KAUST Grant NumberKUK-C1-013-04
Permanent link to this recordhttp://hdl.handle.net/10754/599546
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Abstract© 2015 American Physical Society. The mathematical model of a steadily propagating Saffman-Taylor finger in a Hele-Shaw channel has applications to two-dimensional interacting streamer discharges which are aligned in a periodic array. In the streamer context, the relevant regularization on the interface is not provided by surface tension but instead has been postulated to involve a mechanism equivalent to kinetic undercooling, which acts to penalize high velocities and prevent blow-up of the unregularized solution. Previous asymptotic results for the Hele-Shaw finger problem with kinetic undercooling suggest that for a given value of the kinetic undercooling parameter, there is a discrete set of possible finger shapes, each analytic at the nose and occupying a different fraction of the channel width. In the limit in which the kinetic undercooling parameter vanishes, the fraction for each family approaches 1/2, suggesting that this "selection" of 1/2 by kinetic undercooling is qualitatively similar to the well-known analog with surface tension. We treat the numerical problem of computing these Saffman-Taylor fingers with kinetic undercooling, which turns out to be more subtle than the analog with surface tension, since kinetic undercooling permits finger shapes which are corner-free but not analytic. We provide numerical evidence for the selection mechanism by setting up a problem with both kinetic undercooling and surface tension and numerically taking the limit that the surface tension vanishes.
CitationGardiner BPJ, McCue SW, Dallaston MC, Moroney TJ (2015) Saffman-Taylor fingers with kinetic undercooling. Phys Rev E 91. Available: http://dx.doi.org/10.1103/physreve.91.023016.
SponsorsSWM acknowledges the support of the Australian Research Council via the Discovery Project DP140100933. MD acknowledges support in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The authors acknowledge helpful discussions with John King and Jon Chapman.
PublisherAmerican Physical Society (APS)
JournalPhysical Review E
CollectionsPublications Acknowledging KAUST Support
- Kinetic undercooling in Hele-Shaw flows.
- Authors: Anjos PH, Dias EO, Miranda JA
- Issue date: 2015 Oct
- Comment on "Two-finger selection theory in the Saffman-Taylor problem".
- Authors: Vasconcelos GL
- Issue date: 2001 Apr
- Saffman-Taylor streamers: mutual finger interaction in spark formation.
- Authors: Luque A, Brau F, Ebert U
- Issue date: 2008 Jul
- The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell.
- Authors: Green CC, Lustri CJ, McCue SW
- Issue date: 2017 May
- Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study.
- Authors: Pauné E, Siegel M, Casademunt J
- Issue date: 2002 Oct