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Singularities on Free Surfaces of Fluid Flows
Author(s) -
Milewski P.,
Vandenbroeck J.M.,
Keller Joseph B.
Publication year - 1998
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00077
Subject(s) - conical surface , axial symmetry , free surface , gravitational singularity , stokes flow , flow (mathematics) , surface (topology) , mathematics , plane (geometry) , geometry , mathematical analysis , physics , classical mechanics , mechanics
Isolated singularities on free surfaces of two‐dimensional and axially symmetric three‐dimensional steady potential flows with gravity are considered. A systematic study is presented, where known solutions are recovered and new ones found. In two dimensions, the singularities found include those described by the Stokes solution with a 120° angle, Craya's flow with a cusp on the free surface, Gurevich's flow with a free surface meeting a rigid plane at 120° angle, and Dagan and Tulin's flow with a horizontal free surface meeting a rigid wall at an angle less than 120°. In three dimensions, the singularities found include those in Garabedian's axially symmetric flow about a conical surface with an approximately 130° angle, flows with axially symmetric cusps, and flows with a horizontal free surface and conical stream surfaces. The Stokes, Gurevich, and Garabedian flows are exact solutions. These are used to generate local solutions, including perturbations of the Stokes solution by Grant and Longuet‐Higgins and Fox, perturbations of Gurevich's flow by Vanden‐Broeck and Tuck, asymmetric perturbations of Stokes flow and nonaxisymmetric perturbations of Garabedian's flow. A generalization of the Stokes solution to three fluids meeting at a point is also found.