Exploring Solutions of Nonlinear Rossby Waves with Complete Coriolis Force

Nonlinear Rossby 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 identify the Rossby cnoidal and solitary waves. Qualitative analysis indicates that if the disturbances are independent of latitude, the effect of horizontal components of Coriolis force disappears.