Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T21:03:11.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Short surface waves in a canal: dependence of frequency on curvature

Published online by Cambridge University Press:  29 March 2006

F. Ursell
F. Ursell
Affiliation:
Department of Mathematics, University of Manchester, England
Get access Rights & Permissions [Opens in a new window]

Abstract

Davis has shown by means of a lengthy calculation that, for two-dimensional oscillations in a canal of width 2a, the mth eigenvalue has the form \[ N_m = {\textstyle\frac{1}{2}}m\pi - \frac{\lambda_1+\lambda_2}{4m\pi}+o\bigg(\frac{1}{m}\bigg), \] where λ1/a and λ2/a are the curvatures of the bounding cross-sectional curve C at its vertical intersections with the free surface. Here the same result is obtained more simply.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 63 , Issue 1 , 18 March 1974 , pp. 177 - 181
Copyright
© 1974 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Davis, A. M. J. 1965 Two-dimensional oscillations in a canal of arbitrary cross-section. Proc. Camb. Phil. Soc. 61, 827–846.Google Scholar
Davis, A. M. J. 1969 Short surface waves in a canal: dependence of frequency on curvature. Proc. Roy. Soc. A 313, 249–260.Google Scholar
Lamb, H. 1932 Hydrdynamics, 6th edn. Cambridge University Press.
Ursell, F. 1961 The transmission of surface waves under surface obstacles. Proc. Camb. Phil. Soc. 57, 638–668.Google Scholar