Periodic Structures of Rossby Wave under Influence of Dissipation

A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmosphere. By the reductive perturbation method, we derive the rotational KdV (rKdV for short) equation. And then, with the help of Jacobi elliptic functions, we obtain various periodic structures for these Rossby waves. It is shown that dissipation is very important for these periodic structures of rational form.