Abstract:
Theexplanation of the large-scale dynamics of the giant planets’ atmospheres hasbeen one of the classical problems of geophysical fluid dynamics. With a typicalReynolds number of 1013, Jupiter's atmosphere is one of the most turbulentplaces in the Solar System. The turbulence is strongly affected by buoyancy andCoriolis forces. Planetary rotation and Rossby number of 10-2 render stratified Jupiter's atmospherequasi-two-dimensional (2D). On largest, planetaryscales, quasi-2D turbulence undergoes additional anizotropization due tolatitudinal variation of Coriolis parameter and ensuing generation of Rossbywaves. In certain range of parameters, typical to giant planets, the flowattains some quasi-one-dimensional features with strong zonal east-west jetsdominating the largest scales. The concentration of energy in the zonalcomponents is caused by strongly anisotropic spectral energy transfer. Thisregime is a subset of geostrophic turbulence and has been coined zonostrophicturbulence.
Over the last several decades, awealth of new information has been accumulated from the NASA space missions andvarious theoretical and numerical studies. The Cassini fly-by near Jupiter inDecember 2000 delivered snapshots of Jupiter’s atmospheric velocity fields withunprecedented coverage. Spectral analysis of these fields indicates that thelarge-scale Jovian atmospheric circulation can be characterized as amacroturbulence in the zonostrophic regime in which most of the kinetic energyresides in the slowly evolving, alternating zonal jet flows and whoselarge-scale energy spectrum is strongly anisotropic. The zonalspectrum n-5 is very steep, whilethenon-zonal, or residual spectrum obeys the Kolmogorov–Kraichnan law specific to 2D turbulence in the range of theinverse energy cascade. The spectral data was used toestimate the inversecascaderate e and the zonostrophy index Rb. The ensuingvalue of Rb≥5 belongs well in the range of zonostrophic turbulence whose thresholdcorresponds to Rb≈2.5.
The meridional diffusionof passive scalar in zonostrophic turbulence can be carried out only byturbulent eddies whose size is smaller than the threshold scale . At larger scales the flow is dominated by waves thatprovide no contribution to the scalar diffusion. The meridional diffusivity estimatedtheoretically was compared against data from the dispersion of stratosphericgases and debris resulting from the Shoemaker-Levy 9 comet and Wesley asteroid impacts in 1994 and 2009respectively, and was found to be consistent with estimates for both impacts.
Numericalanalyses of zonostrophic turbulence reveal along with the familiarRossby-Haurwitz waves, a new class of nonlinear waves termed zonons. The zononsform non-dispersive wave packets that propagate in the westward direction withthe velocity equal to the phase speed of the most energetic Rossby-Haurwitzwave. Zonons reside in locations with the maximum meridional shear and areengaged in strong energy exchange with the mean flow. These physical propertiesof zonons point to their identity with solitary Rossby waves.