In this paper, the non-dimensional equivalent barotropic vorticity equation with dissipation and an external vorticity source induced by diabatic heating was reduced to the generalized periodically forced nonlinear Schr#xF6;dinger (NLS) equation similar to the parametrically excited NLS equation derived by Miles (1984) by means of the multiplescale method. This forced NLS equation can be reduced to a low-dimensional ordinary differential equation describing the amplitude and phase of the forced envelope Rossby soliton by the inverse-scattering perturbation method. The numerical calculations indicate that for weaker dissipation the envelope Rossby soliton, under a constant amplitude travelling diabatic heating, exhibits multi-periodic oscillations, and its phase portrait is found to be a limit cycle. However, for the forcing of one-year modulated diabatic heating, the forced envelope Rossby soliton can execute chaotic motion when the controlling parameter reaches a certain extent. In addition, the oscillatory behaviour of the forced envelope Rossby soliton is found to be able to explain the establishment and decay of vortex pair blocking usually observed in two oceans.
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