Envelope solitary Rossby waves and modulational instabilities of uniform Rossby wave trains in two space dimensions

摘要

Envelope solitary Rossby waves and modulational instability of a uniform Rossby wave train in two space dimensions are investigated. It is found that the condition for an envelope solitary Rossby wave to exist is [(3m~2 - k~2) cos~2 θ + (5m~2 + k~2) sin~2 θ]/[3m~2(m~2 - 2k~2) - k~4] > 0, in which k and m are the zonal and meridional wave numbers, respectively, and θ is a fixed angle of orientation representing the modulation direction in two space dimensions. Moreover, under a moderate condition the envelope solitary Rossby wave possesses quasi-stationary dipole structure that can tilt horizontally either westward or eastward due to the change of modulation direction, which resembles observed vortex pair blocking. If there is a set of infinitesimal sideband perturbations imposing on a uniform Rossby wave train, then the condition for instability to occur is 0 < [λ(pk)~2 + Q(qm)~2]λ < 2δb_0~2, where bo is the amplitude of the uniform Rossby wave train, and the restrictions that p 1 and q 1 are required. A noteworthy property is that the instability region of p will become narrower if q increases in the small value limit. On the other hand, it will become wider if the latitude increases for a fixed q.