Near-resonant topographically forced envelope Rossby solitons in a barotropic flow

Abstract

In this paper, a parametrically excited nonlinear Schrödinger (NLS) equation is proposed to describe the near-resonant interaction between dipole envelope Rossby soliton and wave number-two topography under the LG-type dipole near resonance condition in a weak background westerly wind. Based on this equation, the existence and stability of steady soliton are discussed. It is found that the stability of the steady forced soliton depends on the latitude and setting of the background westerly wind. The numerical method is applied to solve the forced NLS equation. It is found that under favourable conditions small-amplitude envelope Rossby soliton in the topographic trough can be amplified through the near-resonant forcing of wavenumber-two topography. In a moderate parameter range, the forced amplified envelope soliton is stable. In particular, in the soliton amplification process the maximum soliton amplitude exhibits aperiodic oscillation. However, in some parameter range, the amplified soliton is unstable and developes finally into a cnoidal wave after a long time. In addition, the time sequences of the instantaneous total stream function field are found to bear a remarkable resemblance to the initiation, maintenance and decay of localized dipole blockings in the north Atlantic ocean observed from the daily weather maps. Thus, in the weak nearly resonant background westerly wind, the near-resonant interaction between dipole envelope Rossby soliton and wave number-two topography seems to be a possible mechanism for dipole blockings observed in the two oceans.