A class of exact solutions of the equation of conservation of the quasi-geostrophic vorticity in a continuously stratified ocean on the β-plane is studied. These are stationary solitary waves traveling east and having horizontal scale comparable with the Rossby deformation radius, which exist due to the balance between the nonlinearity and β-effect. The solutions look like a sum of a barotropic modon and a number of axially symmetric baroclinic components. The baroclinicity, represented in the form of vertical normal modes, introduces an extra “degree of freedom” into the problem (as compared with the barotropic model) and allows for the construction of solutions with continuous pressure, density, velocity, vorticity and acceleration. As an example, the procedures of building solutions with one and two baroclinic modes are described in detail, and the properties of the resulting solitary waves are discussed. It is shown that by inserting real ambient density distributions into such solutions, it is possible to model synoptic eddies in the ocean.
Kizner, Z.. 1997. "Solitary Rossby waves with baroclinic modes." Journal of Marine Research 55, (4). https://elischolar.library.yale.edu/journal_of_marine_research/2240