Free streamline flows with singularities

J. Eggers*, A. F. Smith

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)

Abstract

We rederive and expand upon a method for finding solutions to the two-dimensional irrotational (inviscid) flow equations in the presence of a free surface, found by Hopkinson. This method allows the flow to be driven by placing singularities, like sources or vortices, in the interior of the flow domain. We then apply the method to find a number of novel solutions: separated flow driven by a source, vortices behind a plate and free-surface flow stirred by a double vortex. Free surfaces generically exhibit cusp singularities with a 2/3 power index, similar to those found in very viscous flow.

Original languageEnglish
Pages (from-to)187-200
Number of pages14
JournalJournal of Fluid Mechanics
Volume647
DOIs
Publication statusPublished - 25 Mar 2010

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