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Coherent jets with most of the kinetic energy of the flow are common inatmospheric turbulence. In the gaseous planets these jets are maintained byincoherent turbulence excited by small-scale convection. Large-scale coherentwaves are sometimes observed to coexist with the jets; a prominent example isSaturn's hexagonal North polar jet (NPJ). The mechanism responsible for formingand maintaining such a turbulent state remains elusive. The coherentplanetary-scale component of the turbulence arises and is maintained byinteraction with the incoherent small-scale turbulence component. Theoreticalunderstanding of the dynamics of the jet/wave/turbulence coexistence regime isgained by employing a statistical state dynamics (SSD) model. Here, asecond-order closure implementation of a two-layer beta-plane SSD is used todevelop a theory that accounts for the structure and dynamics of the NPJ.Asymptotic analysis of the SSD equilibrium in the weak jet damping limitpredicts a universal jet structure in agreement with NPJ observations. Thisasymptotic theory also predicts the wavenumber (six) of the prominent jetperturbation. Analysis with this model of the jet/wave/turbulence regimedynamics reveals that jet formation is controlled by the effective value of$\beta$; the required value of this parameter for correspondence withobservation is obtained. As this is a robust prediction it is taken as anindirect observation of a deep poleward sloping stable layer beneath the NPJ.The slope required is obtained from observations of NPJ structure as is thesmall-scale turbulence excitation required to maintain the jet. The observedjet structure is then predicted by the theory as is the wave-six disturbance.This wave, which is identified with the least stable mode of the equilibratedjet, is shown to be primarily responsible for equilibrating the jet with theobserved structure and amplitude.

Statistical state dynamics based theory for the formation and equilibration of Saturn's north polar jet