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oai:recercat.cat:2445/187442025-11-21T05:48:19Zcom_2072_1057col_2072_478823col_2072_478917

Two-finger selection theory in the Saffman-Taylor problem Magdaleno Escar, Francesc Xavier Casademunt i Viader, Jaume Dinàmica de fluids Fluid dynamics We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two unequal fingers advancing with the same velocity but with different relative widths ${\ensuremath{\lambda}}_{1}$ and ${\ensuremath{\lambda}}_{2}$ and different tip positions. For vanishingly small dimensionless surface tension ${d}_{0},$ an infinite discrete set of values of the total filling fraction $\ensuremath{\lambda}={\ensuremath{\lambda}}_{1}+{\ensuremath{\lambda}}_{2}$ and of the relative individual finger width $p={\ensuremath{\lambda}}_{1}/\ensuremath{\lambda}$ are selected out of a two-parameter continuous degeneracy. They scale as $\ensuremath{\lambda}\ensuremath{-}1/2\ensuremath{\sim}{d}_{0}^{2/3}$ and $|p\ensuremath{-}1/2|\ensuremath{\sim}{d}_{0}^{1/3}.$ The selected values of $\ensuremath{\lambda}$ differ from those of the single finger case. Explicit approximate expressions for both spectra are given. 2011-07-07T12:51:47Z 2011-07-07T12:51:47Z 1999 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 1063-651X https://hdl.handle.net/2445/18744 147705 eng Reproducció del document publicat a: http://dx.doi.org/10.1103/PhysRevE.60.R5013 Physical Review E, 1999, vol. 60, p. R5013-R5016 http://dx.doi.org/10.1103/PhysRevE.60.R5013 (c) The American Physical Society, 1999 info:eu-repo/semantics/openAccess 4 p. application/pdf application/pdf The American Physical Society Articles publicats en revistes (Física Quàntica i Astrofísica)