Symmetry analysis for three-dimensional dissipation Rossby waves

Rossby waves, belonging to the most important waves in the atmosphere and ocean, can affect the energy transfer of the atmosphere and ocean and have significant theoretical meaning and research value. In previous research performed with the theory and calculation method limit, the dissipation effect was commonly ignored. However, under the conditions of the weak linear approximation, the magnitude difference between nonlinear and dissipation is small, and the dissipation effect must be considered. In this paper, based on the classic Lie group approach, the (3 + 1)-dimensional quasi-geodetiophic vorticity equation with dissipation effect is solved. With the help of the solutions, we can better comprehend the influence of the dissipation effect on the propagation of Rossby waves.