Quasigeostrophic planetary waves in a two-layer ocean with one-dimensional periodic bottom topography

Abstract

Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [−π/L _b , π/L _b ], where L _b is the periodic length of the topography. When the topographic β is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude.

Keywords:

• Planetary waves
• Two-layer ocean
• Bottom topography
• Topographic mode
• Surface intensified mode

Acknowledgements

The author thanks anonymous reviewers for their helpful comments. The LAPACK library was used for solving the eigenvalue problems and the GFD-DENNOU library was used for drawing the figures. This work was partly supported by a Grant-in-Aid for Scientific Research from the Japan Society of the Promotion of Science.