Skip to main content Accessibility help

Topographic waves in open domains. Part 2. Bay modes and resonances

  • Thomas F. Stocker (a1) and E. R. Johnson (a2)


The topographic wave equation is solved in a domain consisting of a channel with a terminating bay zone. For exponential depth profiles the problem reduces to an algebraic eigenvalue problem. In a flat channel adjacent to a shelf–like bay zone the solutions form a countably infinite set of orthogonal bay modes: the spectrum of eigenfrequencies is purely discrete. A channel with transverse topography allows wave propagation towards and away from the bay: the spectrum has a continuous part below the cutoff frequency of free channel waves. Above this cutoff frequency a finite number (possibly zero) of bay-trapped solutions occur. Bounds for this number are given. At particular frequencies below the cutoff the system is in resonance with the incident wave. These resonances are shown to be associated with bay modes.



Hide All
Ball, F. K.: 1965 Second class motions of a shallow liquid. J. Fluid Mech. 23, 545561.
Johnson, E. R.: 1987a Topographic waves in elliptical basins. Geophys. Astrophys. Fluid Dyn. 37, 279295.
Johnson, E. R.: 1987b A conformal mapping technique for topographic wave problems: semiinfinite channels and elongated basins. J. Fluid Mech. 177, 395405.
Johnson, E. R.: 1989 Topographic waves in open domains. Part 1: Boundary conditions and frequency estimates. J. Fluid Mech. 200, 6976.
Lamb, H.: 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Mysak, L. A.: 1985 Elliptical topographic waves. Geophys. Astrophys. Fluid Dyn. 31, 93135.
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, 155.
Rhines, P. B.: 1969a Slow oscillations in an ocean of varying depth. Part 1. Abrupt topography. J. Fluid Mech. 37, 161189.
Rhines, P. B.: 1969b Slow oscillations in an ocean of varying depth. Part 2. Islands and seamounts. J. Fluid Mech. 37, 191205.
Rhines, P. B. & Bretherton, F., 1973 Topographic Rossby waves in a rough–bottomed ocean. J. Fluid Mech. 61, 583607.
Stocker, T.: 1988 A numerical study of topographic wave reflection in semi-infinite channels. J. Phys. Oceanogr. 18, 609618.
Stocker, T. & Hutter, K., 1986 One-dimensional models for topographic Rossby waves in elongated basins on the f-plane. J. Fluid Mech. 170, 435459.
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, 107120.
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. 307311.
MathJax is a JavaScript display engine for mathematics. For more information see

Related content

Powered by UNSILO

Topographic waves in open domains. Part 2. Bay modes and resonances

  • Thomas F. Stocker (a1) and E. R. Johnson (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.