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Journal article
COMPUTING TIME-PERIODIC SOLUTIONS OF A MODEL FOR THE VORTEX SHEET WITH SURFACE TENSION
Quarterly of applied mathematics, v 73(2), pp 317-329
01 Jan 2015
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We compute time-periodic solutions of a simple model for the vortex sheet with surface tension. The model has the same dispersion relation as the full system of evolution equations, and it also has the same destabilizing nonlinearity (if the surface tension parameter were to be set to zero, then this nonlinearity would cause an analogue of the Kelvin-Helmholtz instability). The numerical method uses a gradient descent algorithm to minimize a functional which measures whether a solution of the system is time periodic. We find continua of genuinely time-periodic solutions bifurcating from equilibrium.
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Details
- Title
- COMPUTING TIME-PERIODIC SOLUTIONS OF A MODEL FOR THE VORTEX SHEET WITH SURFACE TENSION
- Creators
- David M. Ambrose - Drexel UniversityMark Kondrla - Drexel UniversityMichael Valle - Drexel University
- Publication Details
- Quarterly of applied mathematics, v 73(2), pp 317-329
- Publisher
- Brown Univ
- Number of pages
- 13
- Grant note
- Drexel University Office of the Provost DMS-1008387; DMS-1016267 / National Science Foundation through NSF; National Science Foundation (NSF) Steinbright Career Development Office
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000370801800005
- Scopus ID
- 2-s2.0-84930852548
- Other Identifier
- 991019170399804721
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- Web of Science research areas
- Mathematics, Applied