International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 547-557

Propagation of Rossby waves in stratified shear flows

Palani G. Kandaswamy,1 B. Tamil Selvi,1 and Lokenath Debnath2

1Department of Mathematics, Bharathiar University, Coimbatore 641 046, India
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA

Received 5 November 1987; Revised 5 March 1988

Copyright © 1989 Palani G. Kandaswamy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A study is made of the propagation of Rossby waves in a stably stratified shear flows. The wave equation for the Rossby waves is derived in an isothermal atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It is shown that the wave equation is singular at five critical levels, but the wave absorption takes place only at the two levels where the local relative frequency equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that these two levels exhibit valve effect by allowing the waves to penetrate them from one side only. The absorption coefficient exp(2πμ) is determined at these levels. Both the group velocity approach and single wave treatment are employed for the investigation of the problem.