Planetary, inertia–gravity and Kelvin waves on the f-plane and β-plane in the presence of a uniform zonal flow

Yair De-Leon, Itzhak Fouxon, Chaim I. Garfinkel, Nathan Paldor*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A linear wave theory of the Rotating Shallow-Water Equations (RSWE) is developed in a channel on the midlatitude f-plane or (Formula presented.) -plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. Here we show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f-plane similar to the generation of these waves by PV sources such as the (Formula presented.) -effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting Rossby, Poincaré and “Kelvin-like” waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the “no mean-flow” phase speeds does not account for the difference in phase speeds, and the meridional structure is often trapped near one of the channel's boundaries and does not oscillate across the channel. A comparison between the phase speeds of Rossby waves of the present theory and those of the Quasi-Geostrophic Shallow-Water (QG-SW) theory shows that the former can be 2.5 times faster than those of the QG-SW theory. The phase speed of “Kelvin-like” waves is modified by the presence of a mean flow compared to the classical gravity wave speed, and furthermore their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincaré modes are not uniform but change with the zonal wave number, and the convexity of the dispersion curves also changes with the zonal wave number. These results have implications for the propagation of Rossby wave packets: QG theory overestimates the zonal group velocity.

Original languageAmerican English
Pages (from-to)2935-2952
Number of pages18
JournalQuarterly Journal of the Royal Meteorological Society
Issue number738
StatePublished - Jul 2021

Bibliographical note

Publisher Copyright:
© 2021 The Authors. Quarterly Journal of the Royal Meteorological Society published by John Wiley & Sons Ltd on behalf of the Royal Meteorological Society.


  • Doppler shifting
  • Kelvin wave
  • PV sources
  • Rossby waves
  • inertia-gravity waves
  • trapped waves


Dive into the research topics of 'Planetary, inertia–gravity and Kelvin waves on the f-plane and β-plane in the presence of a uniform zonal flow'. Together they form a unique fingerprint.

Cite this