## Services on Demand

## Journal

## Article

## Indicators

- Cited by SciELO
- Access statistics

## Related links

- Similars in SciELO

## Share

## Atmósfera

*Print version* ISSN 0187-6236

#### Abstract

WIIN-NIELSEN, A.. **Investigations of barotropic and baroclinic stability**.* Atmósfera* [online]. 2000, vol.13, n.4, pp.197-221.
ISSN 0187-6236.

The barotropic and the mixed barotropic-baroclinic stability problems are treated using a series expansion in trigonometric functions of the mean zonal velocity and the perturbation streamfunction. A two-level quasi-nondivergent model is used to handle the mixed stability problem, containing both horizontal and vertical wind shears in the basic state. In the present investigation the number of components in the series expansion is limited to four; because the most interesting meridional windprofiles may be simulated within this restriction. The models are formulated on the beta-plane. The eigenvalue problem using these series expansions is of the classical type, but it has to be solved numerically due to the size of the matrix which in the mixed case becomes an 8 by 8 matrix. The results contain the classical solutions produced with simpler assumptions giving, for both the barotropic and baroclinic case, the maximum instability for waves with a wavelength of a few thousands kilometers. However, the present models give in addition weak instabilities for much longer wavelengths for some wind profiles. It is also shown that basic currents with two maxima, corresponding to the subtropical and the polar jets, will be stable in the barotropic case provided the polar jet has a sufficiently large magnitude. The mode with the largest negative wave velocity for the longest waves is still a wave speed comparable to the Rossby wave speed as modified by the south-north dimension of the channel. In the baroclinic case we do not find the same stability of the double jets due to the fact that even the mean values of realistic wind profiles will create instabilities for certain wavelengths. Stability analyses give in the unstable cases the tendency for exponential growth, but cannot due to the assumptions handle the interaction with the basic state. In the last section the nonlinear spectral equations containing the same components have been integrated to illustrate the nonlinear developments in the barotropic case.