The effect of meridional and vertical shear on the interaction of equatorial baroclinic and barotropic Rossby waves

Joseph A. Biello, Andrew J. Majda

Research output: Contribution to journalArticle

Abstract

Simplified asymptotic equations describing the resonant nonlinear interaction of equatorial Rossby waves with barotropic Rossby waves with significant midlatitude projection in the presence of arbitrary vertically and meridionally sheared zonal mean winds are developed. The three mode equations presented here are an extension of the two mode equations derived by Majda and Biello [1] and arise in the physically relevant regime produced by seasonal heating when the vertical (baroclinic) mean shear has both symmetric and antisymmetric components; the dynamics of the equatorial baroclinic and both symmetric and antisymmetric barotropic waves is developed. The equations described here are novel in several respects and involve a linear dispersive wave system coupled through quadratic nonlinearities. Numerical simulations are used to explore the effect of antisymmetric baroclinic shear on the exchange of energy between equatorial baroclinic and barotropic waves; the main effect of moderate antisymmetric winds is to shift the barotropic waves meridionally. A purely meridionally antisymmetric mean shear yields highly asymmetric waves which often propagate across the equator. The two mode equations appropriate to Ref. [1] are shown to have analytic solitary wave solutions and some representative examples with their velocity fields are presented.

Original languageEnglish (US)
Pages (from-to)341-390
Number of pages50
JournalStudies in Applied Mathematics
Volume112
Issue number4
DOIs
StatePublished - May 2004

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Antisymmetric
Vertical
Interaction
Equator
Nonlinear Interaction
Main Effect
Solitary Wave Solution
Solitons
Coupled System
Velocity Field
Heating
Projection
Nonlinearity
Numerical Simulation
Computer simulation
Arbitrary
Energy

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The effect of meridional and vertical shear on the interaction of equatorial baroclinic and barotropic Rossby waves. / Biello, Joseph A.; Majda, Andrew J.

In: Studies in Applied Mathematics, Vol. 112, No. 4, 05.2004, p. 341-390.

Research output: Contribution to journalArticle

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