Interaction of algebraic Rossby solitary waves with topography and atmospheric blocking

• A new equation governing the behavior of Rossby solitary waves is derived, which is called mBO-mKdV-Burgers equation. It is more suitable for describing the Rossby solitary waves when the perturbation is stronger.
• By employing this new model, the features of Rossby solitary waves are studied. Especially, numerical simulation is carried out to investigate the effect of detuning parameter, topographical altitude and dissipation on the interaction of Rossby solitary waves with topography.
• Some mechanisms to generate atmospheric blocking and oscillation phenomenon are explained.

In this article, a new equation governing the behavior of Rossby solitary waves is derived by employing perturbation expansions and stretching transformations of time and space, which is called mBO-mKdV-Burgers equation. The equation is different from the common BO equation, it is more suitable for describing the Rossby solitary waves when the perturbation is stronger. Based on the analytical solution of mBO-mKdV-Burgers equation, the features of Rossby solitary waves including conserved laws, fission property and dissipation effect are studied. It is found that dissipation causes the amplitude and speed of solitary waves decrease; breakup phenomenon will happen during propagation. Finally, numerical simulation is carried out to investigate the effect of detuning parameter α, topographical altitude and dissipation on the interaction of Rossby solitary waves with topography. It is pointed out that with decreasing of detuning parameter α, the propagation speed of solitary waves decreases and the interaction time increases, which is beneficial to form the large amplitude disturbance; with increasing of topographical altitude, the free solitary waves can not cross over topography; decreasing detuning parameter α and increasing topographical altitude are both mechanisms to generate atmospheric blocking; with the occurence of small dissipation, damping oscillation phenomenon will happen.