On the stability of atmospheric waves with low wave numbers

A. WIIN NIELSEN

Abstract

The stability of atmospheric waves with low wave numbers is investigated using a quasi-geostrophic model of the second kind. Such a model is based on the thermodynamic equation, the continuity equation and a rigorous use of the geostrophic relations. The boundary condition at the surface of the Earth is formulated in two ways. The effects of a boundary condition at 1000 hpa, where the vertical p-velocity is zero, is compared with the effects of a second condition, where w is zero. The two boundary conditions are used to determine the stability of the low wave number waves. The second condition introduces waves with large positive and negative phase velocities, especially in the low latitudes, but has also an influence on the stability of these waves. The main result of the comparative investigation is that the more correct boundary condition in general will produce stronger instabilities than the simpler boundary condition. The e-folding times obtained with the more general model is in closer agreement with the results obtained by observational studies.

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