PUBLICATIONS. Journal of Geophysical Research: Planets

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1 PUBLICATIONS Journal of Geophysical Research: Planets RESEARCH ARTICLE Key Points: General circulation depends on the rotation rate of cloud-covered planet Polar mixed Rossby-gravity wave produces heat flux and indirect cell in slow planet s rotation Poleward eddy heat flux influences cloud level jets via E-P flux below the cloud Correspondence to: M. Yamamoto, yamakatu@kyudai.jp Citation: Yamamoto, M., and M. Takahashi (2016), General circulation driven by baroclinic forcing due to cloud layer heating: Significance of planetary rotation and polar eddy heat transport, J. Geophys. Res. Planets, 121, , doi: / 2015JE Received 1 DEC 2015 Accepted 10 MAR 2016 Accepted article online 16 MAR 2016 Published online 5 APR The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. General circulation driven by baroclinic forcing due to cloud layer heating: Significance of planetary rotation and polar eddy heat transport Masaru Yamamoto 1 and Masaaki Takahashi 2 1 Research Institute for Applied Mechanics, Kyushu University, Fukuoka, Japan, 2 Atmosphere and Ocean Research Institute, University of Tokyo, Chiba, Japan Abstract A high significance of planetary rotation and poleward eddy heat fluxes is determined for general circulation driven by baroclinic forcing due to cloud layer heating. In a high-resolution simplified Venus general circulation model, a planetary-scale mixed Rossby-gravity wave with meridional winds across the poles produces strong poleward heat flux and indirect circulation. This strong poleward heat transport induces downward momentum transport of indirect cells in the regions of weak high-latitude jets. It also reduces the meridional temperature gradient and vertical shear of the high-latitude jets in accordance with the thermal wind relation below the cloud layer. In contrast, strong equatorial superrotation and midlatitude jets form in the cloud layer in the absence of polar indirect cells in an experiment involving Titan s rotation. Both the strong midlatitude jet and meridional temperature gradient are maintained in the situation that eddy horizontal heat fluxes are weak. The presence or absence of strong poleward eddy heat flux is one of the important factors determining the slow or fast superrotation state in the cloud layer through the downward angular momentum transport and the thermal wind relation. For fast Earth rotation, a weak global-scale Hadley circulation of the low-density upper atmosphere maintains equatorial superrotation and midlatitude jets above the cloud layer, whereas multiple meridional circulations suppress the zonal wind speed below the cloud layer. 1. Introduction Terrestrial climate model experiments have been performed by many groups working in comparative planetology [e.g., Williams and Holloway, 1982; Del Genio et al., 1993; Mitchell and Vallis, 2010; Dias Pinto and Mitchell, 2014]. The recent discovery of extrasolar Earth-sized planets from advanced astronomical observations encourages us to establish both a unified theory and a common formation mechanism for the general atmospheric circulation of these planets. Aerosols and clouds cover the entire planet and induce diabatic heating in terrestrial middle atmospheres, between the troposphere and the thermosphere (e.g., in the cloud and haze layers on Venus and Titan, in global dust storms on Mars, and in the context of asteroid impacts and supervolcano eruptions on Earth). However, the dynamics of middle-atmospheric superrotation on cloudcovered planets has not yet been fully elucidated. We need to investigate its sensitivity to planetary rotation to comprehensively understand the superrotation on fast and slowly rotating cloud-covered planets. Superrotation, in the general meaning, is a prograde atmospheric rotation faster than the planetary rotation at all latitudes. In this article, prograde zonal flows around the equator are termed equatorial superrotation, and fast prograde zonal flows at middle (high) latitudes are termed midlatitude (high-latitude) jet. On Venus, superrotational flows of ~100 m s 1 are observed in the cloud layer between 48 and 70 km [Newman et al., 1984; Rossow et al., 1990; Sánchez-Lavega et al., 2008; Moissl et al., 2009]. According to Gierasch [1975] and Matsuda [1980], the meridional circulation drives the superrotation with the help of the equatorward eddy momentum flux [Rossow and Williams, 1979]. Venus general circulation model (GCM) results support the so-called Gierasch mechanism. The global mean upward angular momentum flux due to the meridional circulation balances downward flux due to eddies, and equatorward eddy momentum flux is predominant in Venus GCMs [Yamamoto and Takahashi, 2003, 2006; Lee et al., 2007; Lebonnois et al., 2010]. This promising mechanism may also apply to Titan s superrotation [Luz and Hourdin, 2003], which has strong zonal flows of ~100 m s 1 in the stratosphere [e.g., Flasar et al., 1981]. Thus, the Gierasch mechanism is considered as a common process for superrotation on the slowly rotating planets with planetary rotation periods of 16 Earth days (Titan) and 243 Earth days (Venus). However, under the cloud-covered condition in the planetary middle atmospheres, the sensitivity of the Gierasch mechanism to the planetary rotation has not been fully investigated. YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 558

2 Comparisons of atmospheric general circulation models (AGCMs) of Venus have recently been conducted in the International Space Science Institute s (ISSI) Venus climate working group [Lebonnois et al., 2013], based on model configurations of Lee [2006] and Lee and Richardson [2010]. The equatorial superrotation and equator-pole Hadley circulation were globally formed in the numerical experiments. In addition, indirect circulations were locally apparent in the polar regions. In contrast, such indirect cells were not clearly seen in Yamamoto and Takahashi [2003]. In the ISSI project, although the model settings are almost identical, the superrotation and polar indirect cell structures are significantly different among the models. A strong polar indirect cell might have a significant effect on high-latitude jets. In addition to planetary rotation, we consider polar indirect circulation as one of the key phenomena controlling the superrotation strength in the Gierasch mechanism. However, because polar regions are likely affected artificially by polar filters or subgrid diffusion parameterization, it is difficult to fully resolve polar indirect cells in low-resolution models. Thus, high-resolution experiments are needed to simulate the middle atmosphere in the polar regions of cloud-covered planets. Del Genio et al. [1993] examined the sensitivity of superrotation to the planetary rotation for cloud-covered planets, by using an Earth-like GCM. However, the model does not resolve the middle atmosphere above the troposphere. Although Yamamoto and Takahashi [2007, 2008] investigated the effects of changing the obliquity angle of the planetary rotation axis on superrotation and subrotation in the planetary middle atmosphere, the horizontal resolution was too low to fully resolve the polar circulation. By improving the baseline run of the ISSI project [Lebonnois et al., 2013] to higher resolution, the idealized AGCM enables us here to conduct long-term (~50,000 Earth days) simulations of the middle atmosphere and polar dynamics in a cloud-covered planet. The goal of the present work is to understand the general circulation of planets globally covered by cloud or haze, not to reproduce the realistic Venus and Titan superrotations. In the Venus-like model configuration of Lee [2006] and Lee and Richardson [2010], the parameterization of radiative heating (using the equator-pole temperature contrast and thermal damping) is similar to the Held-Suarez benchmark [Held and Suarez, 1994] widely used for Earth-like planets [e.g., Mitchell and Vallis, 2010; Dias Pinto and Mitchell, 2014]. The Venus-like model setting (i.e., the base run of the ISSI intercomparison) is useful to investigate the general circulation of the idealized cloud-covered planet, because the heating maximum is located in the cloud layer. In the present study, we investigate the sensitivity of superrotation and polar indirect circulation to the planetary rotation rate by employing the high-resolution idealized AGCM, which has a heating maximum in the cloud layer above the troposphere. The results reveal the significance of planetary rotation and eddy heat transport in the formation and maintenance mechanism of superrotation on cloud-covered planets. 2. Model and Data Analyses We used the Model for Interdisciplinary Research On Climate (MIROC) GCM [K-1 model developers, 2004; Sakamoto et al., 2012] with a truncation wave number of 106 (T106) and 50 layers, in order to fully resolve the polar waves and circulation. The dynamical core is the same as that of Numaguti et al. [1997] used in our previous Venus GCM [Yamamoto and Takahashi, 2006] and solves the primitive equations on a sphere using a spectral transform method. Similar to Held and Suarez [1994], the Venus model of Lee [2006] is idealized and feasible. In the present study, the model atmosphere with baroclinic forcing due to cloud layer heating is assumed as an idealized cloud-covered exoplanetary atmosphere. Our model setting was identical to the baseline run in the ISSI comparison of the Venus AGCMs [Lebonnois et al., 2013], except for the horizontal resolution (T106). The simplified physical scheme was taken from Lee [2006]. The radiative forcing is given by dt rad =dt ¼ T ½ T 0 ðϕ; PÞŠ=τ; (1) where ϕ is the latitude, P is the pressure, and T 0 ðϕ; PÞ ¼ T ref ðpþþ T 1 ðpþðcosϕ π=4þ: (2) Here T ref (P) was taken from a Venus international reference atmosphere [Seiff et al., 1985]. T 1 (P)(cosϕ π/4) and T ref (P) are shown in Figure 1. The equator-pole temperature difference T 1 (P) was given as a baroclinic forcing due to the cloud layer heating at large distances from the surface. The equator-pole difference T 1 (P) had the maximum value of 60 K around Pa. Under the Venusian reference atmospheric pressure and YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 559

3 Figure 1. Latitude-pressure distributions of T 1 (p)(cosϕ π/4) (K, color shading) and T ref (p) (K, contours). temperature conditions, T was relaxed to the baroclinic reference temperature T 0 by Newtonian cooling τ (25 Earth days), decreasing to 15 Earth days around the uppermost layer. The Newtonian cooling and heating rate in the idealized cloud-covered model are different from the Venusian ones. When the air temperature becomes approximately the reference temperature (T T ref ), the net radiative heating (cooling) rate becomes T 1 (P)(cosϕ π/4)/τ, which is 0.5 K d 1 at the equator and 1.9 K d 1 at thepoleattheheatingmaximum level. If the realistic relaxation time and heating rate are applied to the GCM, a few thousand Venus days (400,000 Earth days) are needed for the equilibrium [Yamamoto and Takahashi, 2009]. It is difficult to conduct such an extremely long-term simulation using the high-resolution model. The use of the simplified radiative heating enables the results to reach equilibrium at a few hundred Venus days in the idealized model. In the ISSI intercomparison [Lebonnois et al., 2013, Figure 8.3], as the result of Newtonian cooling and meridional circulation, the simulated temperature differences became 1 10 K between the equator and pole in statistical equilibrium. Differently from Earth GCMs, the idealized dry model with the zonally uniform forcing does not include mesoscale moist convection, latent heating, and topography. In the ISSI Venus model setting, slowly propagating waves with zonal wave number 1 are predominant, and active baroclinic eddies with high wave numbers are not seen. The time constant of the Newtonian cooling is equal to or shorter than the periods of the predominant waves. In a dynamical situation that the planetary-scale eddies are dissipated by the relatively strong Newtonian cooling and Rayleigh friction and are not dominantly dissipated at the maximum wave number via energy cascade, strong hyperdiffusion may be unnecessary, if numerical instability is suppressed. The strong diffusion may excessively dissipate small-scale gravity waves. In general, although dissipation of large-scale disturbances due to strong hyperdiffusion is very small, it is not zero. The nonzero dissipation for large scales may accumulate in the long-term GCM experiment and influence the poleward flank of the high-latitude jets (Appendix A). In the present study, the e-folding time of the sixth-order ( 6 ) horizontal diffusion at the truncation wave number is set at 30 Earth days. The time constant is much longer than that of the fourth-order diffusion for the Earth s T106 simulation (<24 h) [Kawatani et al., 2011]. The use of such a weak horizontal diffusion is one of the unique points in our long-term high-resolution experiments. The vertical eddy diffusion coefficient was set at 0.15 m 2 s 1, which was given as a minimum value to prevent numerical instability in the GCM. The surface Rayleigh friction has a time constant of 3 Earth days. The uppermost four layers are damped by Rayleigh friction. The time coefficients at the first fourth levels from the top are , , ,and s. The detailed settings and low-resolution results are summarized in Lebonnois et al. [2013] and Lee [2006]. In the present sensitivity experiments, the planetary rotation periods in Experiments (Exp.) V, T, and E were set at 243, 16, and 1 Earth days, respectively. The calculations started from a motionless state and finished when the results were in statistical equilibrium (corresponding to 400 Venus days for Exp. V, 800 Titan days for Exp. T, and 800 Earth days for Exp. E as shown in Figure 2). Upon reaching these equilibrium states, the model outputs were analyzed using a sampling period of 3072 h (128 Earth days) in 3 h intervals for Exps. T and E and 6144 h (256 Earth days) in 6 h intervals for Exp. V. They are averaged over the sampling intervals. The sampling interval and period for Exp. V are longer than those for Exps. T and E, because the planetary rotation and wave-oscillation periods are longer in Exp. V. YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 560

4 Figure 2. Time-pressure distributions of longitudinally mean equatorial zonal winds (m s 1 ; color shading) in (a) Exp. V, (b) Exp. T, and (c) Exp. E. Data analysis of the model output is based on the transformed Eulerian mean (TEM) equation system [Andrews et al., 1987]. The residual mean meridional circulation (RMC) (v, w ) and Eliassen-Palm (E-P) flux (F ϕ EP, F Z EP ) were defined as v ¼ v ρ 0 v θ =θ z =ρ 0; (3) z w ¼ w þ cosϕv θ =θ z =rcosϕ; (4) ϕ F ϕ EP ¼ ρ 0 rcosϕ u v þ u z v θ =θ z ; (5) n h i o F z EP ¼ ρ 0 rcosϕ u w þ f ðucosϕþ ϕ =rcosϕ v θ =θ z ; (6) where u is the zonal flow, v is the meridional flow, w is the vertical flow, θ is the potential temperature, ρ 0 is the mean atmospheric density, r is the planetary radius ( km), f is the Coriolis parameter, and z is the height. Over bar and prime represent the zonal mean and eddy components, respectively. The potential temperature θ in the above equations is defined by θ ¼ T P R=Cp S ; (7) P where R is the gas constant (191.4 J kg 1 K 1 ), C P is the specific heat at constant pressure (900 J kg 1 K 1 ), and P S is the standard surface pressure ( Pa). Instead of the Eulerian mean meridional circulation, the RMC was used in the TEM equation system including the E-P flux. The E-P flux divergence terms of the right-hand side of the equation (3.5.2a) of Andrews et al. [1987] are expressed as ðρ 0 rcosϕþ 1 F EP ¼ rcos ð 2 ϕþ 1 u v cos 2 ϕ ϕ ρ 0 1 ρ 0 u w z þðrcosϕþ 1 cosϕv θ =θ z ϕ u (8) h i z þ f ðucosϕþ ϕ =rcosϕ ρ 1 0 ρ 0 v θ =θ z z : The last two terms due to the eddy heat flux are offset in the advection terms in the right-hand side of the equation (3.5.2a) of Andrews et al. [1987], h i v ðucosϕþ ϕ =rcosϕ f h þ w u i z ¼þv ðucosϕþ ϕ =rcosϕ f þ w u z þðrcosϕþ cosϕv θ =θ z ϕ u (9) h i z þ f ðucosϕþ ϕ =rcosϕ ρ 1 0 ρ 0 v θ =θ z z : Thus, the TEM equation system is composed of the rearranged momentum equations including the E-P flux and RMC. The RMC is used to study the zonally averaged transport of mass center as a direct circulation estimated by the radiative heating/cooling, in which the effect of the eddy-driven heating/cooling is subtracted from the Eulerian average [e.g., Rosenlof, 1995]. The subtracted effect of the eddy-driven heating/cooling is YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 561

5 included in the E-P flux term. Because the divergence/convergence of the E-P flux accelerate/decelerate the zonal mean angular momentum, ρ 0 r cos ϕ(ū + Ωrcos ϕ), the E-P flux represents the eddy angular momentum transport including the effect of the eddy-driven heating/cooling and thus measures the total effect of both eddy momentum and heat fluxes on the zonal mean angular momentum. In the TEM equation system, the RMC is a zonal mean direct circulation driven by the radiative heating/cooling and the E-P flux is a pseudo angular momentum flux including effect of the eddy-driven heating/cooling. It is noted that the E-P flux has an opposite direction to the zonal mean eddy angular momentum flux (F Y, F Z ). Here the zonal mean eddy angular momentum flux is defined as F Y ¼ ρ 0 rcosϕu v (10) and F Z ¼ ρ 0 rcosϕu w : (11) When the horizontal eddy heat flux is zero, the E-P flux (F EP ) in equations (5) and (6) is the same as the zonal mean eddy angular momentum flux (F Y, F Z ) multiplied by 1. In the wave analysis, the names of waves used in meteorology are extended to this article. A wave with eddy cyclonic/anticyclonic flow along the contours of the geopotential height deviation is identified as a Rossby wave. In the slowly superrotating frame, an equatorial mixed Rossby-gravity wave structure with meridional flow across the equator [Matsuno, 1966; Andrews et al., 1987] is extended to the poles, because the equatorial trapping of the wave is weak. When we can see cyclonic/anticyclonic eddy flows on the poleward side of high-latitude Rossby wave and eddy meridional flows across the equator where eddy zonal flows are very small, the wave is indentified as a mixed Rossby-gravity wave [Yamamoto and Takahashi, 2003, Figure 12]. Rossby and mixed Rossby-gravity waves with strong poleward heat fluxandferrelcellareidentified as baroclinic waves. In principle, the poleward heat flux produces the energy conversion from the zonal mean available potential energy in the Lorentz cycle. In the present study, the poleward heat flux and its related Ferrel cell are caused by the baroclinic forcing due to T 1, although the zonal mean field resulting from the baroclinic waves is nearly barotropic. Such baroclinic wave features were found in Dias Pinto and Mitchell [2014]. A Kelvin-Rossby wave is defined as a wave pattern of an equatorial Kelvin (or gravity) wave and a midlatitude Rossby wave with the same frequency and zonal wave number [Yamamoto and Takahashi, 2004, Figure 4]. This might be due to planetary shear instability of Iga and Matsuda [2005] and ageostrophic instability of Wang and Mitchell [2014]. 3. Results Under conditions pertaining to Venus (Exp. V), weak high-latitude jets of >30 m s 1 extend along the zonal mean downward flow to the lower atmosphere below the cloud layer (Figure 3a). Global-scale Hadley circulation is dominant, and polar indirect circulation is also apparent on the high-latitude side of the jets. The indirect circulation is identified as a Ferrel cell. Differently from the Earth s troposphere, the indirect cells are located in the polar regions in and below the cloud layer in Exp. V. These dynamical characteristics have been already simulated in the simplified experiments of Lee et al. [2007] and Lebonnois et al. [2010]. In Exp. T (mimicking Titan s atmosphere with a 16 day rotation period), strong high-latitude jets have speeds of >80 m s 1 in the cloud layer (Figure 3b). The Hadley circulation is seen within and below the cloud layer, but indirect circulation is not seen. This is different from the results for Exp. V. The zonal circulation below the cloud layer is similar to that in the experiment intended to mimic Titan (Exp. T1) of Del Genio et al. [1993], in which the polar indirect circulation is absent. In contrast to the slowly rotating experiments (Exps. V and T), a midlatitude jet of >50 m s 1 is located above the cloud layer on a fast-rotating planet with 1 day rotation period (Exp. E, Figure 3c). A weak global-scale Hadley circulation forms midlatitude jets in the upper atmosphere above the cloud layer. On the other hand, equatorial superrotation and midlatitude jets are not fully developed in the lower atmosphere where the multiple cells are formed between the equator and pole. Polar direct cells split around a latitude of 75 below the clouds and 90 above the surface. The circulation pattern is quite different from that in the cloud-covered Earth experiments (Exp. E) of Del Genio et al. [1993]. In the present work, because the cloud heating in the middle atmosphere is located far from the surface, the circulation pattern is divided at the 10 4 Pa level; the multiple cells consist of strong tropical and midlatitude cells and weak polar cells in and below the cloud YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 562

6 Figure 3. Latitude-pressure distributions of (a c) longitudinally mean zonal winds (m s 1 ; black contours) and stream functions (kg s 1 ; color contours) and (d f) longitudinally mean horizontal eddy heat flux (ρ 0 cosϕθ v, kgkm 2 s 1 ; color shading) and temperature (K, contours) in (Figures 3a and 3d) Exp. V, (Figures 3b and 3e) Exp. T, and (Figures 3c and 3f) Exp. E. The warm color shading in Figures 3a 3c indicates the jet core. The green and blue contours represent clockwise and anticlockwise circulations, respectively. The gray rectangles indicate the cloud layer of the model atmosphere. layer, while the global-scale Hadley cells extend to the poles above the cloud layer. In contrast, because the GCM of Del Genio et al. [1993] covers the Earth s troposphere and does not resolve the middle atmosphere, the distinction of the circulation pattern between the lower and middle atmospheres is not apparent. In the lower atmosphere, the absence of the equatorial superrotation and the presence of the multiple cells are consistent with Mitchell and Vallis [2010] and Dias Pinto and Mitchell [2014], in which a tropical Hadley cell suppresses the equatorial superrotation and extratropical Ferrel cell is located near the midlatitude jet. The mean zonal flows in Exps. V, T, and E are weaker than those in Figure 2a of Yamamoto and Takahashi [2008], because there are large differences in horizontal resolution and radiative heating. In the lowresolution GCM of T21 [Yamamoto and Takahashi, 2008], the polar indirect cell and multiple meridional circulations are not fully resolved, and the strong equatorial superrotation and midlatitude jets are formed in and around the cloud layer. This is different from the results of the present simplified high-resolution (T106) model; the cloud level jet extends to the lower atmosphere in Exp V, and the midlatitude jet forms in the upper atmosphere above the cloud layer in Exp. E. A pronounced poleward eddy heat flux is found in Exp. V (Figure 3d). The heat flux is significantly more poleward and greater relative to Exps. T and E (Figures 3e and 3f). It is produced by meridional winds across the poles, associated with slowly traveling planetary-scale baroclinic waves (Figure 4). The winds across the pole transport heat horizontally in the most predominant mode, whereas they do not effectively transport momentum horizontally. The poleward (equatorward) eddy flows are out of phase by a quarter cycle with respect to the geopotential eddy heights and advect warm (cold) air masses (Figures 4b and 4c). The meridional flows across the equator are predominant at low latitudes, differently from vortical flows at high latitudes. Thus, the wave seen in Figure 4b is identified as a mixed Rossby-gravity wave. The planetary-scale baroclinic wave produces a strong poleward heat flux, and the convergence of the heat flux at high latitudes induces polar indirect cells. The strong poleward heat flux offsets the radiative cooling around the pole. As a YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 563

7 result, the baroclinicity is weak for the wind and temperature fields. The wind shear weakened by the strong heat flux contributes to the formation of slow zonal wind (relative to Venus s zonal wind) within the cloud layer. In the Hovmöller plot of the zonal mean eddy heat flux ( T v, Figure 5), the poleward heat flux is sporadically enhanced. In the baroclinic region below the high-latitude jet core, of which wind speed increases with height, the zonal mean temperature decreases with increasing latitude. The polar temperature gradually deceases over time in the inactive flux period from day 30 to 150 after the start time of the analyses ( Pa, Figure 5a). After the strongest poleward heat fluxes (approximately day 150), the cold area of <536 K disappears in the polar region. This relationship between the poleward eddy heat flux and zonal mean temperature gradient implies the association with baroclinic instability. At Pa (Figure 5b), the heat flux is sporadically strong, although the zonal mean temperature gradient is small associated with a slight decrease of the zonal wind with height. Such strong poleward heat fluxes appear in the region even where the vertical shear of the zonal wind is weak. In Lee [2006] and Yamamoto and Takahashi [2006], polar waves with zonal wave number 1 are predominant. Thus, the presence of such a polar planetaryscale wave might be common in Venus-like planets with an extremely slow rotation rate. Figure 4. (a) Spectrum of horizontal eddy heat flux at Pa in Exp. V. (b) Longitude-latitude distributions of the temperature (K; color shading), geopotential height (m; contours), and horizontal wind (m s 1 ; vectors) components of the most predominant mode (128 day wave) in the flux spectrum. (c) Polar plots of the wind speed (m s 1 ; color shading) and temperature (K; contours) components between 30 and 90 latitudes. The vector indicates horizontal wind velocity of the most predominant mode (m s 1 ). In Exp. T, the horizontal eddy heat flux is much weaker than that in Exp. V. In the context of the absence of the strong poleward heat flux, both significant temperature gradient (lower temperature at higher latitudes) and vertical wind shear (wind speed increasing with height) are likely maintained at high latitudes. Thus, the midlatitude jet increases with altitude below the cloud layer YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 564

8 Figure 5. Time-latitude cross sections of the zonal mean eddy heat fluxes (T v, Kms 1 ; shading) at (a) Pa and (b) Pa. The contours indicate air temperature (K). The flux and temperature are averaged over 3 Earth days. and the wind speed becomes 80 m s 1 in the cloud layer. In Exp. E, the poleward heat flux is seen near the midlatitude cloud base, where the vertical wind shear and meridional temperature gradient are located. Differently from the slowly rotating planet (Exp. V), the baroclinic structure of the zonal mean fields is maintained in the fast-rotating planet (Exp. E). Figure 6 shows the horizontal eddy angular momentum fluxes (ρ 0 rcosϕu v, contours) in the three experiments. The height level of the strongest angular momentum flux increases with increasing planetary rotation. The strong eddy angular momentum fluxes are equatorward near the surface in Exp. V in Figure 6a, dominantly produced by a stationary mixed Rossby-gravity wave (Figure 7a) with meridional flows across the equator. This is the same as Figure 12 in a Venus-like GCM of Yamamoto and Takahashi [2003]. Because the eddy horizontal momentum flux converts the zonal mean kinetic energy to the eddy in the Lorenz cycle, the stationary mixed Rossby-gravity wave is generated by shear or barotropic instability. For strong superrotation (i.e., Exp. T), equatorward eddy angular momentum fluxes are seen below the cloud layer in Figure 6b. Planetary-scale waves contributing to the momentum transport have high-latitude Rossby and low-latitude Kelvin wave structures across the critical latitude (Figure 7b). This wave pattern corresponds to a Kelvin- Rossby wave generated by shear or ageostrophic instability [Yamamoto and Takahashi, 2004; Iga and Matsuda, 2005; Mitchell and Vallis, 2010; Wang and Mitchell, 2014]. The fast high-latitude Rossby wave excited in the vicinity of the strong jet always has the critical latitude on the equatorial side of the jet core and likely couples with the equatorial Kelvin (or gravity) wave with weak equatorial confinement. The Kelvin-Rossby wave is distinguishable from the superposition pattern between equatorial Kelvin and midlatitude Rossby waves with the small different frequencies (i.e., the amplitude modulation between the vertically propagating equatorial Figure 6. Latitude-pressure distributions of horizontal E-P flux (color shading). The contours indicate Eulerian zonal mean horizontal momentum fluxes (ρ 0 rcosϕu v ) in (a) Exp. V, (b) Exp. T, and (c) Exp. E. YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 565

9 Figure 7. Spectra of horizontal eddy momentum fluxes (Figures 7a 7c, right column) and horizontal patterns of the most predominant modes in the flux spectra (Figures 7a 7c, left column) at (a) Pa in Exp. V, (b) Pa in Exp. T, and (c) Pa in Exp. E. The temperature (K; color shading), geopotential height (m; contours), and horizontal wind (m s 1 ; vectors) components are decomposed by the Fourier transformation. 4 day wave and midlatitude 5.7 day baroclinic wave in Yamamoto and Tanaka [1997]). In Exps. V and T, the equatorward eddy momentum fluxes contribute to acceleration of the superrotation at low latitudes. The eddy momentum fluxes due to the mixed Rossby-gravity and Kelvin-Rossby waves correspond to the horizontal eddy mixing in the Gierasch mechanism. In contrast, the angular momentum fluxes are poleward and accelerate the lower part of the midlatitude jets in the cloud layer in Exp. E in Figure 6c. The strongest momentum flux is caused dominantly by a Rossby wave with a phase speed slower than the zonal mean wind speed at midlatitudes (Figure 7c). The eddy temperature component is small and in phase with YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 566

10 the eddy geopotential height at the central latitude of the wave. However, a weak horizontal eddy heat flux is seen around 40 latitude between and Pa (not shown), where the temperature and geopotential are slightly out of phase. In the rapidly rotating planet, the midlatitude Rossby wave does not couple with equatorial wave at the critical latitude, differently from the Rossby-Kelvin wave in Exp. T. On Earth, in general, it is difficult for the midlatitude Rossby wave to laterally interact with the equatorial Kelvin wave with strong equatorial confinement, because the equatorially trapped wave is separated from the midlatitude waves [Wang and Mitchell, 2014]. In the case of the Venus superrotation, growth rates of unstable baroclinic modes with zonal wave numbers 3 6 are large, and unstable modes with zonal wave number 1 are also seen at high latitudes [Young et al., 1984]. Takagi and Matsuda [2006] also reported baroclinic instability with zonal wave number 6 for a solid-body atmospheric rotation with Rossby number of 0.3 and Richardson number of 5. However, the basic flows are quite different from the zonal mean flow in Exp. V. In the weak equatorial superrotation state with the pronounced high-latitude jets (Exp. V), planetary-scale wave zonal wave number 1 and the Ferrel cell are confined in the polar region where centrifugal force and metric term of the highlatitude jet are locally dominant in the jet core (i.e., local Rossby number Ro L is high in the high-latitude jet core, where Ro L =(U / rcosϕ)/(2ωsinϕ) andu is the zonal mean zonal wind speed). The formations of the polar jets, Ferrel cell, and zonal wave number 1 Rossby wave in and around the high Ro L regions might be common to an experiment with slow planetary rotation and high thermal damping rate of Dias Pinto and Mitchell [2014] (their Ω* = 1/20mod experiment). In contrast, the strong equatorial superrotation associated with the Kelvin-Rossby wave in Exp. T is similar to those in superrotating regime of Mitchell and Vallis [2010] and Dias Pinto and Mitchell [2014]. As the atmospheric rotation is increased, the location of the jet is shifted to lower latitudes. Thus, the midlatitude jet likely influences the equatorial superrotation via the Kelvin-Rossby wave around the equatorward flank of the jet. To investigate the influence of the polar eddy heat flux on angular momentum transport, Eliassen-Palm (E-P) fluxes and residual mean meridional circulation (RMC) [Andrews et al., 1987] are introduced in the data analysis (section 2). Because a difference between E-P and zonal mean eddy angular momentum fluxes is caused by the zonal mean horizontal eddy heat flux, a comparison between these two flux types will show the influence of the eddy heat flux on superrotation dynamics. The distributions of the horizontal E-P fluxes (color shading in Figure 6) are quite similar to those of the zonal mean eddy angular momentum fluxes multiplied by 1 (contour in Figure 6). This indicates that the eddy heat fluxes hardly affect horizontal momentum transport. In contrast to horizontal eddy angular momentum transport, large differences between the vertical E-P flux (color shading) and zonal mean eddy vertical angular momentum flux (contour) are seen in Figures 8a 8c. In Exp. V, strong vertical E-P flux is dominantly produced by the horizontal eddy heat flux, because ρ 0 rcosϕ h i f ðucosϕþ ϕ =rcosϕ v θ =θ z is larger than ρrcosϕu w in equation (6). The vertical E-P flux owing to strong poleward eddy heat transport corresponds to downward angular momentum transport in the descent branch of the indirect cells. This is analogous to Earth s baroclinic zone and Ferrel cell [Edmon et al., 1980], although the latitude of the strong flux is located at higher latitudes relative to Earth s one. The strong vertical E-P flux contributes to the extension of the high-latitude jet toward the lower atmosphere below the cloud layer. In Exp. T, because the E-P flux has almost the same magnitude as the zonal mean eddy vertical angular momentum flux, the eddy heat flux does not contribute to the vertical angular momentum transport from the cloud layer to the lower atmosphere. The vertical E-P flux is weak and upward within the cloud layer. These diagnostics seem to indicate a weakening of baroclinic instability and concomitant weakening of downward fluxes of angular momentum. Because the E-P flux does not efficiently transport zonal momentum from the cloud layer to the lower atmosphere, the midlatitude jet in the cloud layer does not extend to the lower atmosphere. In Exp. E, the vertical E-P flux (Figure 8c) and indirect cell (Figure 3c) are produced h i by the poleward eddy heat fluxes of midlatitude Rossby waves (Figure 7c) via ρ 0 rcosϕ f ðucosϕþ ϕ =rcosϕ v θ =θ z in equation (6). This is similar to the Earth s tropospheric baroclinic zone and Ferrel circulation [Edmon et al., 1980]. The vertical E-P flux in Exp. E is stronger than that in Exp. V (Figures 8a and 8c) because of the larger Coriolis parameter f in the fast-rotating planet, although the poleward eddy heat flux is weaker than that in Exp. V (Figures 3d and 3f). YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 567

11 Figure 8. Latitude-pressure distributions of (a c) vertical E-P flux (color shading) and (d f) vertical angular momentum flux due to the RMC (color shading) in (Figures 8a and 8d) Exp. V, (Figures 8b and 8e) Exp. T, and (Figures 8c and 8f) Exp.E.ThecontoursindicateEulerian zonal mean vertical momentum fluxes (ρ 0 rcosϕu w ). To evaluate the effect of the direct circulation (RMC) on the angular momentum transport, the vertical angular momentum flux due to the RMC is defined as AMF Z RMC ¼ ρ 0 rcosϕðu þ ΩrcosϕÞw : (12) In the vertical angular momentum flux due to the RMC (Figures 8d 8f), the residual mean vertical flow transports angular momentum upward at low latitudes and downward at high latitudes in Exps. V and T, as well as in the subtropical region in Exp. E. This indicates that a residual mean globally symmetric cell (with respect to the equator) forms in slowly rotating cloud-covered planets (Exps. V and T), and the polar indirect cells associated with the eddy heat flux are completely removed in the RMC. In high-latitude regions where the RMC transports angular momentum downward, the strong eddy heat flux additionally produces the downward eddy momentum transport (i.e., the upward E-P flux) in Exp. V. Thus, zonal wind weakens in the cloud layer because of the downward angular momentum transports due to the RMC and E-P flux below the jet cores. In contrast, a vertical E-P flux is very weak in Exp. T, while vertical angular momentum fluxes due to the RMC are strong around the equator and±60 latitudes,comparedwithexp.v.thus, because vertical E-P flux is very weak below the jet cores, the strong angular momentum flux due to the RMC likely maintains the fast superrotation in the cloud layer in Exp. T. In the fast-rotating cloudcovered planet (i.e., Exp. E), the vertical angular momentum flux due to the RMC is predominant within a latitude range of ±30. Although weak upward fluxes by zonal mean return flows are also seen at midlatitudes, the strong vertical angular transport is confined to the low-latitude region below and inside the cloud layer, where the superrotation is not fully developed. Figure 9a shows the global budget of vertical angular momentum transport due to zonal mean direct circulation (solid curves) and eddy (dashed curves). Here the vertical angular momentum transport due to zonal mean direct circulation is defined as equation (12) and the vertical angular momentum flux due to eddy is defined as the vertical component of the E-P flux multiplied by 1. As a whole, the RMC transports angular momentum upward, while the eddies transport it downward. Thus, meridional circulation pumps up angular momentum to the middle atmosphere. The flux maxima are located around the maximum of the latitudinally YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 568

12 Figure 9. Vertical distributions of (a) the global mean vertical angular momentum fluxes due to RMC (solid curve) and E-P flux (dashed curve), (b) zonal flow accelerations due to horizontal E-P flux averaged from 15 to 15 in latitude, and (c) zonal flow accelerations due to vertical E-P flux averaged from 60 to 90 in latitude. Results in Exp. V, Exp. T, and Exp. E are shown as black, red, and blue lines, respectively. differential heating (~ Pa) in the all experiments. In Exp. V, the upward flux due to the RMC balances the downward one due to the vertical E-P flux. In Exp. T, the angular momentum flux of the RMC is somewhat larger than the downward one due to the E-P flux. The imbalance between the angular momentum fluxes due to RMC and E-P flux might be offset by the vertical diffusivity parameterized by a coefficient of 0.15 m 2 s 1 and the unresolved eddies with periods nearly equal to or shorter than the sampling interval. Although the vertical E-P flux in Exp. T is weaker than that in Exp. V in Figures 8a and 8b, the global averages of these vertical E-P fluxes have the same magnitude for these two experiments, because the strong E-P flux is confined within the polar regions in Exp. V. In Exp. E, the global mean angular momentum transports are strong in the cloud layer. However, they are weak below the cloud layer, where the multiple cells are predominant. Thus, the multiple cells do not efficiently transport angular momentum vertically in the lower atmosphere. In the upper region above the 10 4 Pa level, where the global-scale Hadley circulation is predominant, the small upward angular momentum flux due to the RMC maintains the equatorial superrotation and midlatitude jet of the low-density atmosphere. The equatorial zonal flow is accelerated by the equatorward angular momentum transport due to the horizontal E-P flux in slowly rotating planets (Figure 9b). The zonal flow acceleration of >0.1 m s 1 d 1 is seen around the cloud base (~10 5 Pa level) in Exp. V and in and above the cloud layer in Exp. T. The large acceleration over the middle atmosphere in Exp. T maintains the strong equatorial superrotation. Differently from Exps. V and T, the equatorial zonal flow is decelerated by the horizontal E-P flux around the cloud layer in Exp. E. The equatorial zonal flow acceleration of >0.1 m s 1 d 1 is seen in the upper atmosphere of log 10 P =2.5. In polar regions for Exps. V and E (Figure 9c), large zonal flow decelerations due to vertical E-P fluxes are found in the cloud layer, while the accelerations are below the cloud base. This means that the vertical E-P flux weakens the high-latitude zonal flow in the cloud layer. In contrast, the strong deceleration of the high-latitude zonal flow does not occur in Exp. T, because the vertical E-P flux is very weak below the jet core in the absence of strong poleward heat flux. In this context, the midlatitude jet does not weaken in the cloud layer for Exp. T. 4. Conclusions In the present study, we have found (i) three different types of middle-atmospheric jet structures (identified by J in Figure 10) depending on the planetary rotation rate of cloud-covered planets and (ii) a poleward eddy heat transport process driven by planetary-scale eddy meridional winds across the poles, which is unique to the slow superrotation state seen in Exp. V (Figure 4). Although the high-latitude wave structure and its related indirect cell are similar to Earth s baroclinic waves and Ferrel cell, the location (polar region) and zonal wave number (unity) of the baroclinic wave in Exp. V are different from those seen in the Earth s troposphere. The baroclinic wave in Exp. V is indentified as a mixed Rossby-gravity wave. The polar waves strongly YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 569

13 Figure 10. Schematics of vertical angular momentum transports due to direct zonal mean meridional circulation (black arrows) and eddies (blue arrows) in (a) Exp. V, (b) Exp. T, and (c) Exp. E. The black arrows indicate the vertical angular momentum flux due to RMC, and the blue arrows indicate the flux due to eddies. The purple arrows indicate the horizontal angular momentum flux due to eddies. The region indicated by J corresponds to the superrotational jet. P and EQ indicate the pole and equator, respectively. affect the atmospheric circulation patterns below the cloud layer in the slow superrotation state. The sensitivity experiment with respect to the planetary rotation rate shows that Ferrel cells are formed around the high-latitude and midlatitude jets in the significantly slow and fast planetary rotations (Exps. V and E), respectively. The strong eddy heat transport induces a polar Ferrel cell and its related downward angular momentum transport (i.e., an upward E-P flux) in Exp. V. Because the descent branch of the polar indirect cell is located below the cloud level jet, the high-latitude jets extend to the lower atmosphere below the cloud (Figure 10a) and thus become weak in the cloud layer. This is just the action of baroclinic instability reducing the vertical shear of the jet. In other words, because the strong eddy heat transport weakens both the horizontal temperature gradient and vertical zonal wind shear below the cloud layer, the high-latitude jets are weak in the cloud layer. The equatorial superrotation is not fully developed in the equatorward flanks of the weak jets, although the eddy momentum fluxes are equatorward in these regions. In this situation, a mixed Rossby-gravity wave dominantly contributes to the equatorial acceleration of the superrotation near the surface in the Gierasch mechanism. In Exp. T, strong equatorial superrotation is formed in the cloud layer by a global-scale Hadley circulation (Figure 10b). Differently from the slow equatorial superrotation in Exp. V, a Kelvin-Rossby wave is the most predominant eddy momentum transporter in the fast equatorial superrotation and dominantly accelerates the equatorial zonal flow via the equatorward eddy momentum flux in the Gierasch mechanism. The strong temperature gradient and its related vertical wind shear are not weakened in the absence of polar indirect cells within and below the cloud layer. In this context, the strong midlatitude jet is likely maintained at the cloud level. In Exp. E, midlatitude jets are developed through small vertical RMC transport in the low-density atmosphere above the cloud layer (Figure 10c). Rossby waves produce poleward momentum and heat fluxes in the cloud layer. Multiple meridional cells are formed inside and below the cloud layer. The tropical Hadley cell does not reach to the poles and is thus confined within the low-latitude region. Because the eddy heat flux is very weak in the extratropical and polar regions of the lower atmosphere (Figure 3f), the midlatitude cells are directly forced by radiative forcing associated with T 1. Thus, the upward branch of the midlatitude RMC cell is seen as the weak upward angular momentum fluxes around ±60 latitudes in Figure 8f. The global mean upward angular momentum transport is ineffective in the lower part of the multiple meridional cells (below the level of log 10 P = 5.5 in Figure 9a). Furthermore, the eddy equatorward momentum flux is not formed in the upper part of the multiple meridional cells, where the upward momentum flux due to RMC is locally strong. In this situation, the Gierasch mechanism does not work, and thus, the superrotation is not fully developed in the cloud layer. In a slow superrotation state (Exp. V), it is difficult for the simulated weak jets to maintain the strong temperature gradient induced by the simplified radiative forcing in accordance with the thermal wind relation. In this situation, the poleward eddy heat flux helps to weaken the horizontal temperature gradient and vertical YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 570

14 zonal wind shear below the cloud layer. In contrast, the fast superrotation state (Exp. T) is maintained in the absence of a strong eddy heat flux and upward E-P flux, because the vertical shear of the superrotational jet is not reduced. The present work suggests that the presence or absence of strong poleward eddy heat flux is one of the important factors in determining whether the slow or fast superrotation state is obtained in the cloud layer through the upward E-P flux (downward angular momentum transport) and the thermal wind relation (vertical shear of the zonal wind below the cloud layer). In Venus and Titan AGCM modeling, some groups have managed to reproduce strong superrotation, whereas others have not. Although previous studies have focused on the zonal mean eddy momentum fluxes, we need to reconsider the mechanisms that maintain or disrupt the strong vertical shear of superrotation by polar eddy heat fluxes under realistic atmospheric conditions unique to each planet (e.g., the presences of gravity waves, thermal tide, convection, dynamical instabilities, topography, and seasonal variation). Appendix A: Sensitivity to the Horizontal Resolution and Diffusion Figures A1a A1c show the zonal wind speed and mass stream function of T21, T42, and T63 experiments for Exp. V at 400 Venus days. As the horizontal resolution is increased, the structures of zonal wind and stream function approach the T106 case. Thus, T106 was applied to the present study. The high-resolution model can resolve the maximum of the horizontal flow at the pole in Figure 4c. The sensitivity to the radiative forcing is beyond the scope of the present study focusing on the planetary rotation and is left to a future. During 5 Venus days after the final time, we applied the sixth-, fourth-, and second-order horizontal diffusions of the e-folding time of 3 Earth days with at the maximum wave number to the restart T106 experiment (Figures A1d A1f). The large diffusion coefficient (i.e., short e-folding time) accelerates the poleward flanks Figure A1. (a c) Latitude-pressure distributions of longitudinally mean zonal winds (m s 1 ; black contours) and stream functions (kg s 1 ; color contours) at 400 Venus days in (Figure A1a) T21, (Figure A1b) T42, and (Figure A1c) T63 experiments. (d f) Latitude-pressure distributions of difference with longitudinally mean zonal velocity in Exp. V (m s 1 ; black contours) averaged over 5 Venus days in the restart experiments with (Figure A1d) sixth-, (Figure A1e) fourth-, and (Figure A1f) second-order horizontal diffusions of the e-folding time of 3 Earth days at the maximum wave number. The warm color shading in Figures A1d A1f indicates the jet core in Exp. V. YAMAMOTO AND TAKAHASHI POLAR WAVE AND SUPERROTATION 571

15 of the high-latitude jets. By choosing the small diffusion coefficient, as far as possible, we aimed to prevent the horizontal diffusion from smoothing zonal wind speed in the polar regions. If small-scale waves are important in the T106 case, waves with higher wave numbers of >42 should produce large difference in the zonal mean structure between T42 and T106. However, the poleward flanks of the high-latitude jets are very similar between T42 and T106. Thus, the higher wave numbers of >42 (resolved in T106) do not largely change the zonal mean polar structure. In contrast, as the parameters of the horizontal diffusion are altered, the poleward flanks of the jets are artificially changed (Figures A1d A1f). This implies that the influences of the horizontal diffusion on large-scale flow accumulate during 5 Venus days and thus change the poleward flanks of the high-latitude jets. Although vertically propagating gravity waves are seen above the cloud layer, these waves are not important in the vertical and horizontal E-P fluxes produced by the planetary-scale waves. The gravity waves decelerate zonal wind near the upper boundary with the strong Rayleigh friction. However, they do not largely influence the dynamics in and below the cloud layer. The upper atmospheric wind deceleration due to the gravity waves and its sensitivity to the horizontal resolution are beyond the scope of the present study, although they are interesting. Acknowledgments This study has been supported by a Japan Society for the Promotion of Science/Ministry of Education, Culture, Sports, Science, and Technology Grantin-Aid for Scientific Research (KAKENHI grant ). The source code of the MIROC GCM was provided under the cooperative research project for climate system research of the Atmosphere and Ocean Research Institute (AORI) at the University of Tokyo, Japan. 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