Correlation analysis on volume vorticity and vortex in late boundary layer transition

In this paper, two functions are introduced to describe the turbulence generation in late flow transition. One is called the volume omega bar (volume Ω¯), which represents the flow rotation or vortex strength. The other is called the volume vorticity, which shows the flow statistical fluctuations. Although they have very different definitions, one is for fluctuation and the other is for rotation, volume Ω¯ and volume vorticity are found highly correlated with a correlation factor greater than 0.9, which means that there is a very close correlation between flow fluctuation and flow rotation (vortex). While the vorticity flux keeps constant in the late flow transition through the integration over any sections either parallel or perpendicular to the flow direction, the volume Ω¯ is greatly increased along the flow direction during the flow transition process. This means that the vortex structures are greatly built up and rotation becomes more and more dominant. On the other hand, the total volume vorticity is also quickly increased, which shows that the fluctuation is stronger. The flow transition is a process with significant volume vorticity increase, which is attributed to two of the following crucial factors: the first one is the lengthening of the vorticity tubes from side boundary due to the vorticity line stretching, distortion, and tangling; the second one is the generation of countless self-closed vorticity rings within the domain. Both the increase of the volume vorticity and the volume Ω¯ can be a significant symbol of the flow transition from the laminar flow to turbulent flow. It also shows that vorticity (tubes or lines) cannot directly represent vortex and should not be simply used as a signal of the turbulent transition process.