Intrinsic Geometric Structure of Turbulent Flow for Newton Fluid

Abstract

Many researches show that the complicated motion of fluid, such as turbulence, cannot be well solved by the Navier-Stokes equation. Chen Zida has founded that the definition of vortex, based on the Stokes decomposition, cannot well describe the local rotation when the velocity gradient is highly asymmetric. Chen reformulates the Stokes S+R decomposition into a general S+R decomposition. By further extending Chen results, this research studies the motion equation of fluid for the case where highly asymmetric velocity gradient is exhibited. The result shows that the classical NS equation does not meet the requirement of angular momentum conservation, which is apparently ignored for infinitesimal velocity gradient of fluid. This paper reformulates the intrinsic geometric description of fluid motion and two additional equations are introduced. Combining with the classical NS equation, the reformulated motion equations are in closed-form. The research shows that the NS equation is good approximation for average flow, so it can not solve the turbulent problem in essential sense. However, this conclusion does not deny that with suitable additional condition for special engineering problem it is still a would-be acceptable approximation.