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Plethora of Cyclones
Around Jupiter's Poles
The NASA space probe Juno has sent back amazing views of Jupiter, in particular the one of the crowd of cyclones in Jupiter's South Polar region.
A cylone is a mass of atmospheric gases rotating about a vertical central axis. It thus has angular momentum. It also has angular momentum due to its movement with its planet's rotation. Since the cyclone's spin axis remains perpendicular to its planet's surface it is precessing as the planet turns. The effect of this forced precessing is to create a torque on the cyclone which causes it to move toward its planet's pole where its spin axis is aligned with the spin axis of the planet. The torue becomes less as the spine axis of the cyclone gets closer to the spin axis of the planet. If the cyclones endure there will be accumulations of cyclones in the polar regions.
Here is a map of the paths of Earth's hurricanes (tropical cyclones in the western North Atlantic).
Similar patterns prevail for tropical cyclones (under different names, such as typhoons) in different regions.
Tornadoes, although much shorter lived and thus travel a shorter distance, show a similar northeasternly pattern. This is shown below for the tornadoes of Oklahoma, Kansas and Nebraska.
So it is not surprising that cyclones gravitate toward the poles. What is surprising is that the cyclones on Jupiter endure under the intense interactions which might occur under such conditions. It must have something to do with the density and viscosity of Jupiter's atmosphere and the fact that Jupiter rotates more than twice as fast as Earth. But the force on a cyclone becomes weaker on the cyclone the closer it gets to the pole.
The equation governing the dynamics of vortices is
where L is the angular momentum of the vortex with repect to its spin axis, The torque τ is the product of the force F on the vortex and the distance r between the center of mass of the vortex and the center of precession.
The equation works both ways. If one end of a toy gyroscope is placed on a pivot point then its weight creates a torque and the gyroscope precesses. If a body possessing angular momentum is forced to precess then a torque on it is created with respect to the center of precession. That torque causes the angular momentum vector to move toward its alignment with the spin axis of the precession.
More details of the mathematics of forced precession of angular momentum are given in Hurricanes.
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