Solitary Rossby waves over variable relief and their stability. Part I: The analytical theory
Abstract
Nonlinear permanent form solutions have been found for the barotropic, quasi-geostrophic divergenceless vorticity equation describing large scale, rotating flows over zonal relief. In the linear limit these solutions are topographic Rossby waves. The analytical procedure is an expansion in two small dimensionless parameters, an amplitude parameter (the Rossby number) and the aspect ratio between North-South (cross-relief) and East-West length scales. Permanent form solutions exist when these two parameters, and the related effects of dispersion and nonlinearity, mutually balance. By the same expansion procedure, an analytical linearized stability theory has been formulated which proves the neutral stability of these solutions to infinitesimal, two-dimensional perturbations.
- Publication:
-
Dynamics of Atmospheres and Oceans
- Pub Date:
- April 1980
- DOI:
- 10.1016/0377-0265(80)90030-5
- Bibcode:
- 1980DyAtO...4..247M
- Keywords:
-
- Dynamic Stability;
- Rossby Regimes;
- Solitary Waves;
- Surface Roughness Effects;
- Vorticity;
- Barotropic Flow;
- Channel Flow;
- Nonlinear Equations;
- Perturbation Theory;
- Wave Equations