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Published on: February 3, 2014
Vortex core dynamics and singularity formations in incompressible Richtmyer-Meshkov instability
Chihiro Matsuoka1, Katsunobu Nishihara
1Department of Physics, Ehime University, 2-5, Bunkyocho, Matsuyama, Ehime 790-8577, Japan.
Summary
The Birkhoff-Rott equation models fluid interface motion in Richtmyer-Meshkov instability. Vortex core dynamics and singularity formation are investigated, revealing dependence on Atwood numbers.
Area of Science:
- Fluid Dynamics
- Instability Phenomena
- Computational Physics
Background:
- Fluid interface motion is crucial in various physical phenomena.
- Richtmyer-Meshkov instability is a key area of fluid dynamics research.
- Understanding vortex sheet dynamics is essential for modeling instabilities.
Purpose of the Study:
- To analyze the motion of fluid interfaces in Richtmyer-Meshkov instability using the Birkhoff-Rott equation.
- To investigate the formation and behavior of singularities and vortex cores.
- To determine the influence of Atwood numbers on these dynamics.
Main Methods:
- Utilizing the Birkhoff-Rott equation for inviscid, incompressible fluid instabilities.
- Coupling the Birkhoff-Rott equation with an evolution equation for vortex sheet strength.
- Analyzing the detailed motion of vortex cores within the Richtmyer-Meshkov instability framework.
Main Results:
- Singularity formation, similar to Kelvin-Helmholtz and Rayleigh-Taylor instabilities, is shown to occur in Richtmyer-Meshkov instability.
- Vorticity accumulation leads to sheet roll-up at singularity points.
- Vortex core trajectories and strengths are found to be dependent on Atwood numbers.
Conclusions:
- The Birkhoff-Rott equation effectively models various fluid instabilities, including Richtmyer-Meshkov.
- Singularity formation and vortex core dynamics are inherent features of Richtmyer-Meshkov instability.
- Atwood numbers play a significant role in governing the behavior of vortex cores.
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