Regime Diagrams of Solutions in an Idealized Quasi-Axisymmetric Model for Superrotation of Planetary Atmospheres

Abstract

 This paper presents regime diagrams illustrating the parametric dependence of dynamical balance in a superrotating atmosphere produced in a quasi-axisymmetric idealized system with strong horizontal diffusion studied previously by the present authors. In this system, the superrotation is maintained by the Gierasch mechanism, which possibly explains the four-day circulation in the atmosphere of Venus. Our previous paper developed a theoretical model of this system to estimate the superrotation strength and showed that the parametric dependence of the superrotation strength can be consolidated into three non-dimensional external parameters.
 The present study analyzes the theoretical model to determine boundaries of the regimes based on the dynamical balance and plots theoretical regime diagrams, which are important to understand the non-linear dynamical system and are useful to clearly describe the parametric dependence. Further, a parametric limit of the theoretical model is also estimated and included in the diagrams. The parametric limit shows both a lower limit for the horizontal diffusion and an upper limit of the superrotation strength in the Gierasch mechanism. The regime diagram demonstrates that the superrotation in the cyclostrophic balance is realized when the horizontal Ekman number is in a certain range whose width is mainly controlled by the vertical Ekman number.
 Numerical solutions covering a vast region in the parameter space are obtained by time-integrations of the primitive equations, and the dynamical regimes in the numerical solutions are compared with the theoretical regime diagrams. The theoretical regime diagrams agree well with the numerical results in most regions, confirming the validity of the theoretical model. Multiple equilibrium solutions are obtained when the horizontal Ekman number is lower than the theoretical limit. Moreover, they show that the Gierasch mechanism can maintain the superrotation even with the horizontal diffusion weaker than the predicted lower limit, but cannot generate superrotation from a motionless state.