Abstract

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 wih 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.

Original languageEnglish
Pages (from-to)245-267
Number of pages23
JournalStudies in Applied Mathematics
Volume100
Issue number3
DOIs
Publication statusPublished - 1 Jan 1998

Fingerprint

Free Surface
Fluid Flow
Flow of fluids
Singularity
Stokes
Perturbation
Angle
Cusp
Horizontal
Potential flow
Free Surface Flow
Isolated Singularity
Potential Flow
Local Solution
Stokes Flow
Steady Flow
Gravitation
Three-dimension
Gravity
Two Dimensions

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Singularities on free surfaces of fluid flows. / Milewski, P.; Vanden-Broeck, J. M.; Keller, Joseph B.

In: Studies in Applied Mathematics, Vol. 100, No. 3, 01.01.1998, p. 245-267.

Research output: Contribution to journalArticle

Milewski, P. ; Vanden-Broeck, J. M. ; Keller, Joseph B. / Singularities on free surfaces of fluid flows. In: Studies in Applied Mathematics. 1998 ; Vol. 100, No. 3. pp. 245-267.
@article{94ee9b8e15294bbdb6ea05b015560656,
title = "Singularities on free surfaces of fluid flows",
abstract = "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 wih 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.",
author = "P. Milewski and Vanden-Broeck, {J. M.} and Keller, {Joseph B.}",
year = "1998",
month = "1",
day = "1",
doi = "10.1111/1467-9590.00077",
language = "English",
volume = "100",
pages = "245--267",
journal = "Studies in Applied Mathematics",
issn = "0022-2526",
publisher = "Wiley-Blackwell",
number = "3",

}

TY - JOUR

T1 - Singularities on free surfaces of fluid flows

AU - Milewski, P.

AU - Vanden-Broeck, J. M.

AU - Keller, Joseph B.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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 wih 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.

AB - 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 wih 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.

UR - http://www.scopus.com/inward/record.url?scp=0038936252&partnerID=8YFLogxK

U2 - 10.1111/1467-9590.00077

DO - 10.1111/1467-9590.00077

M3 - Article

VL - 100

SP - 245

EP - 267

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 3

ER -