Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-21T04:50:10.811Z Has data issue: false hasContentIssue false
  • English
  • Français

A conformal-mapping technique for topographic-wave problems: semi-infinite channels and elongated basins

Published online by Cambridge University Press:  21 April 2006

E. R. Johnson
E. R. Johnson
Affiliation:
JISAO, University of Washington, Seattle, WA 98195, USA Permanent address: Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

The basis of the conformal-mapping method for topographic-wave problems of Johnson (1985) is discussed in greater detail by considering the invariance under conformal mapping of the linear, barotropic, potential-vorticity equation, noted in Davis (1983). A method is presented for using this property to construct further solutions for waves propagating over varying topography. Results are given for semi-infinite channels and elongated basins. A coordinate system is constructed that approaches a Cartesian system exponentially fast with distance from end-walls. For exponentially sloping topography the solutions for infinite channels, semi-infinite channels, and basins have the same structure and dispersion relation as waves in an elliptical basin, discussed in Johnson (1987). The structures presented there can thus be considered as in some sense universal for exponentially sloping topography.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 177 , April 1987 , pp. 395 - 405
Copyright
© 1987 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. 1983 Shelf similar topographies for free continental shelf waves. Geophys. Astrophys. Fluid Dyn. 23, 321–331.Google Scholar
Johnson, E. R. 1985 Topographic waves and the evolution of coastal currents. J. Fluid Mech. 160, 499–509.Google Scholar
Johnson, E. R. 1987 Topographic waves in elliptical basins. Geophys. Astrophys. Fluid Dyn. 37, 279–296.Google Scholar
Mysak, L. A. 1985 Elliptical topographic waves. Geophys. Astrophys. Fluid Dyn. 31, 93–135.Google Scholar
Mysak, L. A., Salvade, G., Hutter, K. & Scheiwiller, T. 1985 Topographic waves in a stratified elliptical basin, with application to the Lake of Lugano. Phil. Trans. R. Soc. Lond. A316, 1–55.Google Scholar
Rhines, P. B. 1969 Slow oscillations in an ocean of varying depth. Part 2. Islands and seamounts. J. Fluid Mech. 37, 191–105.Google Scholar
Rhines, P. B. & Bretherton, F. 1973 Topographic Rossby waves in a rough-bottomed ocean. J. Fluid Mech. 61, 583–607.Google Scholar