On the Dynamics and Stability of Envelope Rossby Solitary Waves Under the Topographic Geostrophic Approximation

Scholars are widely concerned about the research of nonlinear Rossby waves due to their essential importance in understanding the geophysical fluid dynamics. The effects of different topographies on the propagation of barotropic Rossby waves are discussed in this paper. Starting from the classical shallow water equation of uniformly rotating fluid with bottom topography, a new Schrödinger model equation of nonlinear Rossby wave amplitude is obtained by multi-scale spatial-temporal transformations and perturbation expansion method, which has an advantage in characterizing the propagation of the blocking for atmospheres. The evolutionary dynamics of dipole blocking are discussed analytically and are simulated numerically via changing terrain parameters for sinusoidal topography, slope topography, and roughed topography, respectively. The results show that the amplitude increase for sinusoidal bottom topography makes the dipole blocking move faster and enhances the intensity significantly. For sloped topography, the intensity of dipole blocking slowly decreases with increasing topographic slope. At the same time, the effect of the frequency for roughed topography agrees with the slope effect on the dynamics of nonlinear envelope solitary Rossby waves. This theoretical attempt gives a new explanation of the topographic Rossby waves.