Long-term tracking of circumpolar cyclones on Jupiter from polar observations with JunoCam

Icarus 335 (2020) 113405

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Long-term tracking of circumpolar cyclones on Jupiter from polar observations with JunoCam

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F. Tabataba-Vakilia, , J.H. Rogersb, G. Eichstädtc, G.S. Ortona, C.J. Hansend, T.W. Momarya, J.A. Sinclaira, R.S. Gilesa, M.A. Caplingere, M.A. Ravinee, S.J. Boltonf ⁎

a

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA British Astronomical Association, London, UK c Independent Scholar, Stuttgart, Germany d Planetary Science Institute, Tucson, AZ, USA e Malin Space Science Systems, San Diego, CA, USA f Southwest Research Institute, San Antonio, TX, USA b

ABSTRACT

We use observations from the JunoCam instrument on the Juno spacecraft to map the polar regions of Jupiter between 2016 and 2018. These polar maps track the long-term evolution of the pentagonal and octagonal structures of circumpolar cyclones (CPCs). The south-polar pentagonal and north-polar octagonal arrangements of the CPCs have remained largely stable over the last 2 years of observation. The morphologies of individual cyclones also remain largely stable for 1–2 years, although some changes are observed, so that the location of each CPC is uniquely identifiable. At both north and south poles, individual cyclones move around the center to a limited extent, and there is a gap of variable width between one pair of south polar CPCs. Measurements at consecutive closest approaches (perijoves, 53 days apart) show small movements of individual cyclones both eastward and westward. However, the south-polar CPCs have a long-term systematic westward drift rate of 1.5 ± 0.2° per orbit or 0.040 ± 0.005 m/s, whereas north polar CPCs do not show a consistent drift in longitude. Around the perimeter of the southern pentagon, we detect no rapid jet in short-term animations, and we provide evidence that anticyclonic white ovals may have a range of longitudinal drifts between −44 and +15° per orbit (+1.8 to −0.7 m/s). Measurement of the angular velocities within the cyclones shows increasing angular velocity with decreasing radius, except in the inner bright cloud deck of one class of northern CPCs, which are inferred to have smaller or even negative angular velocities very near the center. Tangential wind velocities within the cyclones range up to 100 m/s (and even > 100 m/s in the southern polar cyclone) and are maximal between radii of ~900–1600 km. Overall, we find that the behavior of the polar cyclones constellations compares well to vortex crystal theory, even though the theory does not include anticyclonic vorticity.

1. Introduction One of the scientific goals of the Juno mission to Jupiter is to provide unique views of the polar regions of Jupiter (Bolton et al., 2010). Polar observation is possible around the time of the closest approach to Jupiter, or perijove (PJ), of Juno's 53-day elliptical polar orbit. Both the optical (JunoCam, Hansen et al., 2017) and infrared (Jupiter Infrared Auroral Mapper – JIRAM, Adriani et al., 2017) instruments on the spacecraft have discovered constellations of circumpolar cyclones (CPCs) around the poles of Jupiter (Orton et al., 2017; Adriani et al., 2018). These CPCs have been characterized as mostly stable configurations of eight and five cyclones, distributed around the geographical north and south poles respectively, each with a central cyclone located in close proximity to the pole. While theoretical models of the polar regions of the Jovian atmosphere have long predicted turbulent motions and even multiple cyclones irregularly orbiting the poles (e.g. Cho

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and Polvani, 1996; Theiss, 2006; O'Neill et al., 2015), the discovery of a regular geometric constellation of cyclones was unexpected. Current literature identifies a similarity of the CPCs to the phenomenon of vortex crystals (Adriani et al., 2018; Grassi et al., 2018). These vortex crystals are a phenomenon occurring in turbulent 2-dimensional fluiddynamical systems such as magnetized electron columns (Fine et al., 1995). An analysis of further polar observations is necessary to characterize the long-term evolution and stability of the circumpolar cyclone constellations and compare these to vortex crystals, extending the work of Orton et al. (2017) and Adriani et al. (2018) to include observations covering the first 15 orbits of the Juno mission. The remainder of this paper is arranged as follows. Section 2 summarizes the methods used to transform the JunoCam images into the polar projection maps that are the basis of this work. Section 3 describes the motion of the CPCs over the first two years of the Juno mission, with emphasis on the south polar region as this was imaged more

Corresponding author. E-mail address: [email protected] (F. Tabataba-Vakili).

https://doi.org/10.1016/j.icarus.2019.113405 Received 16 April 2019; Received in revised form 22 July 2019; Accepted 3 August 2019 Available online 15 August 2019 0019-1035/ © 2019 Published by Elsevier Inc.

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thoroughly than the north. Section 4 reviews the morphological features of the individual cyclones. Section 5 considers whether there is any systematic flow around the perimeter of the south polar pentagon. Section 6 reports our measurements of the wind velocities of the cyclones, with separate assessment of the two classes of northern CPCs and the southern CPCs. Section 7 discusses the variation of the wind speeds with radius and how these observations may be understood in terms of physical models. Preliminary accounts of some of these results were presented by Rogers et al. (2018) and Tabataba-Vakili et al. (2018).

for conclusions from JunoCam map products. We have tested the effects of various possible pointing errors for the south pole images taken at highest sub-spacecraft latitude (minimum emission angle), after manual limb-fitting, and find an uncertainty of < 0.2° in the south pole positions. These errors show up in small translational and rotational displacements near the pole, but with no significant shear. Thus, the mapping appears to be robust against all residual pointing issues that we have considered. There could be larger errors in images taken from lower sub-spacecraft latitudes, including the later outbound images which are used to identify CPCs at lower resolution that were not illuminated earlier. Our polar maps are assembled by manually merging polar projection maps of multiple single images, commonly covering up to 2 or 3 h while Juno is outbound viewing the south pole, and a shorter period inbound for the north pole, and thus covering a wider longitude range as the planet rotates. Random inaccuracies in the pole position can be assessed by measuring the scatter of South Pole positions in these composite maps. This was done for four perijoves, finding that 26 out of 30 (87%) of positions were within 0.18° latitude of the mean pole position, and 29 out of 30 (97%) were within 0.28°. The small scatter shows that the uncertainties are less than the variations in position of the SPC. Systematic uncertainties that might have been present at early perijoves, when our processing procedure was still under development, were excluded by repeating, for each perijove, the map projection closest to the south pole using our final processing procedure; all pole positions were within 0.20° of the original determinations. While most JIRAM measurements (Adriani et al., 2018) are consistent with our JunoCam measurements, there is a discrepancy of 0.9° in the latitudinal position of the south polar cyclone during PJ5 (see Section 3.1). Both instruments may have a systematic error in locating the geographical pole. In the JIRAM maps an apparent translational movement in the same direction was noted for all observed CPCs when comparing PJ4 and PJ5 (see Adriani et al. (2018), their Extended Data Fig. 1, lower), and within PJ4 (Grassi et al., 2018), suggesting that pole determinations from JIRAM also have some uncertainty.

2. Images and image processing JunoCam is a visible camera with a 58°-wide field of view. The CCD is covered by four roughly adjacent filter strips that span the 58°. JunoCam is a “push-frame” imager, relying on spacecraft spin to build spatial and spectral coverage without camera mechanisms. Images are taken at a rate of about 3 frames/s as the spacecraft spins at a nominal 2 RPM. Each image is acquired in broadband blue, green, and red filters, or in a narrow-band filter centered on a strong band of methane absorption at 889 nm. The blue, green and red filter strips are about 150 pixels (or about 5°) tall and the methane about twice that. Time-delayed integration of multiple pixel rows is used to build up signal-to-noise ratio for one image, effectively increasing its exposure time. Each resulting image covers a different area of the planet with each of the four filter strips, and the whole planet is covered in all bands by successive images, each of which is taken from a different spacecraft position and orientation. The JunoCam instrument and its operation are detailed in Hansen et al. (2017). 2.1. Processing The transformation of these raw images into maps of the planet requires knowledge of the time each image was acquired, the position and orientation of the camera at those times, and the geometric properties of the camera optics and sensor. The standard model in the planetary science community for such coordinate transformations is the SPICE system (Acton, 1996). Unfortunately, at the start of the Juno orbital mission the supporting SPICE data for JunoCam (especially its image timing, orientation in the spacecraft coordinate frame, and optics distortion) was still being determined from cruise imaging, and the prelaunch data contained significant errors. The work described here uses maps produced using an independently-developed processing pipeline. Manual limb fitting was used to constrain the camera timing, orientation and optical properties. Our best current SPICE data show generally good agreement with these maps, although refinement is still in progress. Since the contrast of Jupiter's cloud tops is mostly subtle, a reflectance distribution function is applied to divide away most of illumination-induced brightness. Gamma stretching (applying a non-linear function to the intensity to emphasize faint or bright features) of each of the three RGB color channels of the resulting flattened image improves contrast of the map. All maps are relative to the IAU System III (L3) definition of prime meridian with westward increasing longitude and the IAU spheroid definition (Archinal et al., 2018).

3. Determination and evolution of cyclone positions Fig. 1 shows typical JunoCam maps of the south polar cluster of cyclones. It shows the five CPCs (numbered 1–5) forming a pentagon around the central south polar cyclone (SPC), but with two permanent asymmetries. The overall CPC structure remains pentagonal over the observed time, but there is always a gap between CPCs-s1 and s2 (‘s’ for south), and the SPC is always offset from the pole towards the gap. (The maps for all perijoves 1–15 are shown in Suppl. Fig. S1.) We measure the pixel positions of the CPCs in the polar-projected maps of the observations for each perijove (PJ), the closest approach to Jupiter of the spacecraft's 53-day orbit, with times and dates of each PJ given in Table 1. From these CPC pixel positions we can then calculate longitudinal and latitudinal positions of the CPCs with regard to both the south pole and the central CPC. Both quantities are given in units of degrees and latitudes are given in planetocentric coordinates. Most of our results are from the south polar region as the south pole has been in sunlight throughout the Juno mission. At the north pole, although JunoCam can view the eight circumpolar cyclones, the central cyclone and the pole itself are currently in darkness. The existence of the northern central cyclone is known from JIRAM data (Adriani et al., 2018). The estimated errors of the positional measurements are connected to both the systematic error of determining the position of the south pole during image processing (see Section 2.2) and the uncertainties of visually determining the center of each CPC in the polar-projected maps. The error of the coordinates of the south pole is estimated at around 0.3° (equivalent to 9 pixels). The visual determination of the center of a CPC is uncertain due to their somewhat irregular shapes. For a clearly visible CPC we estimate an error of ± 5 pixels in the polar

2.2. Camera model and propagation of model errors Geometrical JunoCam calibration is based on the Brown-Conradydistorted family of pinhole-camera models. There is a possibility of slight misalignment of the modeled camera optical axis relative to the spacecraft spin axis. Also, image time data are subject to significant uncertainty. For these reasons there could be systematic errors in the camera pointing which would affect the map projections, particularly the positions of the poles. To minimize these, manual limb-fitting was performed. Nevertheless, residual pointing errors need to be considered 2

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Fig. 1. Polar-projection maps of the Jovian south polar region at PJ9 and PJ 12, from multiple merged JunoCam images, down to 75°S (all latitudes are planetocentric). System III westward longitude (L3) is marked, with zero meridian (L3 = 0) to the left. Resolution is lower in longitude sectors that were only imaged late in the outbound trajectory as they became illuminated. CPCs are numbered in yellow (0 = SPC). In the PJ12 map, the sinuous bright colored band is a long-lived haze band that was illuminated when near the terminator. For maps of all perijoves, see Suppl. Fig. S1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

recurring behavior with a period of 6 PJs (or roughly 320 days). When plotted in polar projection (see Fig. 2c, d) this periodicity is revealed to be an approximately circular motion in counter-clockwise direction (see Suppl. Animation SA1). It is unclear whether the circular motion continues after PJ15 or diverges towards a westward drift. More measurements are needed to identify the long-term periodicity of this motion.

Table 1 List of perijoves with dates and times. Perijove 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Date 2016 August 27 2016 October 19 2016 December 11 2017 February 2 2017 March 27 2017 May 19 2017 July 11 2017 September 1 2017 October 24 2017 December 16 2018 February 7 2018 April 1 2018 May 24 2018 July 16 2018 September 7

SCET (UTC) 12:50:44 18:10:54 17:03:41 12:57:09 08:51:52 06:00:47 05:54:42 21:48:50 17:42:31 17:56:59 13:51:30 09:45:43 05:40:09 05:17:39 01:11:57

3.2. Tracking of south circumpolar cyclones It is evident from inspection of our maps (see Fig. 1 and Suppl. Fig. S1), and confirmed by our measurements (see Fig. 3), that the five southern CPCs retain individual identities and approximate positions over many perijoves. We therefore continue to use the numbering from Adriani et al. (2018). It is also evident from the measured positions that they are not centered around the pole, but around a location closer to the SPC (Fig. 3a). Therefore, in the following analysis of their positional evolution, we recentered both longitudinal and latitudinal distances of the measured CPCs positions around the positions of the SPC. From here on, all longitudinal and latitudinal distances are given relative to the SPC. This means that instead of looking at the vector pointing towards the i'th CPC vCPCi in planetocentric System III coordinates (westward longitude, planetocentric latitude), we derive our distances from VCPCi = vCPCi-vSPC starting with Fig. 3b. This figure depicts the results of our measurements of the CPC positions and their evolution. These measurements show that the overall CPC structure remains pentagonal over the observed time and that each CPC varies its position only slowly in the 53 days perijove observations. We are confident that we are identifying and labeling the same CPCs during each perijove measurement due to the slightly asymmetric distribution of the CPCs. While the average longitudinal distance between the other CPCs is between 63° and 71° (see Fig. 4b–e), the gap between CPCs s1 and s2 has an average width of 97° (see Figs. 3b, 4a). This gap can be identified in each observation and is located roughly between 150° and 250° longitude. The regularity of the gap's position makes it unlikely for the pentagonal structure to rotate by a multiple of 72° during subsequent perijove observations. Fig. 4a depicts the evolution of the width of the gap between CPC s1 and s2. The gap narrows and widens with time, varying strongly between 80° and 120°. The gap has maxima in width during PJ1, 8 and 12 and minima during PJs 3, 11 and 15. From this no overall periodicity can be discerned. Data up to PJ12 did show a correlation between the width of the gap and the latitude of the SPC, in that the gap was wider when the SPC was further from the pole, and thus more displaced in the

projection maps. CPCs that are less well resolved (in that only their outlines are visible) receive a larger error estimate of ± 25 pixels. In those cases where a CPC cannot be made out, the data point is omitted. The error of the distance between two points (e.g. south pole and CPC) propagates from the error of each point. In the case of longitudinal distance, the error propagation is roughly estimated from moving the points by the error value in permutations of all principal directions and taking the mean of the resulting angles. For the latitudinal distance, we calculate a standard deviation from the variances of the two points. 3.1. Movement of the central south polar cyclone Fig. 2a depicts the evolution of the offset of the central south polar cyclone (SPC) from the south pole position in degrees latitude. This distance is seen to vary between 1° and 2.5° latitude. There are two minima that occur in observations around PJ4 and 10. The maximum distance of 2.5° latitude is reached once at PJ7. From PJ12 and onward the latitude of the SPC has remained mostly constant. During the timeframe from PJ12 to PJ15 the SPC moves steadily in westward direction from 215° to 250° (see Fig. 2b). On average the longitude of the SPC is 225°. It varies substantially between 200° and 250° longitude, which corresponds to a distance of 2000 km at 88° latitude. Our measurements covering 14 perijoves suggest a periodicity of the central CPC's location. The longitude of the SPC evolves in a sawtoothlike pattern with maxima at PJs 3, 9, 15. In addition, the latitudinal distance from the pole has minima at PJs 4 and 10. This hints towards a 3

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a) Latitudinal distance from pole

b) Longitude

c) Polar map PJ1-9

d) Polar map PJ9-15

Fig. 2. Motion of the center of the south-polar cyclone (SPC) relative to the south pole, from PJ1 to PJ15 (cf. Suppl. Animation SA1). a) Planetocentric latitude of the SPC. b) Longitude of the SPC in System III. The filled squares at PJ4 and 5 represent measurements for JIRAM observations published by Adriani et al. (2018). c) Polar-projected map of the SPC location for PJ1–9. d) Polar-projected map of the SPC location for PJ9–15.

direction of the gap. But since PJ12, the gap has been shrinking, while the SPC has remained far from the pole. From PJ12 onward the gap in Fig. 4a has been monotonically shrinking down to its lowest value of 83 ± 10°. During this time the distance between CPCs s2 and s3 (see Fig. 4b) reaches a similar value. However, the position of CPC-s2 during this timeframe is difficult to determine due to blurriness. It is, therefore, unclear whether this means that the gap between CPCs s1 and s2 is narrowing, or whether the gap between CPCs s2 and s3 (or two other CPCs) will widen again. Further perijove measurements are required to determine the future evolution

a)

of the gap. 3.3. Drift of south circumpolar cyclones When looking at the cyclone positions separately, a systematic drift can be identified (see Fig. 5). The average drift over the whole observation period is determined by a linear least squares fit of the locations for each cyclone. This results in average drift rates that vary between 1.14 and 1.87°/PJ. Averaging over the five cyclone drifts, we find that the overall CPC structure is rotating about the south pole with Fig. 3. a) Polar-projected chart showing the tracks of all the southern CPCs relative to the south pole, from PJ1 to PJ15 (cf. Suppl. Animation SA1). The longitude scale is System III and the latitude scale is planetocentric. b) Positions of the southern CPCs in a longitude system centered on the SPC, with zero meridian parallel to that of System III. Missing values indicate observations where the respective CPC is not visible. Larger error bars indicate observations where the CPC is visible, but its center is not well defined or blurry. The filled squares at PJ 4 and 5 represent the measurements by JIRAM published by Adriani et al. (2018).

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Fig. 4. Angular distance between adjacent southern CPCs in a longitude system centered around the SPC, with zero meridian parallel to that of System III. Missing values indicate observations where the respective CPC is not visible. Larger error bars indicate observations where the CPC is visible, but its center is not well defined or blurry. The horizontal light blue line depicts the mean value of the gap width. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

1.5 ± 0.2°/PJ. The drift rate of 1.5 ± 0.2°/PJ is considerably smaller than the inherent cyclonic wind speeds of the CPCs. Assuming a planetocentric latitude of 84°S, the drift speed of 1.5 ± 0.2°/PJ is equivalent to 0.028 ± 0.004°/day or 0.040 ± 0.005 m/s. This drift rate is of similar scale as the mean drift rate of the hexagonal feature on Saturn's north pole measured as 0.0128 ± 0.0013°/day between 2008 and 2014 (Sánchez-Lavega et al., 2014). According to Grassi et al. (2018), the south polar CPCs have a maximum wind speed between 80 and 90 m/s. Hence, cyclonic motion strongly outweighs the CPC drift rate, making the pentagonal CPC structure a dynamically stable feature. On the south pole, cyclonic motion rotates clockwise. Our westward drift speed is anti-clockwise and thereby opposed to the sense of direction of the cyclones. While the average drift rates of all the CPCs are comparable, a detailed look shows that their individual time evolution has differences. Especially CPCs s1, s2, and s5 demonstrate a large variability in their locations. At times each of these cyclones is seen to move in a

retrograde direction by up to 10° longitude. Fig. 6 shows the drift rate of each cyclone averaged between three perijoves (i.e. two drift rate measurements). For this calculation the empty data points are filled in with interpolated values of the CPC location. The instantaneous drift rate varies strongly between +7 and −7°/PJ signifying that the drift of the CPCs has a certain “wobble”. It is apparent that there is a correlation between the drift rates of CPCs s1 and s5, being negative between PJs 4 and 6, positive between PJs 8 and 10, negative at PJ 11, and positive during PJs 12 and 13. A similar but weaker correlation can be seen for CPCs s2 and s3, especially from PJ 8 to 13. A possible interpretation of this behavior is connected to the gap between CPCs s1 and s2. The gap could provide more freedom of movement for CPCs s1 and s2. In the event that e.g. CPC s1 shortens the gap, CPC s5 has more freedom of movement as well and is able to move towards CPC s1. Another possibility is that CPCs push against adjacent CPCs and in the case of CPC s5 or s3, a push against CPC s1 or s2 is met with less resistance as these can move towards the gap. A strong 5

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Fig. 5. Similar to Fig. 3 but positions are shown for southern CPCs s1 through s5 separately. The average drift rate was determined using a linear least-squares fit (dashed line). Averaging the drift rate of all CPCs results in a total average drift rate of 1.5 ± 0.2°/PJ (cf. Suppl. Animation SA1).

argument why the gap could be involved here is that CPC s4 has a drift rate that varies only slightly from its average value. This is likely connected to its lower freedom of movement from being farthest from the gap. The short-term variations in the drift rate of individual CPCs vary by ± 7° longitude between perijove measurements. With a temporal resolution of one perijove measurement per 53 days, this variation could be much greater and the real instantaneous drift rate of the CPCs is inconclusive. However, even if CPCs drift at a higher rate than detected, our long-term measurements over the last 2 years show that the evolution of the CPCs is a slow drift with variable distances between CPCs. Overall we find that the south polar constellation of CPCs remains a stable phenomenon, and is rotating slowly with a mean drift rate around the pole of about 1.5 ± 0.2°/PJ observation in retrograde direction.

3.4. North circumpolar cyclones The north pole is not visible in our observations due to the absence of illumination during current north-polar winter. Jupiter's axial tilt is 3.1° and the solstice was in April–May 2018. Only at PJ1 did JunoCam's images show the fringe of the central north polar cyclone (NPC) as identified by JIRAM (Adriani et al., 2018). Therefore, the accuracy of our north pole positions is not well constrained. However, JIRAM data at PJ4 (Adriani et al., 2018) showed that the octagon was symmetrical around a point 0.5° from the pole, and our own maps do not suggest any larger latitudinal offset. Assessment of any motion of the CPCs relative to the North Pole is uncertain for the same reason. JunoCam currently views less than half of the octagonal constellation at each perijove. Juno's mission is planned such that each group of successive four orbits fall at intervals of 90° in L3 (System III longitude), so it takes four orbits to get a goodquality map of the whole constellation. The quartets so far are: PJ1, 3, 4 6

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individual CPCs have retained their individual morphologies over that time span. The changes in positions are minor, and can be modeled (non-uniquely) by assuming rotation of the cluster around the pole, as well as some individual motions. The overall rotation of the cluster in L3 can be estimated by comparing the composite maps made for each quartet of successive perijoves: from PJ1–5 to PJ6–9, rotation of −4 to −5°; from PJ6–9 to PJ10–13, +2°; and a further +4 to +5°of rotation is apparent from PJ13 to PJ14. There appears to be slight irregularity in positions of single CPCs and rotation of the pattern, not surprising given the turbulent surroundings; however, there is no evidence for large lateral displacement of the pattern relative to the pole. To assess the motion of the octagon more systematically, we measure the longitudinal positions of the individual CPCs for each perijove when they were visible (see Fig. 8a, or Suppl. Fig. S3 for detail). This does not reveal a consistent linear drift of the CPC constellation over the whole timeframe. However, it does confirm the general trends noted above. For CPCs with well-established longitudes spanning most of the time from PJ1 to PJ8 (CPC-n1, n3, n5, ‘n’ for North), the average longitudinal drift was either zero or slightly negative (eastward), and sparser data for other CPCs are mostly consistent with this. But from PJ8 onwards, all CPCs showed net positive (westward) drift, at average rates ranging from +1.0 to +2.5°/PJ, and some at even faster rates

Fig. 6. Drift rate for each CPC, from a moving average over 3 perijove measurements ( ± 1 PJ).

and 5; PJ6–9; and PJ10–13 (see Fig. 7). Maps of individual perijoves are shown in Suppl. Fig. S2. Nevertheless, it is evident that the pattern did not change nor move greatly relative to L3 from PJ1 to PJ14, as

Fig. 7. North polar projection maps of the CPCs composited from quartets of perijoves (PJ1-PJ5; PJ6-PJ9; PJ10-PJ13), plus PJ14 with PJ15. Within each set, the longitudes of successive sub-spacecraft tracks were spaced at 90° intervals. A scale of westward System III longitude (L3) is given in panel (a), and planetocentric latitude in (d). Within each panel, the first map is shown with L3 = 0 to the left, and some of the subsequent ones (indicated by asterisk at PJ number) have been rotated by a few degrees and/or translated by several pixels to optimize the register of the CPCs. Multiple colored crosses mark the north pole positions of the component maps. CPCs are labelled in yellow on their outer edges. For individual maps see Suppl. Fig. S2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 7

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Assuming that the central NPC is still present at the pole, CPCs n6, n7, n8 and the NPC form a nearly-square rhomboid of cyclones surrounding the anticyclone. So the octagon is still intact, but with one corner distorted by this anticyclone. The anticyclone could be the same one that JIRAM identified at PJ4 and PJ5 (Adriani et al., 2018). JunoCam has recorded it in this corner, north of CPC-n7, whenever CPC-n7 has been presented within < 40° of the noon meridian (PJ-5, 9, 11 and 16; Fig. 9), and not otherwise; no such features are recorded in other corners of the octagon. Its anticyclonic sense was clearly shown by rotation in map animations (PJ9, Suppl. Animation SA7) or by spiral structure (PJ16, Fig. 9).

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4. Cyclone morphology and evolution At both poles, the CPCs show a range of internal structures. Trailing spiral arms, of variable thickness and coherence, dominate the outer one-third to two-thirds (by radius). The inner one-half to one-third (by radius) usually has a different appearance. Only in one or two south polar CPCs does the cyclonic spiral structure penetrate close to the center. In at least 3 cases, images show possible anticyclonic eddies entangled in the cyclonic spiral arms of the CPCs (see Suppl. Fig. S1b, PJ12, A5; PJ13, A2; Suppl. Fig. S1c, PJ15, A2). Color information is limited due to the low sun angle and overlying haze, but the CPCs consistently appear reddish relative to their surroundings. The north polar CPCs fall into two types, ‘filled’ and ‘chaotic’, which alternate around the octagon (which is therefore also termed a ditetragon). In their inner parts, the CPCs do not have an evident cyclonic spiral structure. Instead, the inner part of the ‘chaotic’ type mostly consists of small-scale cloud streaks and flecks. The inner part of the ‘filled’ type is a large, sharply-bounded, lobate area, which is bright white near the edge but reddish-brown inside and appears to be a continuous cloud deck except for several dark spots which could be holes in the clouds. Sharp junctions between bright and dark parts suggest clouds with vertical structure, and in a few examples, there are points where streaks of the white cloud appear to overlap both the reddish cloud and a dark spot (see Fig. 10a, red arrow). In the central reddish cloud deck of the larger ‘filled’ CPCs, there are often tenuous spiral streaks in opposite sense to those in the periphery (see Section 6.2.2). At the center of the filled CPCs there is a pale whitish disk, usually ~800–1200 km in diameter, sometimes centered on a dark disk, within which irregular white clouds can be seen. Some of the chaotic CPCs also contain a central dark or white disk, ~200–400 km in diameter. The morphologies of the individual CPCs within each cluster have only shown modest changes between PJ1 and PJ14. Details are listed in Suppl. Table S1 and summarized here. In the north, the four filled cyclones have not shown any major changes: CPC-n5 has always been the largest, CPC-n3 and n7 are also large, and CPC-n1 has a smaller core than the others. The four chaotic cyclones have also retained their main characteristics (insofar as we can monitor them): CPC-n4 has always had a ‘filled’ core, though of variable size; CPC-n2 and n8 are finetextured spirals, though the center of CPC-n2 is variable; and CPC-n6 is the most poorly formed, though a tiny round bright region is sometimes resolved, confirming that it is similar to the other coherent cyclones. In the south, all six CPCs have extensive fine-scale spiral structure in their outer parts (see Suppl. Table S2). Where spiral structure is present in the inner parts it is always in the same cyclonic sense. The six CPCs differ in size and in appearance. Some of these individual characteristics have evolved on a timescale of about one year (~7 perijoves) or more, while others have not changed in two years. CPC-s4 is always the largest or equal largest, and often oval, whereas CPC-s2 is always the smallest or equal smallest, except that the SPC is occasionally smaller. CPC-s2 and s3 both included a large dark annulus for more than a year, but then evolved to different forms from PJ12 onwards. CPC-s1, s4 and s5 are all large, fine-textured spirals, with whitish central regions that often appear flocculent (containing scattered white clouds). The SPC

b)

c)

Fig. 8. a) Longitudinal position of the north polar CPCs in System III. Missing values indicate observations where the respective CPC was not visible. Locations of each CPC are plotted separately in Suppl. Fig. S3. b) Polar map of northern CPC positions. c) Latitudinal positions of northern CPCs.

over intervals of only a few perijoves. So the net movement from PJ1–4 to PJ14–15 ranged from zero to +8° in L3, except for CPC-n7 with a net movement of 15°. While most northern CPCs remain in their latitudinal position, we find that CPCs n6, n7, and n8 vary substantially in latitude (see Fig. 8b). Fig. 8c shows that the latitudinal position of CPC n7 moves away from the north pole by about 1.5°, while CPCs n6 and n8 move closer to the pole by 1.0 to 1.5°. At PJ15, CPC n7 is subject to a substantial westward shift in longitude by +10°. This is not a measurement error, since the positional shift has remained stable for PJ16 (see Fig. 9). At PJ16, CPC-n7 was well presented and was still south of the expected latitude, and the images showed a likely explanation of its displacement. The images showed an anticyclonic oval north of it (Fig. 9). 8

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Fig. 9. Displacement of northern CPCn7 with an anticyclone north of it. Excerpts from north polar projection maps at four perijoves, with L3 = 0 to the left; the red cross marks the north pole and a latitude scale is at top right. The CPCs are numbered and the anticyclonic oval is indicated (AO). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

always had a large dark annulus or core, up to PJ14. There was a central white oval (PJ1–8), evolving to a darker center (PJ10–14) though with some light patches. But at PJ15 the central half of the SPC was light and unresolved except for a small dark central bright region. The sizes of the CPCs remain close to the ranges reported by Adriani et al. (2018), with radii of around 2000–2500 km for the northern CPCs and 2800–3500 km for the southern CPCs. These values do not include tenuous outer spiral fringes which add about 1000 km to some diameters (see e.g. Suppl. Tables S1, S2). The Rossby deformation radius LD in Jupiter has been estimated to be between 800 and 1000 km in the polar regions of Jupiter (Read et al., 2006, their Fig. 13). The radii of the CPCs are larger than LD by a factor of 2 to 3.5. This difference is not surprising as the supercritical latitude (Schneider and Walker, 2006), where the LD becomes smaller than the Rhines lengthscale, is in the mid-latitudes on Jupiter. Northward of that latitude, LD does not control the energy-containing lengthscale (see e.g. Chemke and Kaspi, 2015; Wang et al., 2018).

region, at each perijove there are several small AWOs adjacent to the pentagon around 800S, albeit not in any consistent pattern. Here, as elsewhere on Jupiter, AWOs are white ovals with smooth texture and outline, in contrast to the more complex cyclonic structures. In the JunoCam images, AWOs can often be identified by the sense of spiral streaks around their perimeters, and sometimes by motions revealed in our animations (Suppl. Animations SA2, SA5, SA6). Even in the lowerresolution outbound images, they can often be identified by their white oval shape alone. We suggest that some of these AWOs can be tracked over multiple perijoves (see Fig. 11 and Suppl. Fig. S1). In many cases an AWO can be seen in nearby locations at two successive perijoves, sometimes with no others in the vicinity. Under the assumptions that sightings of an AWO at two successive perijoves in nearby locations represent the same longlived feature, and that the AWOs move slowly enough to not circumnavigate the pole within the 53-day interval between two perijoves, we can obtain values for their drift rates and thus estimates for the wind velocities in this region. With these assumptions, we can identify most of these AWOs over multiple perijoves. Four AWOs were tentatively identified from PJ1 or PJ3 to PJ6, labelled ‘A1’ to ‘A4’ in Fig. 11 and Suppl. Fig. S1, in some cases nearly stationary, and in some cases drifting eastwards around the perimeter of the pentagon, in the same direction as the circulations of the CPCs, but at slow and irregular speeds. The largest of these movements between a pair of perijoves was −44° in L3 (1.8 m/s); next were three intervals with an average of −28.8 ± 1.3°/PJ in L3 (1.29 ± 0.05 m/s). At PJ7 or PJ8, three of the previous four AWOs were lost, either disappearing or being replaced by several even smaller ovals, but one (labelled A2) seems to have remained stationary and then slowly drifted westwards with a mean speed of +15°/PJ or 0.67 m/s (possibly influenced by adjacent cyclonic FFRs) until PJ11. Thereafter, if the identification is correct, it may have drifted towards the pole and contacted CPC-s5, where it may have been caught in the cyclonic flow of CPC-s5 and swung almost 360° round it

5. Flow around the polygons To understand the dynamics of the CPC constellation, it is important to know whether there is any systematic flow around it. If there was a rapid jet, it would be detectable by viewing successive images of our polar projection maps, just as this procedure displays the motions in the CPCs and neighboring folded filamentary regions (FFRs). In fact, these animations (e.g. Suppl. Animations SA2, SA5, SA6) indicate that within timeframes of 0.5 to 2 h, there is no visible continuous jet around the perimeter of either CPC polygon. This gives an upper limit for longitudinal winds of ~0.5 deg/h or ~30 m/s. Slower flow could be assessed by tracking of potentially persistent features between perijoves. Cyclonic FFRs are too unstable for this purpose and cannot be confidently recognized after 53 days. Potentially the best tracers are anticyclonic white ovals (AWOs); in the south polar 9

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Fig. 10. High-resolution views of some individual northern CPCs, as indicated: excerpts from the north polar maps, with L3 = 0 approximately to the left. a) PJ1, CPC-n5 (the largest of the filled type), showing the inner counter-spiral (white arrows) and a white cloud overlapping a boundary between the reddish cloud and a dark region. b) PJ6, CPC-n5, again showing the inner counter-spiral (white arrows); animation of this with other images showed counter-rotation at the center. c) PJ11, CPC-n6 (chaotic type): the spiral arms and interior are highly distorted, with a central region that contains scattered white clouds, within which is a circular compact bright region (yellow arrow). d) PJ14, CPC-n2 (chaotic type): a perfect fine-scale spiral with a circular central bright region. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

from PJ11 to PJ15 (see Suppl. Fig. S1b, c). Otherwise, from PJ10 to PJ13, there were only one or two other small AWOs around the periphery of the pentagon, marked A5 and A6 on the maps (Suppl. Fig. S1b, c); if these identifications are correct, both were successively in contact with CPC-s3 and were entrained in its outer circulation. The drift speeds of anticyclones identified here vary between 1.8 m/ s (eastward) to 0.7 m/s (westward). This result compares well to storms at lower latitudes (e.g. Morales-Juberías et al., 2002; Trammell et al., 2014; Simon et al., 2018), which usually have low drift rates (< 10 m/ s) and are located between alternating jets. Overall, we find no evidence for systematic zonal flow around the pentagon, but rather, we find that the AWOs within this region have a range of comparatively slow drifts that are influenced by local interactions with the cyclones.

comparing maps of superimposed consecutive images to reveal the rotations. For each pole, we use two maps at PJ1, three maps at PJ3, and two maps at PJ4. Within each CPC, angular velocities about the apparent center are measured in concentric annuli (from one to six per CPC, see e.g. Suppl. Fig. S4). To measure the angular displacement, the annulus in one image is rotated on screen until it appears registered with its equivalent in the other image. Each annulus is chosen so as to include sufficient features to give a definite angular velocity that is different from adjacent annuli. The stated angular velocity is the consensus for the more distinct features in the annulus, and the “error” value represents the range of values which appear reasonable, or the average of measurements between multiple pairs of images. Uncertainties are present due to real local motions, and also image noise, residual misalignments of maps, and uncertainty in locating the exact center of the CPC. We assume that one degree of latitude equates to 1167 km.

6. Wind velocity of the cyclones 6.1. Approach to velocity measurements

6.2. Angular velocity measurements

The wind velocities within the CPCs are fast enough (0.1 to 0.3°/ min) that they can be measured from JunoCam images taken within 15–30 min. The measurements are performed on our polar-projection maps of individual images, slightly adjusted to optimize alignment by reference to the large-scale features such as CPCs, by visually

Using polar-projection maps from the PJ1, PJ3 and PJ4 images, the angular velocities are measured in concentric annuli in the best-resolved CPCs. Different classes are analyzed separately: southern CPCs, filled northern CPCs, and chaotic northern CPCs. 10

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evident in the outer parts of all measured cyclones, typically at a rate (radial gradient of the tangential wind speed) of ~−3.2 to −5.7 m/s/ 100 km (−3.2 to −5.7 × 10−5 s−1). Apart from the SPC, all CPCs have peak speeds of 64–99 m/s at ~900 < r < 1600 km. The highest wind speed we have detected was within the SPC during PJ3: the central oval had an angular velocity of 0.52 ± 0.03°/min, giving a mean speed of 100 ± 6.5 m/s, and an implied rotation period of 11.6 h. For this angular velocity, the equivalent tangential wind speed at the outer edge of the oval reaches up to ~130 m/s. However, our measurements of the central rotation of the SPC during PJ1 and PJ4 are more modest and the SPC's rotation curve in general is similar to other CPCs. For the wind-speed gradient near the very center of the CPCs, where we find no trackable features, we can give lower limits by assuming that wind speed declines linearly from the middle of the innermost measured annulus to the center, where it is assumed to be zero. Taking those CPCs where rotation was tracked to r < 1000 km, we find minimum gradients ranging from 5.0 to 9.2 × 10−5 s−1 for six northern CPCs, and 6.6–15.4 × 10−5 s−1 for southern CPCs-s1, s4, and the SPC. 6.2.2. Central counter-rotation The three largest of the northern CPCs commonly show traces of counter-spiral structure in the inner regions (i.e., spiral in the opposite sense to the outer regions, indicating that the inner regions are rotating more slowly or even in the opposite direction). It appears either as one or two distinct streaks, or as a subtle tightly wound pattern at the limit of resolution. Up to PJ11, we can consistently see this pattern in CPC-n5 (the largest northern CPC) (Fig. 10) and possibly in CPC-n3 & n7 (the two next largest northern CPCs). Images taken since PJ11 have higher resolution, however, the CPCs in question have been located too close to the terminator for a counter-spiral structure to be visible. On one occasion (during PJ6), an animation of CPC-n5 showed that the central region was definitely rotating anticyclonically, opposite to the rest of the cyclone (see Suppl. Animations SA3, SA4).

Fig. 11. Tentative tracking of small AWOs around the perimeter of the south polar pentagon from PJ1 or PJ3 to PJ6, plotted on the PJ3 map relative to the pole (not relative to the CPCs, which move by a few degrees). AWOs are colorcoded and labelled at their position at PJ3. The final position for A2 (at PJ5) could alternatively represent a merger with A3. (See Suppl. Fig. S1 for identifications on individual maps and continuation to PJ15.)

In every case for which more than one annulus could be measured, the angular velocity increases with decreasing radius, except in the inner bright cloud deck of the northern filled CPCs. The angular velocities are plotted against the cyclone radius (i.e. distance from the center of the cyclone) in Fig. 12a, b, c. For the south polar measurements some kind of inverse relationship is evident. The north polar ‘filled’ measurements are sparse, but could also fall within a similar inverse relationship. The northern ‘chaotic’ cyclone measurements are more scattered, many being slower than for the other classes of cyclones. The inner limit of measurable rotation in most cases is r = ~600–900 km. In close proximity to the center, we observe the following behavior. For the southern CPCs, angular velocities in some cases (SPC, CPC-s1) are still increasing down to r < 750 km, with rotation visible down to r < 400 km. The highest angular velocity is for the smallest radius that we measured, in the center of CPC-s1 at PJ3, 0.52 ± 0.03°/min, giving an implied rotation period of 11.3 h. For the northern ‘chaotic’ CPCs, one example (CPC-n1) shows angular velocity increasing down to very small radius. For the northern ‘filled’ CPCs, the inner bright part does not show a centrally increasing angular velocity: two out of three measured cyclones (CPC-n2, CPC-n4) show a uniform rotation rate over a large span from the edge of the inner bright part inwards. Indeed, in the largest CPC there are signs of inner spiral structure suggesting that the very center rotates less strongly or even, as observed in at least one case, in the opposite direction (see Section 6.2.2).

7. Discussion 7.1. Wind speeds in the CPCs Our velocities can be compared with independent measurements from JIRAM images at PJ4, reported by Adriani et al. (2018) and Grassi et al. (2018). Adriani et al. (2018) measured speeds at a radius of 1500 km in each CPC, which were mostly 55–95 m/s. Grassi et al. (2018) showed detailed wind fields for the NPC and SPC and several other CPCs; they found maximum speeds ranging from ~55 m/s to > 115 m/s at r ~ 1000 km. They show satisfactory agreement with our individual values at PJ4, and with our general finding that wind speeds in most CPCs are highest between radii of ~900–1600 km, ranging from ~64–99 km/s. In this regard the CPCs resemble the largest and strongest terrestrial hurricanes, but are larger; hurricanes on Earth have an average radius of maximal wind speed about 50 km, and overall radii ranging up to ~500 km (see e.g. Hsu and Yan, 1998). In the inner parts of CPCs (i.e. smaller than the radius of maximum tangential wind velocity), Grassi et al. (2018) show smooth declines in speed from r ~ 1000 km to the center. Their values for the mean relative vorticities within this radius (ζ = 2vt/r, i.e. twice the mean radial gradient of the tangential wind speed) range from 15 × 10−5 s−1 for the NPC to 20 × 10−5 s−1 for the SPC, and would be somewhat higher for two other CPCs. These values are consistent with the minimum gradients that we have estimated: 10–18 × 10−5 s−1 for 6 northern CPCs, 13–31 × 10−5 s−1 for 3 southern CPCs. These are larger than mean vorticities reported for lower-latitude cyclonic structures: 6.2 × 10−5 s−1 for a small cyclonic oval in the South South Temperate Belt (Legarreta and Sánchez-Lavega, 2005); 3.6 or 5.1 × 10−5 s−1 for two large dark storms in the North Equatorial Belt (Hatzes et al., 1981; Legarreta and Sánchez-Lavega, 2005); and a mean du/dy ~ 1.9 × 10−5 s−1 for a large FFR or turbulent segment of the South

6.2.1. Analysis of wind speeds The derived tangential wind speeds vt are plotted against radius in Fig. 12d, e, f. Lines are drawn between points representing the same CPC, and substantial differences between individual CPCs are evident. Despite this large overall scatter, the wind speeds have consistent trends with radius, vt rising with r until a maximum is reached, and then decreasing with r. Especially the latter trend of vt decreasing with r is 11

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Fig. 12. a, b, c) Measured angular velocity in °/min of southern and northern CPCs, plotted against radius from the center of each CPC. Horizontal lines signify the width of the measured annulus, vertical lines indicate the error range of the velocity measurement. d, e, f) Tangential wind speeds in m/s of southern and northern CPCs. Lines connecting the data points are inserted to identify measurements of the same cyclone at different perijoves. Vertical lines display the error of the tangential wind speed. For the north pole, ‘filled’ CPCs are displayed as circles and ‘chaotic’ CPCs as crosses. g, h, i) Radius-adjusted tangential wind speeds in m2/s of southern and northern CPCs. The colored lines connect points belonging to the same CPC measured at the same perijove to visualize slopes. Vertical lines indicate error values. The multiplication with the radius in (g, h, i) depicts ranges where the tangential velocity is inversely proportional to the radius (i.e. vt~r−1) as a horizontal line, signifying an ideal irrotational vortex. Consequently, a positive slope shows a proportionality of rγ with γ > −1 and a negative slope shows a proportionality with γ < −1.

Temperate Belt (Morales-Juberías et al., 2002, their Figs. 3 & 4), which is also typical of Jupiter's larger belts in general. However, the overall structures are different: the vortical inner regions of the CPCs have r < /~ 1000 km and are surrounded by large outer spirals which may be irrotational or shielded (see below), whereas all the lower-latitude cyclonic storms have their highest wind speeds near their edges and are embedded in cyclonic belts. Jupiter's anticyclonic storms have been studied more thoroughly, especially the Great Red Spot, whose wind speeds are comparable to the fastest that we have recorded in the CPCs (Sánchez-Lavega et al., 2018). Values for the wind speed gradient or vorticity, on the inner side of the high-speed collar, range from 2 to 11 × 10−5 s−1 (Mitchell et al., 1981; Sada et al., 1996; Choi et al., 2007). In the outer region of a vortex (i.e. beyond the radius of maximum

tangential wind velocity) the tangential wind velocity decreases with radius according to vt ~ rγ where an ideal two-dimensional irrotational (zero vorticity) vortex would have γ = −1. To ascertain the nature of the outer region of the vortex, we have plotted a radius-corrected version of the tangential wind speed in Fig. 12g, h, i. Here we plot vt*r on the x-axis so that a dependence of vt ~ r−1 is depicted by a horizontal line (gradient of zero). Our data for the southern CPCs in Fig. 12g shows that within the given error ranges the outer parts of the cyclones have regions where a zero gradient can be identified in vt*r. Indeed, the SPC (labelled as CPC0 in Fig. 12g) has a range around r = 1200–2000 km (during PJ1) and around r = 1500–3000 km (during PJ4) where a horizontal slope is a possibility. This compares well to measurements taken by Grassi et al. (2018) during PJ4 who found a slope with γ = −1 from r = 2000–2600 km. Overall, we find the 12

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general slope for the outer parts of the CPCs is downward, signifying γ < −1. The north-polar data (Fig. 12h, i) are more sparse, so that the slopes of CPCs-n1 and n-4 are inconclusive. CPCs-n2 and n8 show a slope in the outer regions similar to that observed on the south pole with γ < −1. This result is comparable to the findings of Grassi et al. (2018) who find γ = ~ − 1.4 for the SPC at r > 2600 km and for the NPC (which JunoCam cannot observe). Grassi et al. (2018) concluded from these relationships that the central cyclones on the north and south pole agree well with 2-dimensional shielded vortices. A shielded vortex is surrounded by an area of opposite vorticity, so that the vortex's total vorticity is zero (see e.g. Carton, 1992). Our comparable γ values support this finding. This implies that the flow of the CPCs may be 2-dimensional, so that a possible explanation for the arrangement of the CPCs is vortex crystals. Further analysis of the motions of the cyclones is needed to fully understand the character of the Jovian circumpolar cyclones. For instance, an analysis of the circulation (the integral flow around a closed path) of the CPCs would reveal insights into the average vorticity and the Lagrangian absolute vorticity of these storms (e.g. Dowling and Ingersoll, 1988). These methods could shed light on the thickness of the polar weather layer and the wind fields in the deep wind fields (e.g. Dowling and Ingersoll, 1989). However, as a starting point, this analysis would require a wind vector field with hundreds of vectors (Dowling and Ingersoll, 1988). Our early attempts at reliably extracting such a field with automated correlated image velocimetry have proven to be unsuccessful due to image noise and small pointing errors. The wind vector fields of CPCs during PJ4 provided by Grassi et al. (2018) seem an ideal starting point for this analysis.

Fig. 13. Examples of vortex crystals formed in magnetized electron columns, reproduced from Schecter et al. (1999). Color signifies intensity of vorticity (light green, low; red, high), where vorticity is positive everywhere. Out of many different crystal configurations, these two most resemble the observed patterns on Jupiter's poles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

7.2. Evolution of circumpolar cyclones as vortex crystals Adriani et al. (2018) and Grassi et al. (2018) have identified that the pattern of circumpolar cyclones is in agreement with vortex-crystal observations. Here, we study how well the long-term evolution of the cyclone positions compares to the observed behavior of vortex crystals. Vortex crystals are a phenomenon occurring in 2-dimensional fluiddynamical systems. They have been found in experiments recreating 2dimensional turbulence using magnetized electron columns (Fine et al., 1995). Starting with an initial vorticity distribution, Fine et al. (1995) observed free relaxation of the turbulence. The emerging vortices interact via chaotic advection until they either merge into a single central vortex or reach a meta-equilibrium state, where 3–20 equally-spaced vortices rotate rigidly within a background of uniform vorticity (Fine et al., 1995). This so-called “vortex cooling” has been shown to occur due to random interaction with the background vorticity to form a state of regional maximum fluid entropy (Jin and Dubin, 1998). Numerical simulations of this phenomenon recreate the evolution of vortex crystals well when using inviscid, incompressible 2-dimensional Euler equations in systems with a single sign of vorticity (Schecter et al., 1999). In both simulation and experiment, the vortex crystal state lasts for up to 104 rotations of the pattern, after which small viscous forces dissipate the vortices. Fig. 13 shows two examples of vortex crystals from laboratory experiments that match well with the cyclone constellations observed on Jupiter's poles. The vortex-crystal state does not evolve in a perfectly regular pattern. Studies of the evolution of vortex-crystal systems show that the distance between vortices is variable even when the vortex-crystal state is reached (see Fig. 14, from Jin and Dubin, 2000). Overall, the long-term behavior of the CPCs is generally congruent with that of vortex crystals. The fact that the pentagonal CPC constellation has been observed for the last two years speaks for its stability. The CPCs have a fairly regular drift rate about the central SPC. This compares well to the nearly rigid rotation rate of vortex crystals. The relatively slow drift of the southern CPC constellation of 1.5 ± 0.2°/PJ means we have so far only observed a rotation of the constellation by 22° longitude, so we cannot compare this to the stability of unforced

Fig. 14. Evolution of a simulated vortex crystal over time. Reproduced from Jin and Dubin (2000) (their Fig. 2). Snapshots depict the initialization (t = 0), ‘vortex cooling’ (t = 31.4), and equilibrium (t = 942) phases of vortex crystal evolution. The plot at lower right depicts the variability of the minimal distance between any two vortices in the quasi-stable vortex crystal state. After the initial evolution, the crystal is in a quasi-stable state from t = 200 onwards, with minimum distance varying between 0.14 and 0.18 units.

vortex crystals lasting for 104 rotations. The aberration from true rigid rotation (i.e. the “wobble”) that we find especially for CPCs s1, s2, s5 (Figs. 5, 6) also aligns with the evolution of vortex crystals (see Fig. 14). All these similarities are surprising considering that the atmosphere of Jupiter is much more complex than a nearly inviscid, incompressible, 2-D fluid. A major difference is that the Jovian system is not simply relaxing an initial turbulence, but it receives energy from multiple sources (see e.g. Salyk et al., 2006; Galperin et al., 2014; Read et al., 2016; Young and Read, 2017; Li et al., 2018). The polar region is predicted to receive horizontal poleward flux of vorticity via polewardmoving cyclones (Cho and Polvani, 1996; Theiss, 2006), although this has not yet been possible to observe near the polar region. It may also be subject to deep vertical convection, as well as vertical radiative sources from both the planetary center and the Sun that could provide further sources of turbulent energy (O'Neill et al., 2015; Brueshaber et al., 2019). Lightning is frequent right up to the poles (Brown et al., 2018; Imai et al., 2018). Nevertheless, it is still uncertain whether the polar cyclones are essentially in a 2-D or 3-D regime; gravitational 13

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modelling (Kaspi et al., 2018) gives a depth of 3000 km at low latitudes but a preliminary estimate of 0–500 km near the poles, which could encompass either regime. Future modelling of the CPC clusters may help to constrain their depth. Another large difference between Jupiter and the vortex crystal system is the total vorticity. The laboratory setup for vortex crystals only allows for positive vorticity, whereas the CPCs on Jupiter are likely shielded so that their total vorticity is zero. Jiménez and Guegan (2007) have found shielded vortex crystals in a system with both positive and negative vorticity with periodic boundary conditions. Further simulations of the formations and maintenance of shielded vortex crystals are necessary to fully compare the observed CPCs with vortex crystal theory. Studies of point vortices (see e.g. Aref et al., 2003; Kurakin and Yudovich, 2002; Tur and Yanovsky, 2004; Reinaud, 2019) in more simplified 2D and 3D fluid systems show that the relaxation into an mfold symmetry (i.e. m vortices in a circle) with or without a central cyclone is a common occurrence. However, these simulations disregard many the factors of added complexity discussed above. Since we have observed the stability of the CPC constellations in this paper, two possible conclusions arise. Firstly, the vortex crystallization effect is stronger than the other factors and dominates the flow in the circumpolar region of the Jovian atmosphere. Or secondly, some of these factors (e.g. that the CPCs could be deep columns) might improve the stability of the observed constellations. The asymmetric pentagonal arrangement at the south pole could be explicable on simple geometric grounds if we adopt two conjectures: that the cyclones attain a maximum size (possibly limited by the depth of the weather layer, or more specifically by non-dimensional parameters such as the Burger number, see e.g. Brueshaber et al., 2019, O'Neill et al., 2015), and that they cluster as close to the pole as possible. If the maximum size were the same for all the cyclones, these conjectures would merely lead to hexagonal packing of 6 cyclones centered on a seventh one at the pole, because the effect of the planet's curvature is negligible (< 1% in linear dimension) at > 82° latitude. However, if some dynamical factor causes the SPC to be ~12% smaller than the average size of the cyclones in the polygon, similar to the size range observed, there would be room for only 5.8 cyclones, i.e. five plus a gap. In order to concentrate the cyclonic vorticity as close to the pole as possible, the whole cluster would be displaced from the pole to place the gap furthest from the pole, as observed. This hypothesis also explains why the displacement was greater when the gap was wider, up to PJ12, although the breakdown in this correlation after PJ12 requires some other explanation. A complication is the significant range of sizes of the actual CPCs, from the smallest adjacent to the gap, to the largest opposite the gap. Numerical modelling will be required to establish whether this too is consistent with our hypothesis. In addition, future polar observations with the microwave radiometer (MWR) on Juno may constrain the NH3 distribution underneath the polar CPCs, which could help constrain the depth of the cyclones (see e.g. Bolton et al., 2017). At the north pole, the ditetragonal pattern appears to require a more complex explanation that would go beyond purely geometrical constraints.

anticyclonic white oval (AWO) has grown within one vertex. We find an irregular drift rate of the octagonal structure which becomes more uniformly westward between PJ9 and PJ14. The central-southern polar cyclone (SPC) follows a circular motion between 89°S and 87.5°S latitude and between 200° and 250° longitude. However, between PJs 12 and 15 this motion becomes linear in longitudinal direction, and it is unclear whether the SPC will continue its linear path or revert to a circular motion. We find no clearly identifiable jets around the CPCs for observations within observation windows up to 2 h at a single perijove. We attempt to track AWOs through consecutive perijoves under the assumption that the AWOs are persistent and do not circumnavigate the pole within the 53 day period between measurements. This results in values for the eastward zonal velocity of +1.8 to −0.7 m/s. Individual cyclones commonly retain distinct morphological features for a year or more. Some of these features may be related to the geometry of the polygons: in the south, in relation to the polar offset and the gap; in the north, in relation to the ditetragonal structure of alternating ‘filled’ and ‘chaotic’ classes. In the north, these two classes have remained distinct throughout these two years, and within the ‘chaotic’ class there is one that is always the least well formed, and another that always has a smaller or looser version of the ‘filled’ aspect. Within the cyclones, we have measured angular velocities as a function of radius separately for southern, northern ‘filled’, and northern ‘chaotic’ cyclones. The angular velocity increases with decreasing radius, following similar curves for the southern CPCs and the northern ‘filled’ CPCs, and showing a more scattered, largely slower distribution for the northern ‘chaotic’ CPCs. In the inner bright cloud deck of the northern ‘filled’ CPCs, angular velocities do not increase towards the center; indeed, traces of spiral structure suggest that the very center rotates less rapidly or even, as observed in one case, in the opposite direction. The wind velocities of the CPCs, up to 99 m/s for most (and > 100 m/s in the SPC), are among the highest cyclonic velocities measured for storms on Jupiter. The storms in the polar region have a different radial profile of tangential velocity than the anticyclonic storms found within the banded regions at lower latitudes, which have their highest velocities at the edge of the storm. The polar cyclones have a tangential velocity pattern that is more reminiscent of Earth hurricanes, with rising velocities in the inner region of the storm, and once the radius of maximum tangential wind velocity is reached, declining with an approximately rγ slope in an extensive outer region, where γ ≤ −1. The radius of maximum tangential wind in the polar cyclones on Jupiter, ~900 km < r < 1600 km, is about 20 times larger than in an average terrestrial hurricane. Overall, the polar pentagonal and octagonal structures provide a good comparison with vortex crystal behavior. However, this is surprising, since Jupiter's atmosphere is expected to be more complex than a relaxing 2-dimensional turbulent fluid. It is possible that vortexcrystal theory is applicable to more systems than previously thought or that Jovian polar dynamics behaves largely 2-dimensionally. Further theoretical studies of vortex crystals with positive and negative vorticity and in different settings are needed for a more detailed comparison.

8. Conclusions

Acknowledgements

JunoCam observations of the polar regions of Jupiter show traceable, largely stationary circumpolar cyclones (CPCs). In south polar region of Jupiter, we show that the pentagonal structure of CPCs remains visible during each perijove. While the short-term movement of the CPCs can be erratic, an average drift rate of 1.5 ± 0.2°/PJ or −0.040 ± 0.005 m/s is valid for the pentagonal structure of CPCs. The movement of the CPCs between perijove measurements is likely connected to the variable, roughly 100° wide gap between CPCs s1 and s2. For the north pole, JunoCam data are more sparse, but the octagonal (ditetragonal) structure persists, albeit with distortion as an

The research was carried out at the Jet Propulsion Laboratory, California Institute of Technology under task number 104769 04.02.01.01, under a contract with the National Aeronautics and Space Administration. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.icarus.2019.113405. 14

Icarus 335 (2020) 113405

F. Tabataba-Vakili, et al.

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