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A fluid mechanic's analysis of the teacup singularity
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Barkley, Dwight (2020) A fluid mechanic's analysis of the teacup singularity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476 (2240). doi:10.1098/rspa.2020.0348 (In Press)
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Official URL: https://doi.org/10.1098/rspa.2020.0348
Abstract
The mechanism for singularity formation in an inviscid wall-bounded fluid flow is investigated. The incompressible Euler equations are numerically simulated in a cylindrical container. The flow is axisymmetric with the swirl. The simulations reproduce and corroborate aspects of prior studies reporting strong evidence for a finite-time singularity. The analysis here focuses on the interplay between inertia and pressure, rather than on vorticity. The linearity of the pressure Poisson equation is exploited to decompose the pressure field into independent contributions arising from the meridional flow and from the swirl, and enforcing incompressibility and enforcing flow confinement. The key pressure field driving the blowup of velocity gradients is that confining the fluid within the cylinder walls. A model is presented based on a primitive-variables formulation of the Euler equations on the cylinder wall, with closure coming from how pressure is determined from velocity. The model captures key features in the mechanics of the blowup scenario.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Lagrange equations -- Numerical solutions, Fluid dynamics -- Mathematical models | ||||||
| Journal or Publication Title: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||||
| Publisher: | The Royal Society Publishing | ||||||
| ISSN: | 1364-5021 | ||||||
| Official Date: | 26 August 2020 | ||||||
| Dates: |
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| Date of first compliant deposit: | 23 July 2020 | ||||||
| Volume: | 476 | ||||||
| Number: | 2240 | ||||||
| DOI: | 10.1098/rspa.2020.0348 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | In Press | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | © 2020 The Authors. | ||||||
| RIOXX Funder/Project Grant: |
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