Jupiter-style Jet Stability

Abstract

Abstract Studies of Jupiter’s zonal jets, facilitated by the two Voyager flybys, the Galileo entry probe, the Cassini flyby, and the Juno orbiter have led to two fundamental insights into inviscid shear stability that have implications for a wide range of large-scale fluid systems involving alternating shear instability. The first insight is that the analog of the Mach number for vorticity (Rossby and drift) waves, “Ma,” ensures shear stability via the criterion “Ma”−1 < 1, which includes both Kelvin–Arnol’d branches of stability, and is edged with a shock. A surprise is the well-studied first branch (KA-I), which includes as special cases the textbook shear stability theorems of Rayleigh, Kuo, Charney–Stern, and Fjørtoft, merely corresponds to “Ma”−1 < 0. The second insight is that Jupiter’s tropospheric jets achieve stability via a second branch (KA-II) strategy, a 3/4 layer, undulating control surface supplied by the dynamic topography of the planet’s deep jets, which maintains “Ma”−1 ≲ 1 via stretching vorticity. The deep jets are similarly stabilized by the spherical shape of the planet itself. Although Jupiter-style zonal jet stabilization is precluded by the torus geometry used in hot-plasma fusion reactors, it is directly applicable to the tube with ends geometry used in cool-plasma applications, including antimatter storage at high-energy colliders. In general, the lessons learned from analyzing Jupiter’s jets eliminate much of the guesswork from predicting and controlling inviscid shear instability.