Nonlinear instability of a forced baroclinic Rossby wave

Research output: Contribution to journalArticle

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Abstract

Two-layer, quasi-geostrophic weakly nonlinear and low-order spectral models are developed and used to investigate the instability of forced baroclinic Rossby waves to finite-amplitude perturbations. The results are then applied to the interaction of planetary-scale stationary eddies with synoptic scale transient eddies. The synoptic-scale perturbation modes initially grow exponentially after which they eventually settle into an amplitude vacillation cycle. This vacillation is driven by the linear interference between propagating and stationary synoptic-scale modes with the same zonal and meridional wavenumbers. During this vacillation, the time mean energy of the stationary planetary wave equals its initial value. The asymptotic series expansions are also used to determine the truncation for a fully nonlinear spectral model. The weakly nonlinear and spectral solutions are compared and are found to agree very well. The interaction between planetary-scale stationary eddies with synoptic-scale transient eddies is a nonlinear phenomenon that is very sensitive to the detailed structure of the eddies present. -from Author

Original languageEnglish (US)
Pages (from-to)993-1006
Number of pages14
JournalJournal of the Atmospheric Sciences
Volume45
Issue number6
DOIs
StatePublished - Jan 1 1988

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baroclinic wave
Rossby wave
eddy
perturbation
planetary wave
standing wave
energy

All Science Journal Classification (ASJC) codes

  • Atmospheric Science

Cite this

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title = "Nonlinear instability of a forced baroclinic Rossby wave",
abstract = "Two-layer, quasi-geostrophic weakly nonlinear and low-order spectral models are developed and used to investigate the instability of forced baroclinic Rossby waves to finite-amplitude perturbations. The results are then applied to the interaction of planetary-scale stationary eddies with synoptic scale transient eddies. The synoptic-scale perturbation modes initially grow exponentially after which they eventually settle into an amplitude vacillation cycle. This vacillation is driven by the linear interference between propagating and stationary synoptic-scale modes with the same zonal and meridional wavenumbers. During this vacillation, the time mean energy of the stationary planetary wave equals its initial value. The asymptotic series expansions are also used to determine the truncation for a fully nonlinear spectral model. The weakly nonlinear and spectral solutions are compared and are found to agree very well. The interaction between planetary-scale stationary eddies with synoptic-scale transient eddies is a nonlinear phenomenon that is very sensitive to the detailed structure of the eddies present. -from Author",
author = "Feldstein, {Steven B.}",
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Nonlinear instability of a forced baroclinic Rossby wave. / Feldstein, Steven B.

In: Journal of the Atmospheric Sciences, Vol. 45, No. 6, 01.01.1988, p. 993-1006.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Nonlinear instability of a forced baroclinic Rossby wave

AU - Feldstein, Steven B.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - Two-layer, quasi-geostrophic weakly nonlinear and low-order spectral models are developed and used to investigate the instability of forced baroclinic Rossby waves to finite-amplitude perturbations. The results are then applied to the interaction of planetary-scale stationary eddies with synoptic scale transient eddies. The synoptic-scale perturbation modes initially grow exponentially after which they eventually settle into an amplitude vacillation cycle. This vacillation is driven by the linear interference between propagating and stationary synoptic-scale modes with the same zonal and meridional wavenumbers. During this vacillation, the time mean energy of the stationary planetary wave equals its initial value. The asymptotic series expansions are also used to determine the truncation for a fully nonlinear spectral model. The weakly nonlinear and spectral solutions are compared and are found to agree very well. The interaction between planetary-scale stationary eddies with synoptic-scale transient eddies is a nonlinear phenomenon that is very sensitive to the detailed structure of the eddies present. -from Author

AB - Two-layer, quasi-geostrophic weakly nonlinear and low-order spectral models are developed and used to investigate the instability of forced baroclinic Rossby waves to finite-amplitude perturbations. The results are then applied to the interaction of planetary-scale stationary eddies with synoptic scale transient eddies. The synoptic-scale perturbation modes initially grow exponentially after which they eventually settle into an amplitude vacillation cycle. This vacillation is driven by the linear interference between propagating and stationary synoptic-scale modes with the same zonal and meridional wavenumbers. During this vacillation, the time mean energy of the stationary planetary wave equals its initial value. The asymptotic series expansions are also used to determine the truncation for a fully nonlinear spectral model. The weakly nonlinear and spectral solutions are compared and are found to agree very well. The interaction between planetary-scale stationary eddies with synoptic-scale transient eddies is a nonlinear phenomenon that is very sensitive to the detailed structure of the eddies present. -from Author

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U2 - 10.1175/1520-0469(1988)045<0993:NIOAFB>2.0.CO;2

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