Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T04:58:46.054Z Has data issue: false hasContentIssue false
  • English
  • Français

Topographic waves in open domains. Part 1. Boundary conditions and frequency estimates

Published online by Cambridge University Press:  26 April 2006

E. R. Johnson
E. R. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem is considered of topographic waves propagating on depth gradients in rotating domains. A variational principle is derived for the eigenfunctions and eigenfrequencies of normal modes on a domain, and applied to subdomains of the whole domain. Considering suitable boundary conditions on the open boundary between the subdomain and the remainder of the whole domain gives upper and lower bounds and estimates for the frequencies of normal modes localized in the subdomain without the complication of solving over the whole domain. It is shown that applying a zero-mass-flux condition at the open boundary leads to a lower bound on the frequency whereas requiring a particular form of the energy flux to vanish identically at each point of the boundary provides an upper bound.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 69 - 76
Copyright
© 1989 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

Courant, R. & Hilbert, D., 1953 Methods of Mathematical Physics, vol. 1, §6. Interscience.
Huthnance, J. M.: 1975 On trapped waves over a continental shelf. J. Fluid Mech. 69, 689–704.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, 279–295.Google Scholar
Mysak, L. A.: 1980 Recent advances in shelf wave dynamics. Rev. Geophys. Space Phys. 18, 211–241.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 an elliptical basin, with application to the Lake of Lugano. Phil. Trans. R. Soc. Lond. A 316, 1–55.Google Scholar
Rhines, P. B.: 1969a Slow oscillations in an ocean of varying depth. Part 1. Abrupt topography. J. Fluid Mech. 37, 161–189.Google Scholar
Rhines, P. B.: 1969b Slow oscillations in an ocean of varying depth. Part 2. Islands and seamounts. J. Fluid Mech. 37, 191–205.Google Scholar
Stocker, T. & Hutter, K., 1987a Topographic Waves in Channels and Lakes on the f-Plane. Lecture Notes on Coastal and Estuarine Studies, Vol. 21. Springer.
Stocker, T. & Hutter, K., 1987b Topographic waves in rectangular basins. J. Fluid Mech. 185, 107–120.Google Scholar
Stocker, T. & Johnson, E. R., 1989a Topographic waves in open domains. Part 2. Bay modes and resonances. J. Fluid Mech. 200, 77–93.Google Scholar
Stocker, T. & Johnson, E. R., 1989b Transmission and reflection of shelf waves in a shelf–estuary system. J. Fluid Mech. (submitted).Google Scholar
Trösch, J.: 1984 Finite element calculation of topographic waves in lakes. Proc. 4th Intl. Conf. Appl. Numerical Modeling. Tainan, Taiwan (ed. Han Min Hsia, You Li Chou, Shu Yi Wang & Sheng Jii Hsieh), pp. 307–311.