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The Stability of Some Planetary Boundary Layer Diffusion Equations

Huw C. DaviesAtmospheric Physics ETH, CH-8093 Zurich, Switzerland

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Abstract

A study is made of the stability properties of certain coupled and decoupled nonlinear diffusion equations. The equations are of the form currently used in many high-resolution models to parameterize the stably stratified boundary layer. It is shown that some parameterization schemes for a decoupled thermal diffusion equation possess an unrealistic instability feature. However, the stability of the schemes is demonstrated in the more natural setting of a coupled, momentum and heat, set of diffusion equations.

Abstract

A study is made of the stability properties of certain coupled and decoupled nonlinear diffusion equations. The equations are of the form currently used in many high-resolution models to parameterize the stably stratified boundary layer. It is shown that some parameterization schemes for a decoupled thermal diffusion equation possess an unrealistic instability feature. However, the stability of the schemes is demonstrated in the more natural setting of a coupled, momentum and heat, set of diffusion equations.

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