Periodic Waves in a Running Stream
Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 3-12

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we discuss questions of the existence and calculation of periodic, steady flows over periodic streambeds. There are some surprises.Problems such as this, of flows in running streams, are free-surface problems, and part of the difficulty is that the domain occupied by the fluid is not completely known a priori.
Shinbrot, Marvin. Periodic Waves in a Running Stream. Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 3-12. doi: 10.4153/CMB-1981-001-8
@article{10_4153_CMB_1981_001_8,
     author = {Shinbrot, Marvin},
     title = {Periodic {Waves} in a {Running} {Stream}},
     journal = {Canadian mathematical bulletin},
     pages = {3--12},
     year = {1981},
     volume = {24},
     number = {1},
     doi = {10.4153/CMB-1981-001-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-001-8/}
}
TY  - JOUR
AU  - Shinbrot, Marvin
TI  - Periodic Waves in a Running Stream
JO  - Canadian mathematical bulletin
PY  - 1981
SP  - 3
EP  - 12
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-001-8/
DO  - 10.4153/CMB-1981-001-8
ID  - 10_4153_CMB_1981_001_8
ER  - 
%0 Journal Article
%A Shinbrot, Marvin
%T Periodic Waves in a Running Stream
%J Canadian mathematical bulletin
%D 1981
%P 3-12
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-001-8/
%R 10.4153/CMB-1981-001-8
%F 10_4153_CMB_1981_001_8

[1] 1. Gerber, Robert, Sur les solutions exactes des équations du mouvement avec surface libre d'un liquide pesant. J. de Math. 34 (1962) 185-299. Google Scholar

[2] 2. Beckert, Herbert, Existenzbeweise in der Théorie permanenter Schwerewellen. Arch. Rat. Mech. Anal. 9 (1962) 379-394. Google Scholar

[3] 3. Hewgill, Denton E., Reeder, John, and Shinbrot, Marvin, Some exact solutions of the nonlinear problem of water waves. To appear in Pacific J. Math. Google Scholar

[4] 4. Hilbig, H., Existenzbeweis für Potentialströmungen längs eines Kanals mit welliger Kanalsohle unter Einfluss der Schwerkraft und der Oberflâchenspannung. Arch. Rat Mech. Anal. 51 (1962) 295-303. Google Scholar

[5] 5. Joseph, Daniel D., Domain perturbations: the higher order theory of infinitesimal water waves. Arch. Rat. Mech. Anal. 51 (1962) 295-303. Google Scholar

[6] 6. Krasnosel'skii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations. Macmillan, New York, 1964. Google Scholar

[7] 7. Krasovskii, Yu. P., The theory of steady state waves of large amplitude. Translated in: Soviet Physics Dokl. 5 (1962) 62-65. Google Scholar

[8] 8. Lamb, Sir Horace, Hydrodynamics, 6th ed. Cambridge, at the University Press, 1932. Google Scholar

[9] 9. Maxwell, James Clerk, Capillary action. Encyclopedia Britannica, 11th ed. Cambridge, 1911. Google Scholar

[10] 10. Moiseev, N. N., On the flow of a heavy fluid over a wavy bottom. Prikl. Mat. Mekh. (Russian). 21 (1962) 15-20. Google Scholar

[11] 11. Reeder, John and Shinbrot, Marvin, Three-dimensional, nonlinear wave interaction in water of constant depth. To appear. Google Scholar

[12] 12. Reeder, John and Shinbrot, Marvin, The initial value problem for surface waves under gravity, II and III. Indiana Univ. Math. J. 25 (1962) 1049-1071, and J. Math. Anal, and Appl. 67 (1962) 340-391. Google Scholar

[13] 13. Sattinger, D., On the free surface of a viscous fluid motion. Proc. Roy. Soc. London A 349 (1962) 183-204. Google Scholar

[14] 14. Shinbrot, Marvin, Lectures on Fluid Mechanics. Gordon and breach, New York, London, Paris, 1973. Google Scholar

[15] 15. Shinbrot, Marvin, Water waves over periodic bottoms in three dimensions. To appear in J. of the Inst, of Maths, and Applications. Google Scholar

[16] 16. Shinbrot, Troy, On salient phenomena of stationary waves in water. Undergraduate thesis, Reed College, Oregon, 1978. Google Scholar

[17] 17. Stoker, J. J., Water Waves. Interscience Publishers, New York, 1957. Google Scholar

[18] 18. Wehausen, John V. and Laitone, Edmond V., Surface waves. In: Handbuch der Physik, Fliigge, S., ed., v. IX, pp. 446-778. Springer-Verlag, Berlin, Göttingen, Heidelberg, 1960. Google Scholar

[19] 19. Zeidler, Eberhard, Beiträge zur Théorie und Praxis Freier Randwertaufgaben. Akademie- Verlag, Berlin, 1971. Google Scholar

[20] 20. Zeidler, Eberhard, Topologischer Existenzbeweis für Kapillar-Schwerewellen. Math. Nachr. 49 (1962) 85-99. Google Scholar

Cité par Sources :