Rossby Waves in Zonal Barotropic Flows with Pseudocritical Levels

Abstract

A pseudocritical level is defined as a region where the wave phase speed c equals the zonal basic flow velocity U and, additionally, the background potential vorticity gradient vanishes. In this study Rossby wave propagation is investigated in zonal mean flows when pseudocritical levels are present. For that purpose the barotropic potential vorticity equation linearized about prescribed zonal basic flows is used. The basic flows are constructed such that (i) the amplitude equation for Rossby waves can be solved analytically, (ii) the flows exhibit several pseudocritical levels, and (iii) the flows do not look entirely unrealistic compared to observed zonally averaged flows in atmospheres and oceans. Two examples of basic flows are studied: an unbounded multiple-jet flow on the f plane and a single-jet flow on the ? plane bounded to the south by a reflective wall. It is shown that pseudocritical levels are neither critical levels nor turning points of the flow. Global solutions representing trapped modal waves exist due to the fact that all levels with U = c are pseudocritical. However, ?classical? waveguides for local wave packets are not possible since turning points cannot be reached. Pseudocritical levels are wave attractors for wave packets, and stationary wave packets become stuck on them at particular points, without violating Wentzel?Kramers?Brillouin (WKB) theory. On the other hand, wave packets with nonzero frequency propagate along the pseudocritical level with the local basic flow velocity. Therefore, a pseudocritical level may cause wave focusing and can form a zonal waveguide without the need of turning points or reflective boundaries. Aside from the numerical computation of unstable modes and the construction of mean flows showing pseudocritical levels on the ? plane, all results shown here can be obtained by means of analytical and asymptotical methods. The results may be relevant also for other wave types.