The processes of tropical semi-geostrophic adaptation

In tropical areas, when the zonal or meridional geostrophic equilibrium is destroyed, inertial gravity wave will be excited by ageostrophic motion, with the dispersion of the wave, a new zonal or meridional geostrophic balance will be established again, and it follows an invariant of semi-potential vorticity. Based on the invariant, it should be pointed out that the direction of the zonal or meridional semi-geostrophic adaptation depends mainly upon the meridional characteristic scale of initial disturbance. For the zonal (meridional) semi-geostrophic adaptation, if the zonal characteristic scale of initial disturbance is big (small) enough, then the adaptation process always represents the mutual adjustment between the pressure field and zonal (meridional) flow.