Reflection of Barotropic Rossby Waves in Sheared Flow and Validity of the WKB Approximation

The authors discuss reflection of barotropic Rossby waves in an idealized framework with potential applications to tropical-extratropical and interhemispheric interactions. Meridional propagation of Rossby waves has often been studied using the Wentzel-Kramers-Brillouin (WKB) approximation. The WKB approximation neglects reflection. The authors investigate the amount of reflection in simple shear profiles and attempt to evaluate the validity of using the WKB approximation to understand the meridional propagation of Rossby waves. In addition to solving for the reflection coefficient numerically, exact and approximate forms of the reflection coefficient in certain parameter regimes are derived. An application to the observed climatology is discussed in light of the findings.