Note on a baroclinic analogue of vorticity defects in shear

Abstract

An approach developed recently to study the dynamics of vorticity defects in homogeneous shear flow extends naturally to the case of baroclinic, quasi-geostrophic flow. It is shown that an inviscid geostrophic flow with uniform vertical shear may be destabilized by introducing a ‘potential vorticity defect’, an arbitrarily small but sufficiently sharp and horizontally uniform change in stratification or vertical shear. The linear baroclinic problem is nearly identical to the linear homogeneous problem, with differences arising only from the boundary conditions. The nonlinear baroclinic problem differs substantially from the nonlinear homogeneous problem, as the leading-order baroclinic nonlinearity is the Jacobian of the ‘inner’ streamfunction and potential vorticity in the horizontal plane aligned with the defect. An example of the linear instability is described.