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

Coherent jets containing most of the kinetic energy of the flow are a common feature in observations of atmospheric turbulence at the planetary scale. In the gaseous planets these jets are embedded in a field of incoherent turbulence on scales small relative to the jet scale. Large-scale coherent waves are sometimes observed to coexist with the coherent jets and the incoherent turbulence with a prominent example of this phenomenon being the distortion of Saturn’s north polar jet (NPJ) into a distinct hexagonal form. Observations of this large-scale jet-wave-turbulence coexistence regime raise the question of identifying the mechanism responsible for forming and maintaining this turbulent state. The coherent planetary scale jet component of the turbulence arises and is maintained by interaction with the incoherent small-scale turbulence component. It follows that theoretical understanding of the dynamics of the jet-wave-turbulence coexistence regime can be facilitated by employing a statistical state dynamics (SSD) model in which the interaction between coherent and incoherent components is explicitly represented. In this work a two-layer β-plane SSD model closed at second order is used to develop a theory that accounts for the structure and dynamics of the NPJ. An asymptotic analysis is performed of the SSD equilibrium in the weak jet damping limit that predicts a universal jet structure in agreement with observations of the NPJ. This asymptotic theory also predicts the wave number of the prominent jet perturbation. Analysis of the jet-wave-turbulence regime dynamics using this SSD model reveals that jet formation is controlled by the effective value of β and the required value of this parameter for correspondence with observation is obtained. As this is a robust prediction it is taken as an indirect observation of a deep poleward sloping stable layer beneath the NPJ. The slope required is obtained from observations of the magnitude of the zonal wind component of the NPJ. The amplitude of the wave-6 perturbation then allows identification of the effective turbulence excitation maintaining this combined structure. The observed jet structure is then predicted by the theory as is the wave-6 disturbance. The wave-6 perturbation, which is identified as the least stable mode of the equilibrated jet, is shown to be primarily responsible for equilibrating the jet with the observed structure and amplitude.