Linear stability of steady zonal jet flows induced by a small-scale forcing on a β plane

Kiori Obuse, Shin Ichi Takehiro, Michio Yamada

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We analytically obtain steady isolated zonal jet solutions of the evolution equation of zonal flows on a β plane with a homogeneous zonal flow and a small-scale sinusoidal transversal flow in the background, derived by Manfroi and Young (1999) [9]. It is shown that these steady zonal jet solutions are all linearly unstable. Numerical time integrations of the evolution equation also confirm that the perturbed unstable steady solution becomes a uniform flow in the long run. These results suggest that mergers/disappearances of zonal jets superposed upon background forced two-dimensional turbulence on a β plane or a rotating sphere might be due to the intrinsic instability of the zonal jets.

Original languageEnglish
Pages (from-to)1825-1834
Number of pages10
JournalPhysica D: Nonlinear Phenomena
Issue number22
Publication statusPublished - Nov 1 2011
Externally publishedYes


  • Barotropic flow
  • Beta effect
  • CahnHilliard equation
  • Rotating fluid
  • Turbulence
  • Zonal jet

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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