Polygonal patterns of cyclones on Jupiter: Convective forcing and anticyclonic shielding

From its unique pole-to-pole orbit, the Juno spacecraft discovered cyclones arranged in polygonal patterns around the poles of Jupiter. In a related modeling study the stability of the pattern depends on shielding -- a ring of anticyclonic vorticity surrounding each cyclone. Without shielding the vortices merge. Here we present high-resolution measurements obtained by tracking clouds in sequences of infrared images. There is vorticity of both signs at 200-km scales. The standard deviation is 0.32 times the vorticity of a large cyclone, whose relative vorticity is 0.46 times the planetary vorticity. Shielding exists at large scales, and it has the magnitude and distance from the vortex center predicted in the model. There is horizontal divergence of both signs at 200-km scales, with standard deviation 0.64 times the vorticity standard deviation. We propose that these intense structures are convection and that convection is the principal energy source for the large vortices.

A Note On the Hadamard Kth Root of a Rational Function

Suppose the sequence of Taylor coefficients of a rational function f consists of kth powers of elements all belonging to some finitely generated extension field F of Q. Then it is a generalisation of a conjecture of Pisot that there is a rational function with Taylor coefficients term-by-term kth roots of those of f. The authors show that it suffices to prove the conjecture in the case that the field of definition is a number field and prove the conjecture in that case subject to the constraint that f has a dominant pole, that is, that there is a valuation with respect to which f has a unique pole either of maximal or of minimal absolute value.