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We conduct an in-depth analysis of statistical flow properties calculatedfrom the reference high-resolution Saturn simulation obtained by global climatemodelling in Part II. In the steady state of this reference simulation,strongly energetic, zonally dominated, large-scale structures emerge, whichscale with the Rhines scale. Spectral analysis reveals a strong anisotropy inthe kinetic energy spectra, consistent with the zonostrophic turbulent flowregime. By computing spectral energy and enstrophy fluxes we confirm theexistence of a double cascade scenario related to 2D-turbulent theory. Todiagnose the relevant 3D dynamical mechanisms in Saturn's turbulent atmosphere,we run a set of four simulations using an idealized version of our GlobalClimate Model devoid of radiative transfer, with a well-defined Taylor-Greenforcing and over several rotation rates (4, 1, 0.5, and 0.25 times Saturn'srotation rate). This allows us to identify dynamics in three distinctiveinertial ranges: (1) a ``residual-dominated'' range, in which non-axisymmetricstructures dominate with a -5/3 spectral slope; (2) a ``zonostrophic inertial''range, dominated by axisymmetric jets and characterized by the pile-up ofstrong zonal modes with a steeper, nearly -3, spectral slope; and (3) a``large-scale'' range, beyond Rhines' typical length scale, in which thereference Saturn simulation and our idealized simulations differ. In the latterrange, the dynamics is dominated by long-lived zonal modes 2 and 3 when aSaturn-like seasonal forcing is considered (reference simulation), and a steepenergetic decrease with the idealized Taylor-Green forcing. Finally,instantaneous spectral fluxes show the coexistence of upscale and downscaleenstrophy/energy transfers at large scales, specific to the regime ofzonostrophic turbulence in a 3D atmosphere.

Global climate modeling of Saturn's atmosphere. Part III: Global  statistical picture of zonostrophic turbulence in high-resolution  3D-turbulent simulations