The barotropic stability of the mean winds in the atmosphere

Abstract

This paper considers the stability of a barotropic current on a beta earth. The motion is assumed to be horizontal, non-divergent and barotropic. The current is taken to be of the formU(y)=Asech2by+B. The perturbations are required to approach zero asyapproaches ± ∞. We introduce the non-dimensional wave-numberland a parameter χ, which is a measure of the rotation effect. χ is inversely proportional to β.There are only two kinds of perturbations: symmetric disturbances (those with maximum amplitude aty= 0) and antisymmetric disturbances (those with zero amplitude aty= 0). We find the neutral curve in the (χ,l2)-plane for both types of disturbances. The rates of amplification in the immediate vicinity of the neutral curves are also found. It is seen that the beta effect, which is due to the earth's rotation, tends to stabilize the current. For the symmetric disturbances we find a band of unstable wavelengths when χ > 1/2; and for large χ the estimated curve of the maximum value of the imaginary part of the phase velocity is asymptotic to the lower branch of the neutral curve. The antisymmetric disturbances are more stable than the symmetric disturbances.