A 3D vortex formed by trajectories of the Navier–Stokes equation. (13th November 2015)

• Record Type: Journal Article
• Authors: Wang, Peng; Wang, Xu-Ming
• Is Part Of: Journal of statistical mechanics. (2015:Nov.)
• Publication Date: 2015-11-13
• Subjects: compressible flow -- turbulence; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/11/P11014
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: The 3D Navier–Stokes equation for incompressible fluid is resolved by using the Lie group analysis method. The solution shows a spiral vortex structure and some strange related aspects. There are two running modes of the vortex, up-spiral or down-spiral, and the modes are determined by the viscosity of fluid. The calculated z -directional curl of the velocity presents a zero-piercing, which indicates that the variation from the up-spiral structure to the down-spiral may correspond to the state change of the fluid from gas to liquid. In the corresponding parameter region, there is likely a so-called two-phase-coexistence of gas and liquid. Within the vortex, the dependence of the angle velocity of a mass particle on its radial position is dominated by a Gaussian-like curve in the plane of angle velocity versus radial position. This work provides a vivid description of the vortex that is in accordance with a real vortex structure.