Coherent structures of nonlinear barotropic-baroclinic interaction in unequal depth two-layer model

The nonlinear barotropic-baroclinic interaction theory is of great importance for the understanding of the atmosphere and the oceans. In this paper, a mathematical model based on analytical methods is established to discuss the propagation of the coherent structure of the nonlinear barotropic-baroclinic interaction of two-layer fluids in geophysics. It is the first time that the coupled Boussinesq equations are derived by using perturbation and spatiotemporal extensions transformations to simulate the evolutions of nonlinear barotropic and baroclinic waves. The solitary wave solutions are analytically obtained to explain the excitation, propagation and decrease of the coherent structures. The physical mechanism of the nonlinear wave-wave coherent structures is discussed by considering the effects of different physical factors, such as the topography, the Earth's rotation and the basic shear flow. It is found that both topography and beta parameter have essential effects on the evolutions of the coherent structures. Furthermore, the effect of the unequal-depth parameter on the propagation of coherent structures is discussed. (C) 2021 Elsevier Inc. All rights reserved.