ROSSBY-WAVE EQUATION FOR LONG-WAVELENGTH

It is well known that the nonlinear Rossby wave equation has a dipole vortex solution, the so-called modon, in the short-wavelength regime. For a steady state in the long-wavelength regime, we find an appropria te variable transformation to express the potential vorticity in conse rvation form, and obtain a nonlinear Schrodinger equation for the stre am function. It is found by numerical analysis that the equation has a monopole vortex solution for small separatrix radius.