Singularity formation in a model for the vortex sheet with surface tension

David M. Ambrose

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 1, 102-111

Abstract: In a recent analytical study, the author has proved well-posedness of the vortex sheet with surface tension. This work included using a formulation of the problem introduced by Hou, Lowengrub, and Shelley for a numerical study of the same problem. The analytical study required identification of a term in the evolution equations which can be viewed as being responsible for the Kelvin–Helmholtz instability; this term is of lower order than the surface tension term. In the present work, the author introduces a simple model for the vortex sheet with surface tension which maintains the same dispersion relation and the same destabilizing force as in the vortex sheet with surface tension. For the model problem, it is found that finite-time singularities can form when the initial data is taken from a certain class. For the vortex sheet with surface tension, the only observed singularities thus far in numerical work have coincided with self-intersection of the fluid interface. There is no analogue of self-intersection in the model problem, and thus the singularities observed in the present work may well be related to a previously unobserved singularity for the full vortex sheet problem.

Keywords: Vortex sheet; Surface tension; Singularities (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475409001839
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:1:p:102-111

DOI: 10.1016/j.matcom.2009.06.014

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().