A fluid mechanic's analysis of the teacup singularity

8Citations
Citations of this article
32Readers
Mendeley users who have this article in their library.

This article is free to access.

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.

Cite

CITATION STYLE

APA

Barkley, D. (2020). A fluid mechanic’s analysis of the teacup singularity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2240). https://doi.org/10.1098/rspa.2020.0348

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free