Enhancement of critical layer mixing by barotropic instability

The mixing within a Rossby-wave critical layer is examined, in particular how mixing is affected by barotropic instability during the early critical layer evolution. As discussed in Haynes (1989), barotropic instability typically occurs inside the critical layer when the ratio of cross to along-stream length scales is small, due to the creation of locally non-monotonic regions of potential vorticity, advected by the closed streamlines within the Kelvin cat's-eye. Here we integrate the critical layer evolution numerically, approximating the exact inner solution by a simple topographic forcing. Mixing is diagnosed by calculating the effective diffusivity and the stretching rates of material contours, and is found to increase as the ratio of cross to along-stream length scales decreases and the barotropic instability becomes more pronounced. An extension of the critical layer model from infinite to finite Rossby deformation length is also considered and the dependence of the instability and mixing on this additional parameter is quantified.