THE INSTABILITY OF WIND DISCONTINUITIES AND SHEAR ZONES IN PLANETARY ATMOSPHERES

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  • 1 College of Engineering, New York University
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Abstract

It is shown that perturbations forming at wind discontinuities in the atmospheres of rotating planets are unstable, even though the distribution of the angular momentum of the rotating planet exerts a stabilizing influence. Consequently disturbances can develop spontaneously. Presumably at least some of the markings observed on planets, especially on Jupiter, represent such disturbances. The velocity of these perturbations is found not to differ greatly from the mean velocity of the fluid on both sides of the boundary. Therefore, the determination of planetary velocities of rotation from visual observations of such surface markings appears justified.

At a sharp current discontinuity the amplitude of a perturbation increases faster, the shorter the wave length. At shear zones of finite width only those waves are unstable whose length is greater than five times the width of the shear zone, and those waves will develop most rapidly whose length is about eight times the width of the shear zone. Since in the large-scale atmospheric circulations different wind belts are as a rule separated by finite shear zones rather than by sharp discontinuities very short waves cannot develop because they are not unstable. An empirical check of the relation between the width of the shear zone and the length of the developing perturbations is discussed.

Abstract

It is shown that perturbations forming at wind discontinuities in the atmospheres of rotating planets are unstable, even though the distribution of the angular momentum of the rotating planet exerts a stabilizing influence. Consequently disturbances can develop spontaneously. Presumably at least some of the markings observed on planets, especially on Jupiter, represent such disturbances. The velocity of these perturbations is found not to differ greatly from the mean velocity of the fluid on both sides of the boundary. Therefore, the determination of planetary velocities of rotation from visual observations of such surface markings appears justified.

At a sharp current discontinuity the amplitude of a perturbation increases faster, the shorter the wave length. At shear zones of finite width only those waves are unstable whose length is greater than five times the width of the shear zone, and those waves will develop most rapidly whose length is about eight times the width of the shear zone. Since in the large-scale atmospheric circulations different wind belts are as a rule separated by finite shear zones rather than by sharp discontinuities very short waves cannot develop because they are not unstable. An empirical check of the relation between the width of the shear zone and the length of the developing perturbations is discussed.

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