Linear Instability with Ekman and Interior Friction. Part I: Quasigeostrophic Eigenanalysis

Richard Grotjahn Department of Land Air and Water Resources, University of California, Davis, Davis, California

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Min Chen Environmental Health and Sciences Laboratory, Mobil Oil Corporation, Princeton, New Jersey

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Joseph Tribbia National Center for Atmospheric Research, Boulder, Colorado

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Abstract

The eigenvalue problems for the original Eady model and a modified Eady model (the G model) are examined with no friction, Ekman friction only, and both Ekman and interior friction. When both Ekman and interior friction are included in the models, normal modes show little additional change when compared to the case with Ekman friction only, whereas the relevant “continuum modes” have large negative growth rates. Interior friction has a much greater effect on the continuum modes than on the normal modes because inviscid continuum modes have a delta-function vertical profile of potential vorticity q. In contrast, normal modes have much smoother profiles of q in the interior. Streamfunction profiles for the continuum modes are notably different in the two models. The continuum modes in the more realistic G model have sharp peak amplitudes that are not as broad in the vertical as in the Eady model.

Abstract

The eigenvalue problems for the original Eady model and a modified Eady model (the G model) are examined with no friction, Ekman friction only, and both Ekman and interior friction. When both Ekman and interior friction are included in the models, normal modes show little additional change when compared to the case with Ekman friction only, whereas the relevant “continuum modes” have large negative growth rates. Interior friction has a much greater effect on the continuum modes than on the normal modes because inviscid continuum modes have a delta-function vertical profile of potential vorticity q. In contrast, normal modes have much smoother profiles of q in the interior. Streamfunction profiles for the continuum modes are notably different in the two models. The continuum modes in the more realistic G model have sharp peak amplitudes that are not as broad in the vertical as in the Eady model.

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