A Gardner evolution equation for topographic Rossby waves and its mechanical analysis

Topography plays an important role in the excitation and propagation of nonlinear Rossby solitary waves to atmospheres and oceans. In the present study, we investigate the effect of topography from the approach to topographic Rossby waves, not to the geostrophic viewpoint. It is the first time that a new evolution equation, called Gardner equation, is derived to simulate the propagation of nonlinear Rossby waves amplitude by using the methods of multiple scales and weak nonlinearity. In order to investigate the physical mechanisms of topographic Rossby wave, the shooting method is adopted to solve the Sturm-Liouville model equation with fixed boundary conditions and the Fourier spectral method is used to solve the nonlinear Gardner equation. Numerical results reveal that the magnitude of the meridional topography is more important compared to its meridional frequency on the evolution of nonlinear Rossby solitary waves, also, the variation of planetary vorticity is essential for the propagation of Rossby solitary waves. (C) 2020 Elsevier Inc. All rights reserved.