2009/03/16 by Xiao Jianhua, Jianhua, Xiao
Engineering · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #General Physics (physics.gen-ph) #physics.flu-dyn #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.0903.2689
37 pages, no figures
arxiv created 2009/03/16 · openalex publication_date 2009/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The turbulence field is stacked on the laminar flow. In this research, the laminar flow is described as a macro deformation which forms an instant curvature space. On such a curvature space, the turbulence is viewed as a micro deformation. So, the fluid flow is described by the geometrical field theory of finite deformation. Based on the Lagrange mechanics and the deformation energy concept, using the Least Action Principle, the Euler-Lagrange motion equations are obtained. According to A E Green formulation, the stress concept is introduced by deformation tensor. The fluid motion is described by the multiplication of a macro deformation tensor and a micro deformation tensor. By this way, the geometrical field of fluid motion is well constructed. Then, the spatial derivative of deformation energy is expressed by the gradient of deformation tensors. By this way, the deformation energy related items in the Euler-Lagrange motion equations are expressed by the stress tensor and deformation tensor. The obtained Euler-Lagrange motion equations, then, are decomposed into average deformation equations and turbulence equations. For several special cases, the new results are compared with the conventional Navier-Stokes equation with Reynolds stress modification.The comparisons also show that the Bernoulli Equation is a natural precondition for the conventional Navier-Stokes equation.Generally, the turbulence wave is an inward-traveling wave. Unlike the normal outward-traveling wave related with the average deformation, the inward-traveling wave is the intrinsic feature of turbulence. So, the turbulence is well defined by the equations obtained in this research. For several typical cases, the simplified turbulence wave equations are given out with simple discussion.