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Generalization of Baroclinic Instability and Rossby Wave Saturation Theory

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Part of the Mathematics of Planet Earth book series (MPE, volume 8)

Abstract

This chapter describes a problem of barotropic and baroclinic instability in realistic zonal and non-zonal basic state on a sphere, using three-dimensional (3D) spectral primitive equations derived by the 3D NMFs. The most unstable mode in a realistic zonal basic state, called Charney mode, appears in mid-latitudes associated with the baroclinicity of the subtropical jet. In a zonally-varying basic state, we find that the unstable modes are modified by the regionality of the local baroclinicity of the basic state. Given the zonally varying barotropic basic state, we find that the barotropically most unstable standing mode appears to be the Arctic Oscillation (AO) mode. The eigensolution of the linear baroclinic model (LBM) in this section is regarded as a generalized extension of the 3D normal mode at the motionless atmosphere to those of an arbitrary climate basic state. Some applications of the nonlinear primitive equation models are presented for the nonlinear life-cycle experiment of baroclinic waves. The saturation of the growing Rossby waves produces the characteristic energy spectrum obeying the squared phase speed of Rossby waves. We call it as the Rossby wave saturation theory which explains the observed energy spectrum of the geostrophic turbulence in the phase speed domain.

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Authors and Affiliations

  1. 1.Center for Computational SciencesUniversity of TsukubaTsukubaJapan

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