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发表于 2017-12-20 16:23:51
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首届涡与湍流研讨会成功举办
——各位老师与同学:我们非常荣幸地邀请到 刘超群教授 本周四上午莅临 复旦大学 进步解释 Rortex 的数学定义与物理意义
时间:12月21日(周四)上午 9点开始 计划至 11点半
地点:复旦大学邯郸路校区 光华楼西辅楼208教室(半圆形教室)
欢迎有兴趣的老师与同学 继续来研讨
联系人:谢锡麟 65643938/13601747708
议题: A Mathematical Definition of Vortex Vector and Vortex
摘要: Although Vortex is ubiquitous in nature, its definition is somewhat ambiguous in the field of fluid dynamics. In this absence of a rigorous mathematical definition, considerable confusions appear to exist in visualizing and understanding the coherent vortical structures in turbulence. Cited in our previous studies, vortex cannot be fully represented by vorticity, and vorticity should be further decomposed into a rotational and a non-rotational part, or in other words vortex vector and its shear, respectively. In this paper, we introduce several new concepts, including local fluid rotation at a point and direction of local fluid rotation axis. Furthermore, we’ll examine the direction and strength of local fluid rotation by investigating the kinematics of a fluid element in 2D and 3D flows, and define the vortex vector to describe the local fluid rotation. This can be understood as that the direction of vortex vector is equivalent to the direction of the local fluid rotation axis, and the magnitude of vortex vector is the strength of the location fluid rotation which is the rotational part of the vorticity in the direction of the vortex vector. With these new revelations, we want to present a new definition of vortex as the connected region where the vortex vector is not zero, and it follows three core principles: 1. Local in quantity, 2. Galilean invariant, 3. Unique. In addition, we want to demonstrate that new definition of vortex vector can fully describe the complex vertical structures of turbulence through DNS and LES examples.
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