Nonlinear Shock and Kink Waves with Complete Coriolis Force in Earth's Atmosphere

Nonlinear waves in a Boussinesq fluid model which includes both the vertical and horizontal components of Coriolis force are studied by using the semi-geostrophic approximation and the method of travelling-wave solution. Taylor series expansion has been employed to isolate the characteristics of the linear Rossby waves and to identify the nonlinear shock and kink waves. The KdV-Burgers and the compound KdV-Burgers equations are derived, their shock wave and kink wave solution are also obtained.