The Polygonal Eyes of Wayne Schubert

Several years after the discovery of polygonal eye walls in hurricanes by B. M. Lewis and H. F. Hawkins, T. Muramatsu suggested the connection with instability of the cylindrical shear zone located at the eye wall’s inner edge. Motivated by the latter, Wayne Schubert, along with students and colleagues, began a deep theoretical investigation of the phenomenon. The first step was to review and further investigate the linear instability of a barotropic annular vortex. The asymmetric modes found suggested polygonal shapes; however, the really difficult challenge was to understand which of the shapes (if any) survive at finite amplitude. Remarkably, it was found that under certain conditions, relevant to hurricanes, squares and pentagons were long-lasting features of the nonlinear solutions. Further investigation using more complex systems of equations such as the barotropic model with forcing, the shallow water equations, and finally the primitive equations, have established the validity of the original conjecture that polygonal eyes in hurricanes are fundamentally connected to the barotropic vorticity dynamics of the eye-wall vorticity. This talk will highlight Wayne Schubert’s important contributions to our understanding of this phenomenon.