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Two-way interactions between equatorially-trapped waves and the barotropic flow

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Abstract

Lateral energy exchange between the tropics and the midlatitudes is a topic of great importance for understanding Earth’s climate system. In this paper, the authors address this issue in an idealized set up through simple shallow water models for the interactions between equatorially trapped waves and the barotropic mode, which supports Rossby waves that propagate poleward and can excite midlatitude teleconnection patterns. It is found here that the interactions between a Kelvin wave and a fixed meridional shear (mimicking the jet stream) generates a non-trivial meridional velocity and meridional convergence in phase with the upward motion that can attain a maximum of about 50%, which oscillates on frequencies ranging from one day to 10 days. When, on the other hand, the barotropic flow is forced by slowly propagating Kelvin waves a complex flow pattern emerges; it consists of a phase-locked barotropic response that is equatorially trapped and that propagates eastward with the forcing Kelvin wave and a certain number of planetary Rossby waves that propagate westward and toward the poles as seen in nature. It is suggested here that the poleward propagating waves are to some sort of multi-way resonant interaction with the phase locked response. Moreover, it is shown here that a numerical scheme with dispersion properties that depend on the direction perpendicular to the direction of propagation, namely the 2D central scheme of Nessyahu and Tadmor, can artificially alter significantly the topology of the wave fields and thus should be avoided in climate models.

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Author information

Correspondence to Boualem Khouider.

Additional information

Dedicated to Professor Andrew Majda on the Occasion of his 60th Birthday

Project supported in part by the Natural Sciences and Engineering Research Council of Canada (No. 288339-2004) and the Canadian Foundation for Climate and Atmospheric Sciences (No. GR-7021).

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Ferguson, J., Khouider, B. & Namazi, M. Two-way interactions between equatorially-trapped waves and the barotropic flow. Chin. Ann. Math. Ser. B 30, 539–568 (2009). https://doi.org/10.1007/s11401-009-0102-9

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Keywords

  • Equatorially trapped waves
  • Wave interactions
  • Jet stream
  • Rossby waves
  • Phase locked
  • Dispersion relation
  • Central scheme
  • Climate modeling

2000 MR Subject Classification

  • 65M06
  • 65M12
  • 76B15
  • 76B55
  • 76B60
  • 86A10