### 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 language | English (US) |
---|---|

Pages (from-to) | 341-390 |

Number of pages | 50 |

Journal | Studies in Applied Mathematics |

Volume | 112 |

Issue number | 4 |

DOIs | |

State | Published - May 2004 |

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### 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.

Research output: Contribution to journal › Article

*Studies in Applied Mathematics*, vol. 112, no. 4, pp. 341-390. https://doi.org/10.1111/j.0022-2526.2004.01518.x

}

TY - JOUR

T1 - The effect of meridional and vertical shear on the interaction of equatorial baroclinic and barotropic Rossby waves

AU - Biello, Joseph A.

AU - Majda, Andrew J.

PY - 2004/5

Y1 - 2004/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=2442555009&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2442555009&partnerID=8YFLogxK

U2 - 10.1111/j.0022-2526.2004.01518.x

DO - 10.1111/j.0022-2526.2004.01518.x

M3 - Article

VL - 112

SP - 341

EP - 390

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 4

ER -