The merging dynamics of two-dimensional symmetric vortex pair
Date Issued
2007
Date
2007
Author(s)
WU, BO-HAN
DOI
zh-TW
Abstract
In use of Leonard’s vortex blob method, resurrected by Huang’s blob splitting and merging schemes, this thesis simulates the merging process of a 2D symmetry vortex pair and investigates the merging mechanism and dynamics associated with viscous and inviscid flows.
When the flow is inviscid, we focus on the formation of a sheet-like structure which circulation is advected from one vortex to the other and verify it is responsible for the merger. Then from two aspects, we attempt to explain why such a sheet-like structure is generated. The streamline patterns illuminate the importance of the exchange band, and the Yasuda model explains the deformation of one vortex due to the straining of the other. Moreover, we build a symmetric elliptic vortex model to explore the relationship between the vortex deformation and the exchange band. In inviscid flow the pressure force is the only force. Its variation in time is also studied. Finally we investigate the influence of the initial distance between two vortices. In viscous flows, we verify the cause of merger again, namely the formation of the sheet-like structure. The temporal variations in the streamline patterns and in the pressure field are observed. The effect of diffusion or Reynolds number on the merging process is investigated as well.
To summarize, the investigation shows that when the vortices are close enough, vortices are deformed due to the mutual straining, partial vorticity enters into the exchange band and is advected toward the other vortex, and the sheet-like structure is thus formed, which causes merger. The larger the distance between vortices, the smaller the deformation is, and the farther the vortex is away from the exchange band. Therefore, when the distance is larger than some critical value, vortices will not merge. When the flow is viscous, nonetheless, vorticity will diffuse into the exchange band sooner or later and vortices will eventually merge. Moreover, the viscous effect will also relax the asymmetric deformation of vortices.
Subjects
對稱漩渦對
融合
類渦片結構
交換帶
橢圓漩渦
symmetric vortex pair
merger
sheet-like structure
exchange band
elliptic vortex
Type
thesis
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