Abstract
Abstract This paper presents a methodology for performing complex wavenumber ray tracing in which both wave trajectory and amplitude are calculated. This ray-tracing framework is first derived using a scaling in which the imaginary wavenumber component is assumed to be much smaller than the real wavenumber component. The approach, based on perturbation methods, is strictly valid when this scaling condition is met. The framework is then used to trace stationary barotropic Rossby waves in a number of settings. First, ray-traced Rossby wave amplitude is validated in a simple, idealized system for which exact solutions can be calculated. Complex wavenumber ray tracing is then applied to both solid-body rotation on a sphere and observed climatological upper-tropospheric fields. These ray-tracing solutions are compared with similarly forced solutions of the linearized barotropic vorticity equation (LBVE). Both real and complex wavenumber ray tracings follow trajectories matched by LBVE solutions. Complex wavenumber ray tracings on observed two-dimensional zonally asymmetric atmospheric fields are found to follow trajectories distinct from real wavenumber Rossby waves. For example, complex wavenumber ray tracings initiated over the eastern equatorial Pacific Ocean during boreal summer propagate northward and northeastward into the subtropics over the Atlantic Ocean, as well as southeastward into the Southern Hemisphere. Similarly initiated real wavenumber ray tracings remain within the deep tropics and propagate westward. These complex wavenumber Rossby wave trajectories and ray amplitudes are generally consistent with LBVE solutions, which indicates this methodology can identify Rossby wave effects distinct from traditional real wavenumber tracings.
Highlights
Ray tracing is often used to explore the propagation of Rossby waves with stationary or near-stationary phase speeds
Complex wavenumber ray tracings initiated at 3.728N, 858W propagate east-northeastward over the linearized barotropic vorticity equation (LBVE) model solution anomaly in the vicinity of Cuba (Fig. 12b)
As in our perturbation approach, the MD93 Complex wavenumber ray tracing (CRT) fall into three general groupings: 1) propagation northward to the region of subtropical convergence over and west of Mexico; 2) propagation over the Caribbean, Cuba, and in some instances into the North African–Asian jet; and 3) propagation southward to about 108S and eastward
Summary
Ray tracing is often used to explore the propagation of Rossby waves with stationary or near-stationary phase speeds. In the presence of dissipation, typically only decaying complex wavenumber waves are considered physically meaningful (Budden and Terry 1970; Jones 1970; Kravtsov 2005); in this study the ray-traced medium is to be treated as inviscid and complex relationships arise naturally from the dispersion relation. It is possible, though by no means definitive, that growing modes, if reasonably confined, represent spatial instabilities. Note that if a 5 0 (i.e., ki 5 0, etc.), Eq (2.17) degenerates to a constant amplitude on the WKBJ local scale
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