On Rossby waves modified by weak sinusoidal shear

Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 (1988) On Rossby waves modified by weak sinusoidal shear. Geophysical and Astrophysical Fluid Dynamics, 40 (3-4). pp. 225-237. ISSN 0309-1929 doi: 10.1080/03091928808208826

Abstract/Summary

The spatial structure of beta-plane Rossby waves in a sinusoidal basic zonal flow U 0cos(γ,y) is determined analytically in the (stable) asymptotic limit of weak shear, U 0γ2 0/β≈1. The propagating neutral normal modes are found to take their greatest amplitude in the region of maximum westerly flow, while their most rapid phase variation is achieved in the region of maximum easterly flow. These results are shown to be consistent with what is obtained by ray-tracing methods in the limit of small meridional disturbance wavelength.