On the dynamical nature of Saturn’s North Polar hexagon

• Main Author: , LMD
• Format: Report
• Language: unknown
• Published: Open Science Framework 2018
• Subjects: The Sun and the Solar System; Other Computer Sciences; Statistical, Nonlinear, and Soft Matter Physics; Astrophysics and Astronomy; Partial Differential Equations; Categorical Data Analysis; Other Earth Sciences; FOS Earth and related environmental sciences; Numerical Analysis and Computation; Numerical Analysis and Scientific Computing; Tectonics and Structure; Other Applied Mathematics; Plasma and Beam Physics; OS and Networks; Statistics and Probability; Statistical Methodology; Stratigraphy; Geophysics and Seismology; Physical Sciences and Mathematics; Applied Mathematics; FOS Mathematics; Information Security; Ordinary Differential Equations and Applied Dynamics; Stars, Interstellar Medium and the Galaxy; Other Astrophysics and Astronomy; Cosmology, Relativity, and Gravity; Paleobiology; Instrumentation; Environmental Sciences; Probability; Graphics and Human Computer Interfaces; Geology; Special Functions; Mathematics; Non-linear Dynamics; Cosmochemistry; Earth Sciences; Computer Sciences; Geomorphology; Physics; External Galaxies; Design of Experiments and Sample Surveys; Applied Statistics; Fluid Dynamics; Physical Processes; Institutional and Historical; Dynamic Systems; Statistical Theory; Artificial Intelligence and Robotics; Glaciology; Databases and Information Systems; Other Physics; South Pole; South pole
• Online Access: https://dx.doi.org/10.17605/osf.io/rvdmx; https://osf.io/rvdmx/

An explanation of long-lived Saturn’s North Polar hexagonal circumpolar jetin terms of instability of the coupled system polar vortex - circumpolar jet isproposed in the framework of the rotating shallow water model, wherescarcely known vertical structure of the Saturn’s atmosphere is averaged out.The absence of a hexagonal structure at Saturn’s South Pole is explainedsimilarly. By using the latest state-of-the-art observed winds in Saturn’spolar regions a detailed linear stability analysis of the circumpolar jet isperformed (i) excluding (“jet-only” configuration), and (2) including(“jet+vortex” configuration) the north polar vortex in the system. A domainof parameters: latitude of the circumpolar jet and curvature of its azimuthalvelocity profile, where the most unstable mode of the system has azimuthalwavenumber 6, is identified. Fully nonlinear simulations are then performed,initialized either with the most unstable mode of small amplitude, or withthe random combination of unstable modes. It is shown that developingbarotropic instability of the “jet+vortex” system produces a long-livingstructure akin to the observed hexagon, which is not the case of the“jet-only” system, which was studied in this context in a number of papersin literature. The north polar vortex, thus, plays a decisive dynamical role.The influence of moist convection, which was recently suggested to be at theorigin of Saturn’s north polar vortex system in the literature, is investigatedin the framework of the model and does not alter the conclusions.