Effect of quadric shear basic zonal flows and topography on baroclinic instability

On the β plane approximation, the two-layer quasigeostrophic mode is used to study the baroclinic instability of the quadric shear basic zonal flows on a uniform bottom topography. The phase speed and growth rate of instability waves are functions of the shear zonal basic flows and bottom topographic slope. The study focus is on the effects of topography and the quadric shear basic zonal flows (the second derivative of basic zonal flows is not zero). The meridional slope destabilise (stabilise) zonal flows, it plays an unstable role in disturbance, moreover the effect of the second derivative of basic zonal flows is to accelerate the instability of disturbance. The zonal slope always destabilises the zonal basic flows through zonal and meridional wavenumber. Moreover, the effect of the second derivative of basic zonal flows is to accelerate the instability of disturbance.