Polygonal patterns of cyclones on Jupiter: Convective forcing and anticyclonic shielding

32 From its unique pole-to-pole orbit, the Juno spacecraft discovered cyclones arranged in 33 polygonal patterns around the poles of Jupiter. In a related modeling study the stability of the 34 pattern depends on shielding -- a ring of anticyclonic vorticity surrounding each cyclone. 35 Without shielding the vortices merge. Here we present high-resolution measurements obtained 36 by tracking clouds in sequences of infrared images. There is vorticity of both signs at 200-km 37 scales. The standard deviation is 0.32 times the vorticity of a large cyclone, whose relative 38 vorticity is 0.46 times the planetary vorticity. Shielding exists at large scales, and it has the 39 magnitude and distance from the vortex center predicted in the model. There is horizontal 40 divergence of both signs at 200-km scales, with standard deviation 0.64 times the vorticity 41 standard deviation. We propose that these intense structures are convection and that convection 42 is the principal energy source for the large vortices.

Jupiter 15 . Saturn's northern hemisphere has a hexagon, which is a meandering zonal jet at 75° 73 whose six excursions in latitude give it a hexagonal shape 16 17 18 19 20 . But the hexagon has no 74 closed-streamline structures, i.e., no vortices, and exists by a different mechanism from the polar 75 cyclones on Jupiter.

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In a related modeling paper with some of the same authors, Li20 7 , we created cyclones 78 that have the observed gross properties -maximum velocity and radius, and arranged the 79 cyclones into polygonal patterns around the pole to see which ones are stable. This approach 80 reveals the importance of shielding -a ring of anticyclonic vorticity surrounding each of the 81 cyclones. Shielding is important in tropical meteorology. It determines whether tropical cyclones 82 merge, drift apart, or orbit each other 21222324 . In Li20 the radius of the anticyclonic ring divided 83 by the radius of maximum cyclonic velocity must be less than 4.5 in order to get a stable 84 pattern 7 . A larger ratio leads to merging and ultimately a single polar cyclone. Anticyclonic 85 vorticity is present in the models discussed earlier 891011 , but apparently it does not organize into 86 shields that are strong enough to prevent merging.

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In the present paper our measurement objective was to measure the velocity throughout 89 the north polar region at scales down to ~100 km. From the velocity field we would compute the 90 vertical component of vorticity and horizontal divergence. One goal was to look for shielding to 91 see if the theory of Li20 might apply to Jupiter. The other goal was simply to explore the hidden 92 world of small-scale motions. We found shielding, but we also discovered a world where 93 horizontal divergence and convergence rivaled the vorticity, and vorticity of both signs rivaled 94 that of the large-scale cyclones.

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The vertical component of vorticity due the planet's spin is 2Wcosq and is called f, the 99 planetary vorticity, where W is the planetary rotation rate and q is colatitude. The increase of f 100 with northward distance, df/dy = 2Wsinq/a is called b, where a is the radius of the planet. On

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Earth it causes cyclones to drift poleward 2122 . An important length scale at mid-latitudes is L b = 102 (V/b) !/# , where V is a characteristic velocity. It roughly matches the widths of the zonal jets on 103 Jupiter and Saturn 25262728 . The length scale enters in criteria for zonal jet stability 29 , and it is also 104 the scale below which the flow is dominated by turbulence and above which it tends toward 105 alternating zonal jets. With small-scale vortices as an initial condition, the flow evolves through 106 a state of propagating waves and then tends toward alternating zonal jets 30 . However, at the 107 poles, where b tends linearly to zero, a length scale based on minus its gradient g = − / = 108 2W/a 2 is more appropriate. The length scale is L g = (V/g) !/$ , and for V = 80 m s -1 it is about 109 10,500 km. L g represents the radius of the circle around the pole inside of which the effect of the 110 vortices -turbulence --is greater than the effect of b and the jets. Note that L g is the distance

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The ratio of divergence to vorticity at 150-300 scales also points to convection. In units What to do next? On the observation side, we will pursue the brightness power spectrum 305 vs. spatial scale and the covariances of vorticity, divergence, and infrared brightness. The latter 306 has a resolution of ~16 km, and the derived divergence and vorticity have a resolution of ~100 307 km. Low brightness is an indicator of high clouds, which could be a sign either of upward 308 velocity or upward displacement. That effort is a separate paper and has been submitted 50 . We 309 will study Jupiter's white ovals, which also have been observed by JIRAM 51 . On the theory side, 310 one should revisit the polar vortex models that are forced by small-scale convection 891011 .

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Although lacking a beta effect, there are models that produce large scale vortices from small-312 scale convection in rapidly-rotating fluids 5253 , and that too should be pursued.

314 315
Methods 316 317 Table S1 in the SI gives the archival filenames and our working names for the 48 images  and knowing its r, we did two separate least squares fits, in both cases for the five an coefficients 367 in Eq.
(2) 370 371 For a good fit, the parameter r0 must be close to the radius of the velocity maximum. It was 372 chosen to be 1060 km for ∂ϕ F ∂r ⁄ and 1200 km for v D. We analytically integrated the expression 373 for cyclostrophic balance starting from ϕ F = 0 at r = 0 to get ϕ F (r) in Figure 4, and we analytically 374 differentiated the expression for velocity to get ζ ̅ (r  Infrared image of the northern hemisphere as seen by JIRAM 2. The circle at 80° latitude is about 12,000 km from the pole. The radiances have been corrected for nadir viewing, with bright yellow signifying greater radiance and dark red signifying lesser radiance. Because of these corrections and the nonlinearity of the Planck function, one can only say that the average brightness temperature is somewhere in the range 215-220 K. The gures shown in this paper cover the central cyclone and the two cyclones at 135° and 315° east longitude, respectively. The two dark features at 120-150° east, whose laments spiral toward their centers in a clockwise direction, are anticyclones.

Figure 2
Vorticity (top row) and divergence (bottom row) derived from two determinations of the wind eld using separate data (left and right), termed n0103 and n0204. The long dimension of each rectangle is ~20,000 km, and the smallest features are ~100 km in diameter. Each determination is derived from a series, each of which consists of 12 adjacent images laid side by side. The seams between the 12 images are visible as faint vertical lines. The white spaces are regions where the image entropy36 was below a threshold needed for reliable cloud-tracked wind analysis. They cover 1.8% and 2.1% of the pixels in the left and right maps, respectively. For further information, see the Methods section Histograms of vorticity (left) and divergence (right) for the maps shown in Figure 2. The vorticity and divergence scales are the same, and the colors are the same as those used in Figure 2. The number above each color bin is the percentage of pixels in that bin.

Figure 4
Mean azimuthal velocity and vorticity (top row) and mean gravitational potential and potential vorticity (bottom row). The tted curve for velocity (blue) is almost covered by the data points (black). Please see manuscript .pdf for full caption.

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