The dynamical nature of the hexagonal cloud pattern on Saturn’s north pole was unexplained by planetary science for ≈ 35 years since its first observation. Nothing like the hexagon has ever been seen on any other planet. The lack of a similar pattern on the south pole has been another unsolved problem.
Early visible observations of the Voyager 1&2 fly-by of Saturn in 1980-1981 revealed the hexagonal cloud pattern of Saturn’s north pole at about 77 ◦N planetographic latitude. This pattern has been observed again in the 1990s by the Hubble Space Telescope, and then in the 2000s by the Cassini orbiter. Early interpretation of long-lived hexagonal pattern by Allison et al. (1990) indicated the anticyclonic North Polar Spot (NPS) vortex, visible at that time in the vicinity of the hexagon, as a main cause for the hexagonal shape of the polar jets. The disappearance of the NPS between 1995 and 2004 invalidated this scenario.
Although some laboratory experiments and numerical models could address the questions of the nature and certain characteristics of the hexagon (Vatistas et al., 1994; Marcus and Lee, 1998; Jansson et al., 2006; Bergmann et al., 2011), in all of the aforementioned essays the hexagonal shape resulted from a vortex street formed by developing barotropic instability of the jet, with cyclonic and anticyclonic vortices at poleward and equator-ward sides of the jet, respectively. The vortices forming the street were too large and too strong, with respect to observations. By proposing an ad hoc vertical shear of the jet, Morales-Juberias et al. (2015) simulated a hexagonal pattern with sharp potential vorticity (PV) similar to observations; however, both vertical shear and the putative meridional temperature gradients accompanying the vertical shear of the polar jet are yet to be confirmed.
Rostami et al. (2018) proposed an alternative approach to the problem in the framework of barotropic rotating shallow water (RSW) model, in the polar tangent plane approximation and could reproduce a hexagonal pattern similar to observations. This study elucidated the dynamics of the hexagon and its strong relation to Saturn’s north polar vortex (NPV). The RSW model which is applied in this study combines simplicity with dynamical consistency and, with the astronomical parameters of Saturn being given, contains a single adjustable parameter: the effective Rossby deformation radius. It is demonstrated that the hexagon arises primarily from the barotropic instability of the observed pattern of the zonal jet and polar vortex.
This study makes use of a detailed linear stability analysis of the observed zonal jets in the vicinity of both the north and south poles on Saturn in the framework of standard rotating shallow water (RSW) equations. It was shown that an azimuthal wavenumber 6 pattern (hexagon) is a dominant mode in the northern hemisphere over a reasonable range of parameters, but not in the southern hemisphere. A novel result is the decisive dynamical role of NPV which stabilizes the hexagonal pattern, without creating a strong “vortex street,” during the fully nonlinear dissipationless evolution of the instability; at the same time, the evolution of circumpolar jet alone ends up with growing vortex streets at each side of the hexagon.
These findings are described in the article entitled On the dynamical nature of Saturn’s North Polar hexagon, recently published in the journal Icarus. This work was conducted by Masoud Rostami, Vladimir Zeitlin, and Aymeric Spiga from the Université Pierre et Marie Curie (UPMC).
References:
- Allison, M., Godfrey, D. A., Beebe, R. F., 1990. A wave dynamical interpretation of saturn’s polar hexagon. Science 247 (4946), 1061-1063.
- Bergmann, R., Tophoj, L., Homan, T., Hersen, P., Andersen, A., Bohr, T., 2011. Polygon formation and surface flow on a rotating fluid surface. Journal of #uid mechanics 679, 415-431.
- Jansson, T. R. N., Haspang, M. P., Jensen, K. H., Hersen, P., Bohr, T., May 2006. Polygons on a rotating #uid surface. Phys. Rev. Lett. 96, 174502.
- Marcus, P. S., Lee, C., 1998. A model for eastward and westward jets in laboratory experiments and planetary atmospheres. Physics of Fluids 10 (6).
- Morales-Juberias, R., Sayanagi, K. M., Simon, A. A., Fletcher, L. N., Cosentino, R. G., 2015. Meandering shallow atmospheric jet as a model of Saturn’s north-polar hexagon. The Astrophysical Journal Letters 806 (1), L18.
- Rostami, M., Zeitlin, V., Spiga, A., 2017. On the dynamical nature of Saturn’s north polar hexagon. Icarus 297, 59 – 70. https://doi.org/10.1016/j.icarus.2017.06.006
- Vatistas, G. H., Wang, J., Lin, S., 1994. Recent findings on kelvin’s equilibria. Acta Mechanica 103 (1), 89-102.