Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T07:12:02.748Z Has data issue: false hasContentIssue false
  • English
  • Français

Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom

Published online by Cambridge University Press:  17 February 2009

G. C. Hocking
G. C. Hocking
Affiliation:
Applied Mathematics Department, University of Adelaide, Adelaide, S.A. 5000.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Solutions are found to several problems involving a line source or sink beneath a cusped free surface, over several different impermeable bases. These are compared with known exact and numerical solutions, and with other work, both theoretical and experimental, on similar problems.

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 4 , April 1985 , pp. 470 - 486
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Abramowitz, M. and Stegun, I. A. (eds.), Handbook of mathematical functions (Dover, New York, 1970).Google Scholar
[2]Craya, A., “Theoretical research on the flow of nonhomogeneous fluids”, Houille Blanche 4 (1949), 44–55.CrossRefGoogle Scholar
[3]Gariél, P., “Experimental research on the flow of nonhomogeneous fluids,” Houille Blanche 4 (1949), 56–64.Google Scholar
[4]Domb, C. and Sykes, M. F., “On the susceptibility of a ferromagnetic above the Curie point”, Proc. Roy. Soc. London Ser. A 240 (1957), 214–228.Google Scholar
[5]Huber, D. G., “Irrotational motion of two fluid strata toward a line sink” J. Engng. Mech. Div. Proc. Amer. Soc. Civ. Engrs. 86, EM4 (1960), 71–85.Google Scholar
[6]Peregrine, D. H, “A line source beneath a free surface”, Mathematics Research Center, Univ. Wisconsin Rep. 1248 (1972).Google Scholar
[7]Sautreaux, C., “Mouvement d'un liquide parfait soumis à la pesanteur. Détermination des lignes de courant”, J. Math. Pures Appl. (5) 7 (1901), 125–159.Google Scholar
[8]Tuck, E. O. and Broeck, J. M. Vanden, “A cusp-like free-surface flow due to a submerged source or sink”, J. Austral. Math. Soc. Ser B 25 (1984), 443–450.CrossRefGoogle Scholar
[9]Tuck, E. O., “On air flow over free surfaces of stationary water”, J. Austral. Math. Soc. Ser. B 19 (1975), 66–80.CrossRefGoogle Scholar
[10]Broeck, J. M. Vanden, Schwartz, L. W. and Tuck, E. O., “Divergent low-Froude-number series expansion of non-linear free-surface flow problems”, Proc. Roy. Soc. London Ser A 361 (1978), 207–224.Google Scholar
[11]Van Dyke, M., “Analysis and improvement of perturbation series”, Quart J. Mech. Appl. Math. 27 (1974), 423–450.CrossRefGoogle Scholar
[12]Wehausen, J. V. and Laitone, E. V., “Surface waves”, in Handbuch der Physik 9 (ed. Flügge, S.), (Springer, Berlin, 1960).Google Scholar
[13]Yih, C. S., Dynamics of non-homogeneous fluids (Macmillan, New York, 19675).Google Scholar