On the dynamics of coupled envelope structures for barotropic–baroclinic interaction with Bottom Topography

Nonlinear barotropic–baroclinic interaction is of great theoretical importance in gaining a deeper understanding of the physical mechanisms of atmospheric or oceanic motions. Based on the classical two-layer quasi-geostrophic potential vorticity (2LQGPV) conservation model, this paper derives the nonlinear Schrödinger equation describing the Rossby wave amplitude evolution under the $\beta$-plane approximation, combined with multiscale analysis and small-parameter expansion methods. The influence of different forms of bottom topography on the evolution mechanism of the nonlinear barotropic–baroclinic interaction and the blockage effect is highlighted. The results show that the barotropic stream function dominates the generation process of the baroclinic stream function, and at the same time the baroclinic stream function has a perturbing effect on the barotropic stream function. Topography is an essential factor for dipole excitation or decay, with up-convex topography more likely to cause dipole blockage, while sloped topography and down-concave topography have a weaker effect. This finding reveals the significant influence of topography in wave–wave interactions. These results further enrich the theory of nonlinear barotropic–baroclinic interactions and provide a new theoretical framework and explanation for understanding wave–wave and wave-stream interactions.