Numerical simulation of harmonic, and trapped, Rossby waves in a channel on the midlatitude β-plane

Hezi Gildor, Nathan Paldor*, Shimon Ben-Shushan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The applicability of two competing wave theories of the rotating shallow-water equations, the harmonic planetary waves and the trapped planetary waves, is examined by solving the equations numerically in a zonal channel on the midlatitude β-plane. The examination is carried out by initializing the numerical shallow-water solver by harmonic and trapped waves and comparing the temporal evolution to that expected from the corresponding wave theory. The simulations confirm that harmonic waves provide accurate approximations for the temporal evolution in narrow channels while trapped waves do so in wide channels. The transition from a narrow channel to a wide channel occurs when the non-dimensional number (Formula presented.) (where L is the channel width, Rd is the radius of deformation, a is Earth's radius and ϕ0 is the latitude of the centre of the channel) is increased above a threshold value that larger than 4 and that depends on the meridional mode number of the trapped wave. Numerical solutions of the nonlinear equations show that, for the same wave amplitude, trapped waves approximate the nonlinear solutions in a wide channel for much longer times than harmonic waves in a narrow channel.

Original languageAmerican English
Pages (from-to)2292-2299
Number of pages8
JournalQuarterly Journal of the Royal Meteorological Society
Issue number699
StatePublished - 1 Jul 2016

Bibliographical note

Publisher Copyright:
© 2016 Royal Meteorological Society


  • planetary waves
  • shallow-water waves
  • trapped waves


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