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Published on: February 17, 2019
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A fluid mechanic's analysis of the teacup singularity.
1Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|September 14, 2020
Summary
This study investigates singularity formation in fluid flow, revealing that wall confinement pressure is key to velocity gradient blowup. Numerical simulations of the Euler equations support finite-time singularity evidence.
Area of Science:
- Fluid dynamics
- Computational physics
- Mathematical modeling
Background:
- Investigating singularity formation in inviscid wall-bounded fluid flow is crucial for understanding fluid behavior.
- Prior studies suggest evidence for finite-time singularities in such flows.
Purpose of the Study:
- To investigate the mechanism of singularity formation in inviscid wall-bounded fluid flow.
- To analyze the interplay between inertia and pressure in driving singularity formation.
Main Methods:
- Numerical simulation of incompressible Euler equations in a cylindrical container.
- Axisymmetric flow with swirl was simulated.
- Pressure field decomposition using the linearity of the pressure Poisson equation.
Main Results:
- Simulations corroborated evidence for finite-time singularity.
- The pressure field confining fluid within cylinder walls was identified as the primary driver of velocity gradient blowup.
- A model based on primitive-variables formulation of Euler equations on the cylinder wall was developed.
Conclusions:
- The study highlights the critical role of wall confinement pressure in singularity formation.
- The developed model captures essential mechanics of the blowup scenario.
- Findings advance understanding of fluid flow singularities.
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