The application of the nonlinear quasi-geostrophic equations to an isolated eddy in the western continental slope region in the Gulf of Mexico is examined for a two-layer ocean model with realistic bottom topography. For a model with realistic thickness ratio (the lower-layer is 10 times thicker than the upper layer) in the western continental slope region, a linear relation between the stream functions of the upper and lower layers is suitable. This mode slightly deviates from the pure barotropic mode and is coined quasi-barotropic mode. The nonlinear quasi-geostrophic potential vorticity equations in the two-layer ocean reduce to a nonlinear quasi-barotropic potential vorticity equation with a bottom interaction term and a stratification term. Form-preserving solutions, or solitons, have been found. In the linear limit, the solutions are topographic Rossby waves. The analytical procedure is an expansion in a small dimensionless parameter ?, or equivalent Rossby number. Permanent-form solutions exist under the weak-nonlinearity and long-wavelength approximations. The solution is shown to be a limiting form for nonlinear dispersive systems propagating northward without changing their shape along the topographic wave guide in the western continental slope region of the Gulf of Mexico. The theory yields a propagational speed which is linearly dependent upon the amplitude of the disturbance. The stable, form-preserving eddy is characterized as a Kirchhoff vortex, and the kinematical properties of the Kirchhoff vortex are used to determine the stream function of eddies detected by satellite-tracked drifters in the western Gulf of Mexico. A linear relationship is found between the amplitude of the deduced stream function of the eddy and its observed northward translational velocity over the continental slope, which supports the hypothesis that some meso-scale eddies interacting with the continental slope behave as solitons.
