Periodic structures of oceanic Rossby wave under the influence of wind stress

A simple oceanic barotropic potential vorticity equation on β-plane with the influence of wind stress is applied to investigate the nonlinear Rossby wave in a shear flow. By the reductive perturbation method, we derived the rotational modified KdV (rmKdV for short) equation. And then with the help of Jacobi elliptic functions, we obtain various periodic structures for these equatorial Rossby waves. It is shown that the wind stress is very important for these periodic structures of rational form.