The Lagrangian governing equations of a rotating,compressible, viscous atmosphere

In this paper, the Lagrangian equations of motion, thermodynamics, continuity and diffusion of a rotating, compressible, viscous atmosphere are derived. It is shown that the pressure force and Laplacian terms involving velocity, temperature and concentration in the Eulerian system become nonlinear in the Lagrangian system. In the case that these Laplacian terms can be neglected, the governing equations in the Lagrangian system can be greatly simplified, and particle dynamics and dispersion can be investigated.