfer and supercritical fluids #Mathematical physics #Mathematics #Mechanics #Open-channel flow #Physics #Plane (geometry) #Quantum mechanics #Reynolds number #Tensor (intrinsic definition) #Thermodynamics #Turbulence #Wind and Air Flow Studies #physics.flu-dyn
paper · pdf · doi:10.1088/1873-7005/aa7406
published as Fluid Dyn. Res. 49 (2017) 045507 · Initially this article was part of arXiv:1602.05022.v1, but to reduce length this content was removed from the final versions arXiv:1602.05022.v2 and arXiv:1602.05022.v3, with which there is no overlap
arxiv created 2017/03/01 · openalex publication_date 2017/05/18 · arxiv updated 2017/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract Recent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">DNS</mml:mi> </mml:math> results (Gerolymos and Vallet 2016 J. Fluid Mech. 807 386–418) have provided data for the terms in the transport equations for the components of the dissipation tensor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ε</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">ij</mml:mi> </mml:mrow> </mml:msub> </mml:math> in low-Reynolds turbulent plane channel flow. The present paper extends the previous results by a detailed analysis of the behaviour of various mechanisms in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ε</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">ij</mml:mi> </mml:mrow> </mml:msub> </mml:math> -transport equations (production, diffusion, redistribution, destruction), with particular emphasis on the component-by-component comparison with the corresponding mechanisms in the transport equations for the Reynolds-stresses r ij . The splitting of the pressure terms for the wall-normal components into redistribution and pressure-diffusion reveals substantially different behaviour near the wall. The wall-asymptotics of different terms in the transport equations are studied in detail, and examined using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">DNS</mml:mi> </mml:math> data. Both <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">DNS</mml:mi> </mml:math> data and wall-asympotic analysis show that the anisotropy of the destruction-of-dissipation tensor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ε</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>ε</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">ij</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> is fundamentally different from that of r ij or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ε</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">ij</mml:mi> </mml:mrow> </mml:msub> </mml:math> , never approaching the two-component state at the solid wall.