Abstract
The effect of the horizontal component fH of the planetary vorticity on the symmetric stability of zonal flow is investigated using the linearized Boussinesq equations on the f -plane. It is shown that, as in the case of neglecting fH, the stability under full-component Coriolis force is determined by the sign of the potential vorticity. It is also revealed that even in such a generalized situation, the movement associated with the symmetric instability can be decomposed into two independent motions, i.e., the buoyancy oscillation (or instability) modified by the Coriolis force and the inertial oscillation (or instability) modified by the buoyancy. The squared product of their frequencies remains proportional to the potential vorticity of the zonal flow. Meanwhile, the horizontal component of the planetary vorticity is found to exhibit both stabilizing and destabilizing effects, although there is a wide range of stable regions that are not affected by fH. The existence of fH also causes an asymmetry such that the stability changes depending on the sign of the vertical shear of the zonal flow, even if the Richardson number and the dimensionless relative vorticity are maintained constant.
