Mechanisms of Superrotation in Slowly-Rotating and Tidally-Locked Planets

TL;DR

This paper develops a two-level primitive-equation framework to unify the mechanisms of atmospheric superrotation on slowly rotating and tidally-locked planets. By analyzing both linear responses (Matsuno–Gill-like patterns for tidally-locked planets and Rossby–Kelvin interactions for slow rotators) and nonlinear integrations across a broad parameter space, the authors show that equatorial acceleration arises from eddy momentum flux convergence driven by vertical coupling and wave interactions, with drag and vertical structure playing crucial roles. Nonlinear results reveal that tidally-locked planets often exhibit strong superrotation at low thermal inertia and modest drag, but can subrotate at high radiative relaxation times, while RK instabilities govern superrotation in axisymmetric slow rotators and can contribute during spinup in tidally-locked cases. The work provides a coherent, continuum-based understanding of superrotation mechanisms across planetary bodies, bridging simple models and GCMs and highlighting when and how different wave processes dominate the spinup and maintenance of fast equatorial jets.

Abstract

Superrotation is a common feature of quickly rotating gas giants, slowly rotating planetary bodies, and tidally-locked planets. In this paper we compare and contrast the mechanisms of superrotation in slow rotators and tidally-locked planets. We cover a wide range of planetary properties, varying in particular the thermal Rossby number Ro_T (controlled by planetary size, rotation rate, and instellation) and a radiative relaxation timescale T_rad (which parameterizes atmospheric optical thickness). We use a two-level model that contains the principal mechanisms for superrotation in both regimes yet remains analytically tractable. Linearizations of the model elucidate the behavior of superrotation-inducing eddies. In tidally-locked planets a Matsuno-Gill-like structure organizes the eddy effects but of itself is insufficient to produce superrotation; baroclinicity and low-level drag are additional essential ingredients. Nonlinear integrations further explore the superrotating regimes and exhibit significant time variability even in statistical equilibrium. Not all tidally-locked regimes superrotate: subrotation arises at high T_rad (optically thick atmospheres) and weak low-level drag. On axisymmetrically-forced slow rotators, superrotation is always linked to a previously identified Rossby-Kelvin instability. Perhaps surprisingly, the instability itself is also linked to the spinup of superrotation in some tidally-locked regimes. Finally, we explore the continuous transition in the mechanisms of superrotation from axisymmetrically-forced to tidally-locked planets by applying a progressively stronger asymmetric equatorial forcing. The Matsuno-Gill pattern quickly dominates over traveling planetary Rossby-Kelvin waves in forcing superrotation, although both mechanisms can coexist. These results provide a unified view of superrotation mechanisms across a wide range of planetary bodies.

Figures (14)

• Figure 1: Vertical discretization of the 2-level atmospheric model. A staggered grid is employed, where pressure velocity is defined on the full levels $p=0, p_0/2, p_0$, and horizontal velocities, geopotential heights and potential temperatures are defined on the half levels $p_1 = p_0/4$ and $p_2 = 3p_0/4$.
• Figure 2: Solution of the Matsuno--Gill problem \ref{['eqn:mom_lin_1']}--\ref{['eqn:thermo_lin_2']} with $E=0.02$, $\mathcal{S} = 0.05$, and $Ro_T T_\mathrm{rad} = 20$, and its eddy momentum flux convergence. (a) Upper-layer geopotential $\Phi_1$ (shading) and wind $\bm{u}_1$ (arrows). (b) EMFC in the upper layer (solid), its horizontal convergence component (red dashed), and its vertical convergence component (red dotted) (see eq. \ref{['eqn:EMFC1']}). (c, d) As (a,b), except for the lower layer (see eq. \ref{['eqn:emfc2']})
• Figure 3: Gill model properties on the sphere with different input parameters. (a) Scaled upper-layer EMFC. (b) Scaled lower-layer zonal wind. The black line shows the vertically integrated reference potential temperature profile at the equator. Drag-free solutions (dashed) are obtained analytically in Appendix A. Solutions with low-level drag (solid) are obtained numerically.
• Figure 4: RK eigenmodes with $E=0$, $\mathcal{S} = 0.05$, and $T_\mathrm{rad} = 200$. (a) Upper layer geopotential $\Phi_1$ (shading) and wind $\bm{u}_1$ (arrows), for $Ro_T = 10$ and $\alpha = 0$, corresponding to $Fr = 4.7$ and $L_d / \phi_0 = 0.4$. The thick blue line shows the local Rossby number, i.e. $Ro_T$ times the background wind profile (scale at the bottom of the panel). (b) Upper layer EMFC and its decomposition, as in Fig. \ref{['fig:Gillpattern']}b. (c, d) As (a,b), except with $Ro_T = 2.5$ and $\alpha = 0.5$, corresponding to $Fr = 4.7$ and $L_d\phi_0 = 0.28$. The mode amplitudes are normalized by their mean upper layer kinetic energy.
• Figure 5: Equilibrium equatorial jet speed in tidally-locked planets. (a) Upper-level zonal-mean zonal wind speed $\overline{u_1}$ averaged 2$^\circ$S-2$^\circ$N, as a function of $Ro_T$ and $T_\mathrm{rad}$. (b) Same as (a), multiplied by $2Ro_T$. In both plots, the hatched region marks simulations for which $\overline{u_1}$ switches sign more than 10% of the time in the last 700 rotation periods of the simulation. The thick black line marks the transition from superrotation to subrotation. In (b), black markers show approximate parameters for known tidally-locked terrestrial planets: GJ1132b ($\blacksquare$), LHS 1140 b ($\times$), Trappist 1b ($+$), Trappist 1c ($\blacklozenge$), Trappist 1d ($\bullet$), 55 Cancri e ($\blacktriangledown$), Kepler 10b ($\blacktriangle$). White-filled markers show approximate parameters for known hot Jupiters: HD 189733b ($\square$), HD 209458b ($\times$), HD 149026b ($+$), HAT-P-7b ($\lozenge$), WASP-18b ($\circ$), WASP-12b ($\triangledown$). Planets that fall outside of the regime diagram are brought to the nearest value; arrows are used to indicate planets for which $T_\mathrm{rad} < 5$ or $Ro_T > 20$. See Appendix C for details on the parameters and estimation.