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- Title
Complex singularity analysis for vortex layer flows.
- Authors
Caflisch, R.E.; Gargano, F.; Sammartino, M.; Sciacca, V.
- Abstract
For all Graph $Re>10^3$, Graph $\mu {\theta ^{\omega \mathcal {C}} 1}$ and Graph $\mu {\theta ^{\omega \mathcal {C}} 1}$ are approximately equal to Graph $1/2$, whereas, for Graph $Re=10^3$, they have higher values, close to Graph $0.9$, see table 1. At Graph $t\approx 5.9$, that is when the third winding forms in Graph $\mathcal {C}$, Graph $\theta ^{\omega \mathcal {C}} 1$ collapses to Graph $s(0)=0$ with the symmetric singularity Graph $2{\rm \pi} -\theta ^{\omega \mathcal {C}} 1$. In figure 15 we show the paths in the complex plane of Graph $\theta 1^{X \mathcal {C}}$ and Graph $\theta 2^{X \mathcal {C}}$ (Graph $\theta 1^{Y \mathcal {C}},\theta 2^{Y \mathcal {C}}$ have the same positions) for various Graph $Re$. However, after time Graph $t\geqslant 1.3$, the characters Graph $\mu {\theta ^{\omega \mathcal {C}} 1}$ and Graph $\mu {\theta ^{\omega \mathcal {C}} 2}$ of Graph $\theta ^{\omega \mathcal {C}} 1$ and Graph $\theta ^{\omega \mathcal {C}} 2$ have been reliably determined. In figure 14( I a i ), we represent the singularities in the complex plane Graph $(\theta,\theta {im})$, for different Graph $Re$, at Graph $t s=1.507$ and at Graph $t {1w}$ the time when the first winding forms in Graph $\mathcal {C}$.
- Subjects
EULER equations; RICHTMYER-Meshkov instability; SCIENTIFIC literature; RAYLEIGH-Taylor instability; VORTEX motion; MATHEMATICAL complex analysis
- Publication
Journal of Fluid Mechanics, 2022, Vol 932, p1
- ISSN
0022-1120
- Publication type
Article
- DOI
10.1017/jfm.2021.966