Fluid Dynamical 2D Simulations of Jupiter's South Polar Region Based On JunoCam Image Data
Authors: Eichstädt Gerald , Hansen Candice , Orton Glenn 
Published: March 2020

&lt;p&gt;During almost every perijove pass in more than three years of Juno's ~53-day polar orbits around Jupiter, its wide-angle visible-light camera, JunoCam [1], has imaged Jupiter's south polar region [2].&lt;/p&gt;&lt;p&gt;We sought to determine whether these images could be used for prognostic &amp;#8220;weather forecasts&amp;#8221; in Jupiter. One of the simplest fluid dynamical models suitable for forecasting dynamical behavior of essentially barotropic incompressible flows of very low viscosity is the 2D Euler fluid. Vortex methods [3] are particularly suitable for modeling the resulting turbulence.&lt;/p&gt;&lt;p&gt;Sequences of images taken with a cadence of several minutes reveal small motions of the cloud tops within the illuminated area of the pole. The south pole itself has been visible in the twilight.&lt;/p&gt;&lt;p&gt;Raw JunoCam image data are transformed into an equidistant south-polar azimuthal map, roughly illumination-adjusted, high-passed with local contrast-normalization, and registered.&lt;br&gt;A streamfunction describing the velocity field approximately is derived from a sequence of consecutive maps of a common perijove flyby. Running a Monte-Carlo approach for stereo correlation repeatedly with different pseudo-random number sets returns an ensemble of streamfunctions.&lt;br&gt;The Laplacian of a streamfunction returns the vorticity values for a randomized 2D vortex particle seed as initial conditions of a grid-free vortex method. Applying the Biot-Savart law [3, p.19ff] on a 2-spherical geometry to the vorticity field returns the velocity field. A single-step explicit Runge-Kutta method of order 4 or 5 and fixed time steps advects the 4th-degree Gaussmollified vortex particles. Measuring the area of their Voronoi cells (Dirichlet/Thiessen polygons) reassesses the radius of the vortex particles. The method allows for some divergence. An approximately inviscid and incompressible 2D-flow is simulated over 2 up to 54 real-time days or about one Juno orbital period. The randomized nature of the method induces simulation ensembles for a given streamfunction by repeated runs.&lt;/p&gt;&lt;p&gt;Reducing the streamfunction to a Morse-Smale complex returns idealized model vortex seeds.&lt;/p&gt;&lt;p&gt;JunoCam images of the south polar region taken during a perijove pass provide an ensemble of dynamical data. These initial conditions extend to ensembles of forecast runs of the 2-spherical dynamics of the visible cloud tops in Jupiter's south polar region. We find that JunoCam images of&lt;br&gt;Jupiter's south polar region allow for reasonably plausible forecasts of the dynamics of the observed area with grid-free 2D vortex methods over at least a few days.&lt;/p&gt;&lt;p&gt;[1] C.J. Hansen, M.A. Caplinger, A. Ingersoll, M.A. Ravine, E. Jensen, S. Bolton, G. Orton.&lt;br&gt;&lt;em&gt;Junocam: Juno&amp;#8217;s Outreach Camera.&lt;/em&gt; Space Sci Rev 2013:475-506, &lt;em&gt;2017&lt;/em&gt;&lt;br&gt;[2] F.Tabataba-Vakili,J.H.Rogers,G.Eichst&amp;#228;dt,G.S.Orton,C.J.Hansen,et al. &lt;em&gt;Long-term Tracking of&lt;/em&gt;&lt;br&gt;&lt;em&gt;Circumpolar Cyclones on Jupiter From Polar Observations with JunoCam&lt;/em&gt;. Icarus 335, 113405,&lt;br&gt;&lt;em&gt;2020&lt;/em&gt;.&lt;br&gt;[3] G.-H. Cottet, P. D. Koumoutsakos, &lt;em&gt;Vortex Methods: Theory and Practice&lt;/em&gt;, Cambridge University&lt;br&gt;Press, &lt;em&gt;2000&lt;/em&gt;&lt;/p&gt;