On the Shear Instability without Over-reflection

Abstract

Examined is the barotropic instability problem of a discontinuous zonal flow with a boundaryon a 5-plane as well as the steady wave problem. It is found that instability occurs but over-reflectiondoes not. This result is different from that in the Kelvin-Helmholtz (K-H) instability problem of astably stratified Boussinesq fluid (Lindzen and Rosenthal, 1976). The difference is due to the absenceof an outgoing neutral normal mode in the present problem.The piecewise-linear barotropic shear layer on a /3'-plane is also examined in the similar manner.Again instability occurs but over-reflection does not. Further, the K-H instability problem with arigid wall above the critical level is re-examined. These results suggest that there is no exact correspondencebetween over-reflection of a neutral wave and a shear instability.