摘要
The issue whether transition from laminar flow to turbulent flow on a flat plate should be characterized as a vorticity redistribution process or a vorticity increasing process is investigated by a high-order direct numerical simulation on a flat plate boundary layer.The local vorticity can either increase or decrease due to tilting and stretching of vortex filaments according to the vorticity transport equation while the total vorticity cannot be changed in a boundary layer flow in conforming to the Fppl theorem of total vorticity conservation.This seemingly contradictory problem can be well resolved by the introduction of a new term:volume vorticity of a vorticity tube,defined as vorticity flux timed by the vorticity tube length.It has been shown that,although vorticity flux must keep conserved,the total volume vorticity is significantly increased during boundary layer transition according to our direct numerical simulation(DNS)computation,which directly results from the lengthening(stretching and tilting)of vortex filaments.Therefore,the flow transition is a process with appreciable increase of volume vorticity,and cannot be only viewed as a vorticity redistribution process.
The issue whether transition from laminar flow to turbulent flow on a flat plate should be characterized as a vorticity redistribution process or a vorticity increasing process is investigated by a high-order direct numerical simulation on a flat plate boundary layer. The local vorticity can either increase or decrease due to tilting and stretching of vortex filaments according to the vortieity transport equation while the total vorticity cannot be changed in a boundary layer flow in conforming to the F6ppl theorem of total vorticity conservation. This seeming- ly contradictory problem can be well resolved by the introduction of a new term： volume vorticity of a vorticity tube, defined as vorticity flux timed by the vorticity tube length. It has been shown that, although vorticity flux must keep conserved, the total volume vorticity is significantly increased during boundary layer transition according to our direct numerical simulation （DNS） computation, which directly results from the lengthening （stretching and tilting） of vortex filaments. Therefore, the flow transition is a process with appreciable increase of volume vorticity, and cannot be only viewed as a vorticity redistribution process.
基金
supported by Department of Mathematics at University of Texas at Arlington
the Chinese Scholarship Council(CSC)for financial support
