Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Finite three-dimensional surface waves in circular channels


Author: Lester Q. Spielvogel
Journal: Quart. Appl. Math. 29 (1972), 493-507
DOI: https://doi.org/10.1090/qam/99750
MathSciNet review: QAM99750
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Abstract: This paper is concerned with finite surface waves in incompressible fluid in circular channels or bowls. Fluid circulates through these channels and is contained in them by the action of an axial gravitational force. Under certain velocity conditions permanent waves of finite magnitude may be solutions to the differential equations of motion. These waves are related to the cnoidal and solitary waves of the infinite straight channel. Using stretching techniques on the nonlinear differential equations, we derive expressions for the wave shape, the critical velocity condition, and relations to waves in straight channels. The irrotational case is thoroughly treated and a short discussion of the rotational case is included. The fact that these waves deform continuously into those already derived for straight channels is also discussed. The most important result, however, is that stretching techniques have been shown to describe finite waves progressing in curved trajectories. While it is true that the trajectories are dictated by the curvature of the containing vessels, it is apparent that this technique may very well be useful in describing finite wave shape and trajectories for waves near beaches and breakwaters.


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DOI: https://doi.org/10.1090/qam/99750
Article copyright: © Copyright 1972 American Mathematical Society


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