Fluid planetary dynamics in Jupiter and Saturn
Authors: Singh Simranjeet 
Published: March 2020

&lt;p&gt;&lt;strong&gt;Title: Fluid planetary dynamics in Jupiter and Saturn&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Simranjeet Singh*, Dr. Moritz Heimpel&lt;/p&gt;&lt;p&gt;&lt;em&gt;University of Alberta, Edmonton, AB T6G 2R3, Canada&lt;/em&gt; &amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Abstract:&lt;/strong&gt; Despite around numerous years of observations in jets and vortices in the atmosphere of giant planets like Jupiter and Saturn are still debatable. Bands of Jupiter consists of powerful winds. High latitude jets flow in eastward direction. The equatorial flow model has been shown here but not the shallow layered model due to more focused on the radial flow field of Jupiter and Saturn. Our findings are based on the interpretation of output data provided by Juno and Cassini spacecrafts.&lt;/p&gt;&lt;p&gt;We used MagIC code to run the planetary models with the solutions of Navier-Stokes equations coupled with anelastic and Boussinesq approximations. To analyse the fluid interaction between zonal flows in Saturn and Jupiter and the result of the circulation models of these planets dominated by zonal flow. This manifest itself as a pattern similar to the Jupiter&amp;#8217;s band. But Saturn has somewhat a different storyline as near to the equator, Saturn&amp;#8217;s bands gradually gets wider. &amp;#160;&lt;/p&gt;&lt;p&gt;By making use of the conservation of momentum (Navier-Stokes) (MagIC):&lt;/p&gt;&lt;p&gt;&amp;#961;((&amp;#8706;u/&amp;#8706;t) + u.&amp;#8711;u) = -&amp;#8711;p + (1/&amp;#181;) + (&amp;#8711;xB)xB + &amp;#961;g - 2&amp;#961;xu + &amp;#8711;.S&lt;/p&gt;&lt;p&gt;U and B are the respective velocity and magnetic fields in the system, p is the pressure (includes centrifugal forces) and S signifies the rate of strain tensor. The above equations set the base line for the flow field. These flow fields can be read by the generation of output files, which involves the overall scenario of the planets, which includes Kinetic energy of the system varying with time, exchange of magnetic flux, dipole movement, heat exchange with Nusselt number, angular momentum conservation of inner core and mantle and many other parameters, which demonstrate the precise picture of belts in Jupiter and Saturn. Since the output is in terms of non-dimentional quantity, which makes easy to visualise the results for the giant planets. Results are dynamic and so are the interpretation when Ra varies with the factor of two.&lt;/p&gt;&lt;p&gt;To conclude here, although there is loads to describe but precisely the flow of our numerical simulation is indeed dominated by geostrophic zonal flows. The flow is directly proportional to the radial symmetry, as it grows and diminishes accordingly. The effect of these codes suggest that zonal flow scaling can be analysed separately with high degree of magnitude precision inside and outside the tangential cylinder. The jet streams in these giant planets are insensitive and will continue to remain similar over next few centuries, according to this research.&lt;/p&gt;&lt;p&gt;Important References (limited to space):&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;ul&gt;&lt;li&gt;Effects of compressibility on driving zonal flow in gas giants, T. Gastine, J. Wicht (2011).&lt;/li&gt;
&lt;li&gt;Simulation of equatorial and high-latitude jets on Jupiter in a deep convection model, Moritz Heimpel (2005).&lt;/li&gt;
&lt;li&gt;Simulation of deep-seated zonal jets and shallow vortices in gas giant atmospheres, Moritz Heimpel (2015).&lt;/li&gt;
&lt;li&gt;Zonal flow scaling in rapidly-rotating compressible convection, T. Gastine (2013).&lt;/li&gt;
&lt;li&gt;Anelastic convection-driven dynamo benchmarks, Jones (2011)&lt;/li&gt;
&lt;/ul&gt;