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date: 24 January 2021

# Atmospheric Circulation on Venus

• Masaru YamamotoMasaru YamamotoResearch Institute for Applied Mechanics, Kyushu University

### Summary

Venus is a slowly rotating planet with a thick atmosphere (~9.2 MPa at the surface). Ground- and satellite-based observations have shown atmospheric superrotation (atmospheric rotation much faster than solid surface rotation), global-scale cloud patterns (e.g., Y-shaped and bow-shaped structures), and polar vortices (polar hot dipole and fine structures). The Venusian atmospheric circulation, controlled by the planet’s radiative forcing and astronomical parameters, is quite different from the earth’s. As the meteorological data have been stored, understanding of the atmospheric circulation has been gradually enriched with the help of theories of geophysical fluid dynamics and meteorology.

In the cloud layer far from the surface (49–70 km altitude), superrotational flows (east-to-west zonal winds) exceeding 100 m/s and meridional (equator-to-pole) flows have been observed along with planetary-scale brightness variations unique to Venus. The fully developed superrotation, which is ~60 times faster than the planetary rotation, is maintained by meridional circulation and waves. For the planetary-scale variations, slow-traveling waves with stationary and solar-locked structures and fast-traveling waves with phase velocities of around the superroational wind speeds are dominant in the cloud layer. Thermal tides, Rossby waves, Kelvin waves, and gravity waves play important roles in mechanisms for maintaining fast atmospheric rotation. In the lower atmosphere below the cloud layer, the atmospheric circulation is still unknown because of the lack of global observations. In addition to the limited observations, the atmospheric modeling contributes to deep understanding of the atmospheric circulation system. Recent general circulation models have well simulated the dynamical and thermal structures of Venus’s atmosphere, though there remain outstanding issues.

### Introduction

Venus is a terrestrial planet with a slow rotational period of 243 Earth days (hereafter, “day” indicates Earth day: 24 hours). The planet is approximately the same size as the earth (Venus’s mean radius is 6052 km and Earth’s mean radius is 6371 km). The tilt of the rotation axis is 177° to the orbit, which means that Venus rotates in the opposite direction that the earth rotates. The seasonal variation of the climate is very small. The period of revolution is 225 days and the Venusian solar day equals 117 days. Figure 1 shows the vertical structure of the atmosphere. The atmosphere is composed primarily of CO2 (~9.2 × 106 Pa at the surface), which contributes to maintaining high air temperature at the surface (~735 K). Cloud and haze cover the planet and absorb solar and infrared (IR) fluxes, which induces global circulation, thermal tides, and mesoscale convection. The main cloud layer of sulfuric acid is located between 49 and 70 km above the surface, and haze layers exist above and below the cloud layer. At the surface, of which the elevation ranges from -2 to 11 km, the topographical and thermal heterogeneities also influence the atmospheric circulation.

Figure 2 shows postprocessing images at various wavelengths taken by the Venus orbiter Akatsuki (Nakamura et al., 2016). Atmospheric circulation and waves on Venus have been obtained by analyzing time-sequential images. The circulation and cloud features unique to Venus (e.g., the superrotation, polar vortex and huge bow-shape structure) have been observed. Superrotation is the rotation of the atmosphere at a speed higher than that of the surface. Because the north pole of Venus is in the same celestial hemisphere relative to the invariable plane of the solar system as Earth’s north pole, superrotational (subrotational) flow corresponds to westward (eastward) zonal flow. The fast atmospheric motion of >100 m/s was identified by the 4-day rotation of large-scale ultraviolet (UV) markings, which appear in photos taken at observatories (Boyer, 1973; Dollfus, 1988). Further satellite-based observations revealed that the 4-day rotation corresponds to fully developed superrotation (fast zonal circulation) and fast traveling planetary-scale waves (Y- or Ψ‎-shaped wave patterns), which are 60 times faster than the planetary surface rotation. Along with fast zonal circulation and waves, meridional circulation is inferred from cloud tracking. The polar vortex has chaotic and long-lived structures. Hot dipole rotates around the poles and is surrounded by a cold collar: a relatively cool band at around 60° latitude. In the vortices, fine structures and filaments are often seen as an S-shaped pattern.

In the following sections, observations and the fundamental dynamics of the atmospheric circulation below ~100 km altitude on Venus are reviewed. Based on observational and theoretical investigations, classical mechanisms for formation and maintenance of the atmospheric circulation are discussed. Recent general circulation models reproducing observational features help to deduce the atmospheric circulation system from the ground- and satellite-based observations and help to propose possible dynamical processes of the atmospheric circulation. These recent advances and future perspectives are marshaled, along with the accompanying issues.

### Overview of Atmospheric Circulation on Venus

#### Fundamentals of Atmospheric Circulation

The global-scale wind system (i.e., general circulation) is closely related to the thermal structure as determined by the momentum equation, the hydrostatic approximation, the continuity equation, and the thermodynamic energy equation expressed in the spherical coordinate system on the rotating planet (e.g., Andrews, Holton, & Leovy, 1987). Although the governing equations are essentially the same among the terrestrial planets, the scale of the forces used in the equations is different. For example, the Coriolis force, which is an inertial force that acts on the horizontal atmospheric motion on Venus, is much smaller than that on the earth. Instead of the Coriolis force, the metric terms related to fast zonal wind are predominant in the superrotating atmosphere of 100 m/s. In such a dynamical system, the force balance in the meridional direction is

$Display mathematics$(1)

where u is the zonal wind velocity observed from the surface, ϕ‎ is latitude, r is the planetary radius, P is the atmospheric pressure, and ρ0 is the atmospheric density (Leovy, 1973). This is called a cyclostrophic balance, which is important in discussing the zonal wind speed at mid and high latitudes on slowly rotating planets. By combining the equations of state and hydrostatic balance, the cyclostrophic thermal wind equation is described in pressure coordinates as

$Display mathematics$(2)

Here, T is air temperature, R is the gas constant, P0 is the reference pressure, and $ξ=−ln(P/P0)$. By vertically integrating the thermal wind equation, the zonal wind velocity can be estimated from temperature measurements.

The radiative imbalance between the dayside and nightside hemispheres produces thermally induced, global-scale horizontally propagating waves, called thermal tides, in the middle atmosphere. Diurnal (zonal wavenumber 1, 117-day period) and semidiurnal (zonal wavenumber 2, 58.5-day period) thermal tides are predominant in and above the cloud layer. In the atmospheric region between the altitudes of 100 km to 150 km, the maximum dayside temperature is located at the subsolar point according to 4.3 μ‎m measurements from the Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) onboard Venus Express (Peralta, López-Valverde, Gilli, & Piccialli, 2016). The temperature decreases radially toward the morning and evening terminators. In the upper atmosphere (~90 to ~200 km altitude), the subsolar-to-antisolar circulation cell and superrotating zonal flow are driven by the dayside and nightside contrast of the extreme ultraviolet, UV, and IR heating (Gérard et al., 2017; Schubert et al., 2007). The atmospheric circulation is influenced by the wave vertically traveling from the middle and lower atmosphere.

The radiative energy balance forms the vertical changes of the static stability. The measure of atmospheric static stability S is defined by

$Display mathematics$(3)

where g is gravity acceleration and Cp is specific heat at constant pressure, which depends on air temperature. Because Cp ranges from 1.181 × 103 J kg-1 K-1 (0 km) to 7.38 × 102 J kg-1 K-1 (100 km) (Seiff, Schofield, Kliore, Taylor, & Limaye, 1985), the dependence on temperature of the specific heat capacity affects static stability and potential temperature. S can be rewritten by the Brunt–Väisälä frequency N, which is widely used in discussing wave propagation and instability:

$Display mathematics$(4)

These measures of atmospheric static stability are important in the dynamics of the general circulation and waves. S is positive and higher than 10 K/km above altitudes of 60 km, where waves can propagate vertically. In contrast, S is low below altitudes of 60 km. Neutral or unstable layers were observed at altitudes of 50 to 55 km, ~25 km, and near the surface. The lower part of the neutral layer at an altitude of 50 to 55 km is heated by the abrupt vertical change of the IR flux at the bottom of the optically thick cloud. The IR heating at the cloud bottom induces mesoscale convection and microscale turbulent convection. In the convective layer, the unstable temperature profile produced by the radiative flux convergence is relaxed to an adiabatic temperature gradient by convection (i.e., convective adjustment process), which generates gravity waves in the upper stable layer and produces local convective mixing (i.e., enlarges vertical eddy diffusion). The vertical structures of the static stability and wind strongly influence the amplitudes and frequencies of resonant waves (e.g., Covey & Schubert, 1982; Smith et al., 1993) and the growth rates of Kelvin-Helmholtz and baroclinic instabilities (e.g., Lindzen, 1990). Several review articles (e.g., Schubert et al., 1980) suggest that the multiple cell structure below the cloud layer (i.e., the separation of the meridional circulation between the cloud layer and surface) is associated with the cloud-heating maximum located far from the surface and/or the presence of the multiple neutral layers. Thus the radiative forcing and thermal structure unique to Venus could complicate the atmospheric circulation structure.

#### Large-Scale Wind Structure

Wind data were obtained from in-situ and remote-sensing observations using entry and landing probes, balloons, tracking of cloud and distinct emission features, Doppler spectroscopy techniques, and cyclostrophic thermal wind measurements. Global, climatological features of Venus’s atmospheric circulation are inferred by compiling these wind data. Sánchez-Lavega, Lebonnois, Imamura, Read, and Luz (2017) and Schubert et al. (2007) reviewed wind observations from previous Venus missions. Here characteristics of the wind structures are briefly summarized.

Vertical profiles of zonal winds below altitudes of 70 km were obtained from Venera and Pioneer-Venus probes (Figure 3; Kerzhanovich & Limaye, 1985; Schubert et al., 1980). The zonal and meridional wind velocities were ≤ ~1 m/s below altitudes of 10 km. The zonal wind gradually increased with elevation between altitudes of 10 and 50 km. For several probes, the vertical shear was roughly zero near the surface and around an altitude of 55 km. The absence of the wind shears may be caused by convective mixing in the neutral layers of S ~ 0 K/km. The zonal wind speeds abruptly increased with elevation in the upper clouds and became ~100 m/s at the cloud top. The wind velocities measured by these probes are consistent with those measured by the Vega 1 and Vega 2 balloons (66–69 m/s at ~53 km altitude; Preston et al., 1986) and with the long-term averages of cloud tracking winds in the cloud layers (~100 m/s at 65–70 km, ~60 m/s at ~ 60 km and at 45–50 km altitude; e.g., Sánchez-Lavega et al., 2017). Therefore, the zonal winds have speeds of ~100 m/s at the cloud top and have strong vertical shears in the upper cloud layer.

Horizontal wind distributions obtained from tracking of small-scale features of brightness contrast in the cloud layer (i.e., cloud tracking) are shown in Figure 4 (Hueso, Peralta, & Sánchez-Lavega, 2012; Rossow, Del Genio, & Eichler, 1990). The wind velocities around the cloud top (65–70 km altitude) were measured by brightness contrast at UV wavelengths (280–380 nm). The zonal-mean wind indicates the longitudinally averaged wind over the dayside hemisphere, not over the entire globe. The mean zonal winds are roughly constant in the meridional profiles and have speeds of ~100 m/s, although there are long-term variations of the wind. At high latitudes, the zonal wind linearly decreases toward the poles. The poleward meridional wind, measured by tracking of brightness contrast at UV wavelengths, is predominant over the dayside hemisphere. The poleward flow could be interpreted as a manifestation of the upper branch of a Hadley cell. However, because the wind velocity includes the strong poleward components of the thermal tides, the zonal-mean structure of a Hadley cell over the globe is still unknown. Winds measured by 1.74 μ‎m from the Venus Express indicate nightside winds between the altitudes of 45 to 50 km. The mean wind speed is 60 m/s in low and mid-latitudes between 0° and -60° latitude, but it decreases toward the poles at high latitudes. The cloud tracking winds for each orbit largely changes with time. The mid-latitude jet cores were often observed around the cloud top during orbits 900 and 907 of the Venus Express, and the wind speeds were 20 to 40 m/s higher than those of the middle and lower clouds measured at 965 nm (Khatuntsev et al., 2017). On July 11–12, 2016, zonal winds measured at 2.26 μ‎m by the Akatsuki orbiter had an equatorial jet core of ~90 m/s in the middle and lower cloud layers, while the cloud-top winds derived from 365 nm and 2.02 μ‎m measurements were ~110 m/s within -40° to 40° latitude (Horinouchi et al., 2017).

Latitude-pressure distributions of the zonal wind were obtained by vertically integrating the cyclostrophic thermal wind equation using the meridional gradient of measured air temperature (Newman, Schubert, Kliore, & Patel, 1984; Piccialli et al., 2012). The zonal wind increases with elevation in altitudes between 45 and 60 km, where the air temperature decreases with increasing latitude. Around the cloud top, the maximum wind speed of 110 to 140 m/s is seen around 45° latitude. The winds decrease with elevation above the cloud top, where the air temperature increases toward the poles. Thus the strong midlatitude jet structure around the cloud top is seen in the wind field derived from the cyclostrophic thermal wind. The cyclostrophic winds are higher than the UV cloud tracking winds. Although the reason of the inconsistency is not yet understood, Piccialli et al. (2012) suggest that the observation altitudes may not be the same between the two measurements and that the cyclostrophic approximation may be made less accurate by the wind acceleration/deceleration due to eddies.

The ground-based Doppler spectroscopy measurements have revealed complex circulation in the region between the cloud top and thermosphere (70–120 km). The observations of visible sunlight radiation reflected at the upper clouds and atmospheric CO2 absorption have measured the wind speeds at altitudes of 65 to 75 km (e.g., Machado, Luz, Widemann, Lellouch, & Witasse, 2012; Widemann, Lellouch, & Campargue, 2007). The Doppler spectroscopy and Venus Express cloud tracking results have shown agreement on measurements of wind velocities (Machado, Widemann, Luz, & Peralta, 2014; Machado et al., 2017). Wind speeds at 90 to 110 km have been measured from CO absorption lines at millimeter and submillimeter wavelengths (e.g., Lellouch, Paubert, Moreno, & Moullet, 2008; Schloerb, Robinson, & Irvine, 1980) and from CO2 non-LTE IR emissions (e.g., Goldstein et al., 1991; Sornig et al., 2008). These ground-based observations are summarized in Limaye and Rengel (2013) and show the coexistence of superrotation and subsolar-to-antisolar circulation, of which winds are variable and the maximum wind speeds are much greater than 100 m/s.

Tracking of bright spots and filaments observed at 1.27 μ‎m (from O2) is used to infer local motions at altitudes of 90 to 110 km (Gorinov, Khatuntsev, Zasova, Turin, & Piccioni, 2018; Hueso et al., 2008; Soret, Gérard, Piccioni, & Drossart, 2014), although it is questionable whether these airglow can be considered as passive tracer in the tracking. The global mean wind fields in the nightside (Gorinov et al., 2018) showed two opposite flows from terminators to midnight. The eastward wind speed from the morning side exceeded the westward from evening by 20 to 30 m/s. The NO bright spots observed by Pioneer Venus and Venus express have also been used for inferring the circulation with the help of thermospheric model studies. According to Stiepen, Gérard, Dumont, Cox, and Bertaux (2013), the bright spots’ shift from the antisolar point (around 2 h in the morning) and the difference with the O2 airglow indicate that superrotating zonal winds were weak near 97 km but play an important role near 115 km.

#### Waves

Horizontal structures of mesoscale gravity waves and convective motions were seen in high-resolution images (e.g., Peralta et al., 2008; Piccialli et al., 2014), and their vertical structures were inferred from radio occultation measurements (Ando & Imamura, 2015; Hinson & Jenkins, 1995; Tellmann et al., 2012). Convective penetration into stable regions occurs in the convective layer located between the upper and lower stable regions (~55 km altitude) and produces gravity waves (Baker, Schubert, & Jones, 2000a, 2000b; Imamura et al., 2014; Lefèvre, Spiga, & Lebonnois, 2017; Leroy & Ingersoll, 1995; Yamamoto, 2014). The radiative-dynamical cloud feedback is a possible wave-generation mechanism in the cloudy atmosphere (Gierasch, Ingersoll, & Williams, 1973). When the vertical displacement of an air parcel containing cloud particles changes the optical depth in the lower clouds through particle condensation and evaporation, the cloud radiative heating rate also changes around the top and bottom of the lower cloud. The enhanced heating by the vertical motion is called radiative-dynamical cloud feedback heating (CFH). CFH enhances convective motions and their related gravity waves (Yamamoto, 2003). In addition, gravity waves might be generated by surface topography (Young et al., 1987), breaking of planetary-scale wave (Yamamoto, 2001), and Kelvin-Helmholtz instability (Imamura, 1997).

Thermal tides forced by solar heating (Fels & Lindzen, 1974; Pechmann & Ingersoll, 1984; Takagi & Matsuda, 2005, 2006) have been observed in the middle atmosphere. Diurnal and semidiurnal tides with large amplitudes were found above the cloud top in the equatorial longitude–height cross sections of air temperature (Schofield & Taylor, 1983). In particular, the vertical propagation of semidiurnal tides was clearly seen in the solar-fixed longitude-altitude cross-section of equatorial air temperature. According to the Fourier-fitting data of the Pioneer Venus Orbiter Infrared Radiometer (PV OIR; Elson, 1983; Pechmann & Ingersoll, 1984) and the Venera-15 IR spectrometry (Zasova, Khatountsev, Ignatiev, & Moroz, 2002), semidiurnal thermal tide was predominant at low latitudes in the middle atmosphere, whereas diurnal thermal tide was predominant at high latitudes around an altitude of 60 km. During the Venus Express observation, the amplitude of the polar diurnal tide observed by VIRTIS was much weaker than that observed by the PV OIR (Peralta et al., 2012). The Venus Express Radio Science experiment detected a diurnal thermal tide at high latitudes (Tellmann et al., 2009). The horizontal structure of the thermal tides at the cloud top was obtained from UV cloud-tracking wind in the dayside hemisphere (Limaye, 1988). The poleward wind component of the tides was stronger than that of the Hadley cell (Smith & Gierasch, 1996).

Planetary-scale waves at the cloud top were observed by large-scale UV markings and eddy components of the cloud-tracking winds. The periods and phase velocities of the waves vary over time. In the spring of 1979, planetary-scale UV fluctuations oscillated with a 4-day period at low latitudes and a 5-day period at mid-latitudes. The wave period was 4 days over the whole latitude in spring 1980 and 5 days in spring 1982 (Rossow et al., 1990). For UV images from 2006 to 2011, 5-day wave signals were slower than the fast zonal wind (> 100 m/s) in the upper cloud region, though a 4-day wave signal of the eddy zonal wind was faster than the slow zonal wind (< 90 m/s) in summer 2007 (Kouyama, Imamura, Nakamura, Satoh, & Futaana, 2015). The rotation periods of wave-like signatures at altitudes between 58 and 64 km were 3.5 days in May 2007, 4.9 days in November 2007, and 8.4 days in August 2010 based on the assumption that zonal wavenumber 1 was dominant (Hosouchi, Kouyama, Iwagami, Ohtsuki, & Takagi, 2012). According to the ground-based observations, large-scale NIR markings rotating with a 5.5-day period were observed in low-latitudinal regions (Crisp et al., 1991). The waves corresponded to the planetary-scale waves in the middle and lower cloud layers.

Many works (e.g., Covey & Schubert, 1982; Del Genio & Rossow, 1990) suggest that the equatorial waves with phase velocities faster than the mean zonal wind speeds are identified as equatorial Kelvin waves, and the mid-latitude waves with velocities slower than the mean zonal wind speeds are identified as Rossby waves. Fundamentals of these waves are described in standard meteorological textbooks (e.g., Holton, 2004; Lindzen, 1990). These planetary-scale waves with periods of three to eight days are generated and amplified by resonance responses to surface disturbances (Covey & Schubert, 1982), shear instability (Iga & Matusda, 2005), cloud feedback heating (Smith, Gierasch, & Schinder, 1992, 1993), barotropic instability (Elson, 1978), and baroclinic instability (Young, Houben, & Pfister, 1984). These wave theories are well summarized in review articles (e.g., Read, 2013; Sánchez-Lavega, Lebonnois, Imamura, Read, & Luz, 2017).

UV images taken from Mariner 10 showed swirling bright/dark clouds around the poles, indicating vortical motions. Polar hot dipoles and a cold collar were found by the Pioneer Venus orbiter radiometric temperature experiment (Taylor et al., 1979). The two warm maxima rotated around the pole with a period of ~3 days (Schofield & Diner, 1983), and the cold collar had longitudinal contrast. Fine morphology of polar vortices and their temporal changes were observed at multiple wavelengths by the Venus Express (e.g., Luz et al., 2011; Piccioni et al., 2007). A double spiral structure was detected in the southern polar region. The morphology and rotation rates varied with time. The single or double spirals were seen in the high-resolution images, and a tripe structure was rarely seen. High-temperature filament swirled around the warm core and extended to one or two other warm cores. This was often seen as an S-shaped pattern in the polar warm oval. The centroid of rotation of the vortex was displaced from the pole by ~3° and migrated around the pole. From the observations of the Venus Express, the relative potential vorticity calculated from the polar cloud-tracking wind suggests that barotropically unstable waves may be locally induced (Garate-Lopez et al., 2013). The observed temperature variation with a period of ~3 days has a barotropic structure (Ando et al., 2017). According to analyses of dynamical instability, the three-day wave with zonal wavenumber 2 consisting of the warm poles is generated by barotropic and/or baroclinic instabilities (Elson, 1982; Young et al., 1984). An S-shaped vortex structure similar to the observed images is well simulated in the nonlinear barotropic model (Limaye et al., 2009).

In the dayside cloud top region, Y-shaped UV brightness patterns (the Y tilted by 90°) consisting of planetary-scale equatorial and polar dark bands have been observed (Belton, Smith, Schubert, & Del Genio, 1976; Imai et al., 2016; Rossow, Del Genio, Limaye, & Travis, 1980). In the season when equatorial and midlatitude UV variations have the same oscillation period, a linear combination of Kelvin and Rossby waves can produce the Y-shaped wave pattern (Covey & Schubert, 1982). However, when the equatorial 4-day and midlatitude 5-day variations dominate (e.g., spring 1979), the linear combination of the two waves with different periods cannot maintain the Y-shaped structure; therefore it appears as an inverse Y-shaped feature, which is not observed. In dynamical models of Yamamoto and Tanaka (1997, 1998), amplitude modulation of a baroclinic Rossby wave by the equatorial Kelvin wave forms the Y-shaped structure without the inverse Y-shape. The Y-shape morphology is also reproduced as distortions of the wave structure by the Venus winds (Peralta, Sanchez-Lavega, Lopez-Valverde, Luz, & Machado, 2015), and as trajectories of clouds advected by meridional wind and equatorial waves (Smith et al., 1992, 1993). A stationary, interhemispheric bow-shaped structure was found in mid-IR and UV images from the Akatsuki orbiter (Figure 2), and it is suggested that it is forced by mountain topography (Fukuhara et al., 2017).

The dynamics of the polar vortex and planetary-scale wave patterns are still unsolved. The modeling efforts of these phenomena are briefly described in the following section.

### Dynamics and Modeling Efforts of Venus’ Atmosphere

#### Dynamics of Superrotation: Fundamentals

Venus’s superrotation, with wind speeds of ~100 m/s, is a topic of great interest in geophysical fluid dynamics. The dynamics of the fully developed superrotation has been theoretically investigated since the late 1960s (Gierasch et al., 1997; Read, 2013; Read & Lebonnois, 2018; Sánchez-Lavega et al., 2017; Schubert et al., 2007). The intensity of the superrotation is measured by the specific angular momentum m [≡ r cosϕ‎ (Ωr cosϕ‎ + u)] for the atmosphere and m0 [≡ r cosϕ‎ (Ωr cosϕ‎)] for the motionless state (u = 0), where r is the planetary radius, ϕ‎ is latitude, Ω‎ is the planetary rotation speed, and u is the zonal wind velocity observed from the surface. The governing equation of m is

$Display mathematics$(5)

where v and w are meridional and vertical wind velocities, respectively. Overbar and prime indicate zonal average and deviation from the average, respectively. According to Read (2013), a measure of “local” superrotation s is defined as

$Display mathematics$(6)

and a measure of “global” superrotation SG is defined as

$Display mathematics$(7)

where M is the total angular momentum integrated over the whole atmosphere and M0 is the total angular momentum of the motionless state. These definitions mean that dynamical evolution of angular momentum in the atmosphere determines the intensity of the superrotation. The angular momentum is supplied from the planet’s solid body via surface friction due to the subrotation near the surface. The angular momentum of the superrotation is transported to the cloud levels by (a) vertical Reynolds stress ($ρ0u′w′¯$) of wave or convection and (b) meridional circulation with the help of the equatorward eddy angular momentum flux. These two mechanisms accelerate the fast superrotation in the cloud layer.

In the superrotation mechanism caused by vertical Reynolds stress, the cloud-level angular momentum forming the equatorial superrotation is pumped up from the lower atmosphere via the eddy angular momentum flux of $ρ0u′w′¯$ (i.e., the vertical Reynolds stress multiplied by r cosϕ‎). Because angular momentum and its flux, including a factor of cosϕ‎, become relatively larger at lower latitudes, the dynamical process efficiently works at the equator. The superrotation mechanism is classified into three scenarios related to vertically tilting convection, thermal tides, and equatorial Kelvin waves. In the first scenario (Figure 5a), large-scale equatorial convective cells are vertically titled by dynamical instability (Thompson’s mechanism; Thompson, 1970) and a slowly migrating heat source (moving flame mechanism; Schubert & Whitehead, 1969) in the longitude-height cross section between the surface and cloud layer. The upward convective momentum flux produces the superrotation in the upper part of the convective cell. In the mechanism by thermal tide (Fels & Lindzen, 1974; Figure 5b), the superrotation is produced by vertical wave propagation via the wave mean-flow interaction. The thermally forced internal gravity waves with phase velocity c slower than the zonal-mean wind speed ($c) are generated in and around the cloud-top solar heating maximum and propagate downward and upward from the heating region. The convergence of the vertical eddy momentum flux in and around the heating maximum produces the equatorial superrotation in the upper cloud layer. In the superrotation mechanism by equatorial Kelvin wave (Figure 5c), which is essentially an internal wave with a velocity of $c>u¯$ and confined within lower latitudes (Leovy, 1973), the fast wave propagates vertically from the lower atmosphere and accelerates the equatorial zonal flow at and around the critical level ($c=u¯$), where the vertical momentum flux is absorbed in the linear wave theory. Similarly, Hou and Farrell (1987) proposed the superrotation mechanism via critical-level absorption of gravity waves.

The superrotation mechanism by meridional circulation (Figure 5d) is well known as the Gierasch–Rossow–Williams mechanism (Gierasch, 1975; Rossow & Williams, 1979). The zonal-mean meridional circulation transports the angular momentum upward at the equator and downward at the poles via the flux $m¯w¯$. The equatorward eddy flux $m′v′¯$ accelerates $m¯$ in the equatorial upward branch of the circulation cell and decelerates it in the polar downward branches. Then, the equatorial angular momentum becomes larger than the polar momentum because of the equatorward eddy momentum flux. With such distribution of the angular momentum, the globally averaged vertical angular momentum flux, due to the zonal-mean vertical flow, is upward. Thus the meridional circulation efficiently pumps the angular momentum up to the cloud layer during the spin up of the superrotation. Matsuda (1982) simulated the formation of the superrotation on the assumption of large horizontal diffusion and meridional circulation. The equatorward eddy momentum transport is produced by a Rossby wave due to barotropic instability (Rossow & Williams, 1979), by a Kelvin-Rossby wave (a pair of an equatorial Kelvin wave and a high-latitude Rossby wave with the same frequency) due to shear instability (Iga & Matsuda, 2005) and barotropic, ageostrophic instability (Wang & Mitchell, 2014) and by the vertically and laterally propagation of thermal tides (Yamamoto & Takahashi, 2006) and equatorial waves (Imamura, 2006).

After the global superrotation is fully developed in the Gierasch–Rossow–Williams mechanism, the globally averaged upward angular momentum flux of the meridional circulation balances the downward flux of eddies (vertical propagating gravity waves and eddy diffusion; Yamamoto & Takahashi, 2006), while the vertically integrated equatorward angular momentum flux of eddies balances the poleward flux of the zonal-mean circulation (Lebonnois et al., 2010).

#### General Circulation Modeling: Simplified General Circulation Models

The atmospheric general circulation model (GCM) has been used as a tool for investigating formation and maintenance of the superrotation. Formation is studied by investigating how the superrotation spins up from the motionless state. Maintenance is studied by investigating how the fast zonal flow is maintained in a realistic superrotating atmosphere. This section focuses on these two processes in recent GCM works since 2000; historical overviews of Venus GCMs were given by Lewis, Dawson, Lebonnois, and Yamamoto (2013) and Sánchez-Lavega et al. (2017).

Under Venus-like conditions with a high surface pressure of ~90 atm and slow planetary rotation of 243 days, the fully developed equatorial superrotation of > 100 m/s is spun up from the motionless state by long-term time-integration of GCMs using solar heating rates and Newtonian cooling (Yamamoto & Takahashi, 2003, 2006). Although the simplified GCMs (Lee, Lewis, & Read, 2005, 2007) produce the superrotation, wind intensities are different among the several dynamical cores using the equator-to-pole contrast and Newtonian cooling (Lee & Richardson, 2010). Lebonnois et al. (2013) revealed large differences among the dynamical cores of the Venus GCMs under Venus-like idealized conditions similar to Lee and Richardson (2010). Although the model setups were similar, because low-resolution models were used to conduct long-term time integrations, the difference caused by the numerical methods likely appeared in the intercomparison. In the idealized models with high horizontal resolutions, a decadal oscillation between superrotation and subrotation was simulated in an experiment of 1° longitude × 1° latitude (Parish et al., 2011), whereas the general circulation in a spectral model simulated with a truncation wavenumber of 106 (T106, Yamamoto & Takahashi, 2016) was similar to that in Lee et al. (2007). Thus a further comparison study is needed to fully understand the characteristics of the dynamical cores in the long-term GCM simulations in order to apply them to the realistic full-physics Venus GCMs.

Simplified GCMs with zonal-mean heating produce equatorial superrotation by Hadley circulation with the help of the equatorial eddy momentum flux (i.e., Gierasch–Rossow–Williams mechanism). In contrast, according to a simplified GCM with a diurnal cycle (Yamamoto & Takahashi, 2004, 2006), the global superrotation is produced by the Gierasch–Rossow–Williams mechanism, whereas the cloud-top equatorial superrotation is accelerated by thermal tides. This means the coexistence of both the Gierasch–Rossow–Williams and thermal tide mechanisms, as was also simulated in the realistic GCMs including radiative transfer (Lebonnois et al., 2010). Thus discussion about the formation and maintenance of the superrotation should be separated into the global superrotation based on the globally averaged angular momentum balance and the local (equatorial) superrotation based on the local momentum balance. Yamamoto and Takahashi (2006) showed that thermal tides accelerate the equatorial superrotation at the cloud top, whereas the equatorward momentum flux of the Kelvin-Rossby wave accelelrates the superrotatin near the cloud base. Thus the momentum transporter locally producing equatorial superrotation differs at different levels of elevation.

For simplified GCMs it is difficult to produce the fast zonal wind under realistic Venus radiative heating, as was indicated by Hollingsworth, Young, Schubert, Covey, and Grossman (2007). Additional heating, such as the surface temperature contrast and the enhancement of the heating rate around an altitude of 55 km, is required to reproduce the lower atmospheric superrotation below the cloud layer. To resolve this issue in the formation of the superrotation, developments of realistic radiative and small-scale gravity wave processes unresolved in GCM are needed.

The aforementioned GCMs have been used for investigating the formation process from an initially motionless state to a superrotation state. In contrast, the presence of the superrotation has been assumed as an initial condition or background flow in several GCMs, in order to focus on the maintenance mechanism of the superrotation and the wave dynamics in the superrotating atmosphere. Yamamoto and Takahashi (2012) assumed a background zonal flow in the GCM instead of an initial motionless state. This is an extension of wave mean-flow interaction mechanistic models (Newman & Leovy, 1992; Yamamoto & Tanaka, 1997) to Venus middle-atmosphere GCMs (VMAGCM). The VMAGCM with a realistic solar forcing below 80 km and Newtonian cooling is utilized as the tool for investigating meridional circulation and waves in Venus’s middle atmosphere. In the presence of meridional circulation and thermal tides, dynamical effects of the equatorial waves were examined using the simplified VMAGCM. In the case of the equatorial forcing with a 5.5-day period and zonal wavenumber 1, the superrotation is fully developed at the cloud top and base. The 5.5-day wave is apparent at the cloud base, whereas the 4-day wave is generated at the cloud top. The simulated waves correspond to the equatorial 5.5-day NIR marking and 4-day UV dark band. The VMAGCM experiments (Yamamoto & Takahashi, 2012, 2015, 2018) show Y-shaped wave patterns formed by the amplitude modulation of the Kelvin and Rossby waves in the presence of thermal tides, polar dipole formed by transient baroclinic waves, a cold collar enhanced by the diurnal tide, and year-to-year variation of the zonal wind.

Initially superrotating zonal flows have been used in GCMs by Kido and Wakata (2008) in the context of the multiple states of the superrotation. Recently, maintenance of the superrotation and its related waves were investigated on the assumptions of an initial realistic superrotation and static stability in a T63 experiment with 120 layers using the AGCM for Earth simulator (Sugimoto, Takagi, & Matsuda, 2014). The atmospheric circulation in the middle atmosphere is in equilibrium in a short-term experiment under the initial condition, which satisfies the cyclostrophic thermal wind. The realistic GCM simulated planetary-scale Kelvin and Rossby waves, along with thermal tides (Sugimoto et al., 2014) and dynamics of the polar vortex (Ando et al., 2016, 2017). The polar waves are formed by barotropic waves and consistent with the Venus Express observations. The cold collar and its longitudinal variation were simulated. Sugimoto et al. (2017) developed an assimilation model with the observation data made by the Venus Monitoring Camera of the Venus Express. Their high-resolution simulations using an initially superrotating state are useful to elucidate the dynamical processes in the presence of the superrotation (i.e., how the superrotation is maintained in the middle atmosphere).

#### General Circulation Modeling: Development of Full-Physics GCMs

Toward modeling realistic Venus general circulation and climate, radiation and gravity wave parameterizations have been developed by several research groups. The Venus GCM has been developed at the Laboratoire de Meteorologie Dynamique (Lebonnois et al., 2010; Lebonnois, Sugimoto, & Gilli, 2016). Solar heating computed from look-up tables (Crisp, 1986) and a radiative transfer model based on a net exchange rate method for IR radiation (Eymet et al., 2009) were implemented in the model. This GCM assumed horizontally uniform clouds with vertical distributions of their optical parameters. Unlike Venus GCMs using Newtonian cooling, dynamical effects of the IR heating around the cloud base were considered in the simulation with the radiative transfer. Based on the finite-difference dynamical core, the Venus GCM simulations of Lebonnois et al. (2010) were calculated with horizontal grids of 48 (longitude) × 32 (latitude) and 50 vertical levels (from the surface to ~95 km altitude). In these simulations, the diurnal cycle and topography were taken into account, and the dependence on temperature of Cp was considered in the model. Thus the circulation simulated with the full radiative transfer is very different from that with the simplified radiative forcing (with no diurnal cycle) using the Newtonian cooling. This indicates the importance of the radiative transfer process and diurnal cycle. In the model that started from a motionless state and included full radiative transfer and topography, the zonal wind speed has a maximum value of ~60 m/s at the cloud top in the equatorial region, and the meridional circulation is divided into several cells. Hadley-type cells are driven in and above the cloud layer and accompanies the regional circulation cells in the regions below 50 km altitude. The zonal wind below the clouds is very slow (< 5 m/s) compared to the observations. The budget of angular momentum shows that the global superrotation is formed and maintained by the Gierasch–Rossow–Williams mechanism with equatorward eddy angular momentum fluxes and zonal-mean meridional circulations, while diurnal and semi-diurnal thermal tides propagating vertically in the equatorial region above the cloud top contribute to the maintenance of the equatorial superrotation.

The thermal structure simulated in later work was compared with VIRTIS-H/Venus Express temperature retrievals in and above the upper clouds, where thermal tides dominate (Migliorini et al., 2012). In the high-resolution models of 96 (longitude) × 96 (latitude), the boundary layer scheme was improved and the simulation started from an initial superrotating state (Lebonnois et al., 2016). This work shows that the modeled zonal wind field is similar to the one that is observed and emphasizes the roles of thermal tides and the presence of baroclinic wave activity in the cloud layer.

Ikeda (2011) developed a full radiative transfer model for a Venus GCM based on the discrete ordinate and adding method. Solar and IR radiative transfers were considered in this model. A radiative transfer code, based on the k-distribution method and two-stream (upward and downward) method, was applied to absorption, emission, and scattering due to gas and aerosols in spectral range of solar and IR radiations. The radiative transfer scheme and convective adjustment were implemented in a Venus version of the Center for Climate System Research/National Institute for Environmental Studies GCM with a T21 horizontal model resolution and 52 levels for the domain from the surface to ~90 km altitude. The seasonal variation and surface topography were not considered in the model. The simulated air temperature is close to the Venus International Reference Atmosphere (Seiff et al., 1985) below 40 km altitude and colder above and in the cloud layer. The zonal-mean flow has a high speed of ~50 m/s at the cloud top, whereas it has very low speed (< 5 m/s) below 50 km altitude. This zonal wind structure is similar to that from Lebonnois et al.’s (2010) study. To investigate the effect of small-scale gravity waves in the lower-atmospheric superrotation, the gravity wave processes of Hou and Farrell (1987) were assumed in an additional experiment. The superrotation in the lower atmosphere is maintained by critical-level absorptions of gravity waves, and the zonal-mean flow with a velocity of ~80 m/s is maintained at the equatorial cloud top. Although this experiment, which includes gravity-wave parameterization, is in better agreement with the observed superrotation, the validity of the wave energy flux and the forcing mechanism near the surface should be further investigated.

The Oxford Planetary Unified (Model) System for Venus was developed by Mendonça and Read (2016) and was based on a finite-difference dynamical core (version 4.5.1 of the UK Meteorological Office Portable Unified Model) and a radiative transfer model used by Mendonça, Read, Wilson, and Lee (2015). The temperature-dependent specific heat formulation used by Lebonnois et al. (2010) improved the boundary layer and convection adjustment schemes. In the radiative model, a two-stream radiative code was applied to solar radiation, and a thermal radiation code based on an absorptivity/emissivity formulation (neglecting scattering) was applied to IR radiation. The simulations used a grid spacing of 5° × 5° with 37 layers and assumed a fixed distribution of clouds and a flat surface. Realistic superrotation at the cloud level is driven by thermal tides and planetary waves, whereas it is weak in the deep atmosphere. The structure of the zonal wind is similar to those from previous GCM experiments conducted by Lebonnois et al. (2010) and Ikeda (2011), though the wind speeds at the cloud top differ among the models.

#### Toward Understanding Realistic Features of Atmospheric Circulation on Venus

Because a simultaneous global observation network has not been constructed for Venus, it is difficult to directly obtain global atmospheric circulation features from the available observations. Even in the well-observed cloud region, it is not easy to measure the global wind structure at the same time. Furthermore, three-dimensional atmospheric circulation is mostly unknown in the deep atmosphere below the cloud. Although there are difficulties in obtaining the meteorological data, long-term multiple-wavelength observations over the globe are expected to elucidate the cloud-level circulation and waves. Observations of wind and trace gases below the cloud level are also needed to understand the lower-atmospheric circulation. In addition to these observations, the GCM is useful for elucidating the three-dimensional structures of the superrotation and waves. However, large differences in atmospheric circulation are shown even for similar models (Lebonnois et al., 2013). Furthermore, for simulations using the same GCM, the zonal wind is sensitive to different model parameters.

In discussing how the fast zonal flow is maintained in the realistic superrotating atmosphere, the global angular momentum budget is not fully understood. For example, although the thermal tides can locally accelerate the equatorial zonal wind around the cloud top, it is still unknown whether they contribute to the global mean vertical angular momentum transport. The global angular momentum budget analysis is essential to understanding why Venus’ superrotation is developed over a whole atmosphere (why SG is greater than unity) and how it is globally maintained. In addition, the inspection of angular momentum conservation in Venus GCMs should also be needed for long-term simulations (Lebonnois et al., 2012; Lee & Richardson, 2012).

Surface processes are very important for understanding atmospheric circulation. Near-surface winds induce orographic waves over the mountains and the surface subrotation supplies angular momentum to the atmosphere via surface drag. According to GCM experiments using Venus’s topography, the lowermost-level flow had a maximum velocity of ~27 m/s in the simulation with the topography and planetary boundary layer scheme of the Spalart–Allmaras model (Herrnstein & Dowling, 2007). In contrast, the lowermost-level flow was sufficiently decelerated by surface drag, and the topography-induced wind speed was a few meters per second in Yamamoto and Takahashi’s (2009) experiment. The discrepancy of the surface winds between the models was not fully examined. Lebonnois and Schubert (2017) suggested that density-driven separation of N2 from CO2 can occur in Venus’s deep atmosphere, based on experiments on the supercritical fluids under high-pressure conditions. If so, the related molecular diffusion and natural density-driven convection must also be considered in the surface and planetary boundary layer models. Thus further observation and model investigation under high pressure and temperature conditions are needed. In particular, the radiative and thermodynamic processes in the deep atmosphere are highly important for accurate simulation of the atmospheric circulation.

Venus’s topography influences the global atmospheric circulation via surface torque and stationary waves. The dynamical effects of the topography are discussed in several works. If the orographic waves have a large momentum flux and propagate vertically, they decelerate the zonal wind at upper levels. The significant asymmetry between northern and southern hemispheric winds is formed under surface conditions with large wind velocity (Herrnstein & Dowling, 2007), whereas such a large asymmetry is not formed under conditions with small surface wind velocity (Yamamoto & Takahashi, 2009). The asymmetry of the zonal wind in a preliminary experiment conducted by Lee et al. (2007) is opposite of that in an experiment conducted by Herrnstein and Dowling (2007). Unlike in these previous studies, the superrotation is enhanced by accounting for topography in Lebonnois et al. (2010), compared to the experiment without topography. Significant asymmetry in the zonal wind is not seen, though there is asymmetry in the meridional circulation below the cloud layer. Orbiter explorations of Venus found conspicuous variation of cloud-top zonal flow (Bertaux et al., 2016) and a large-scale stationary bow-shaped brightness pattern (Fukuhara et al., 2017) (Figure 2b) over the Aphrodite Terra. These works emphasize the importance of local wind deceleration and three-dimensional propagation by the orographically forced waves. However, the mechanisms of these processes have yet to be fully understood.

Dynamical linkages between the lower atmosphere and the cloud layer are also key factors for understanding Venus’s atmospheric circulation. If meridional circulation in the cloud layer reaches the surface, the Gierasch–Rossow–Williams mechanism might produce global superrotation. It is not clear, however, what happens if meridional circulation driven in the cloud layer does not reach the surface. In this case, it is difficult for the Gierasch–Rossow–Williams mechanism to operate efficiently, because the vertically separate meridional circulations do not directly pump up angular momentum from the surface to the cloud top. In such a vertical separation of the circulation, the vertical angular momentum transportation due to the waves plays a crucial role in the formation of the superrotation (e.g., Yamamoto & Tanaka, 1997). For example, if the equatorial Kelvin wave and gravity waves with phase velocities faster than zonal-mean wind velocity are forced below the cloud layer or at the surface, they contribute to the maintenance of the equatorial superrotation via the critical-level absorption below and within the cloud layer. In addition, if the thermal tide reaches the surface of the ground and produces near-surface subrotational flow, the subrotation supplies the angular momentum to the atmosphere (Takagi & Matsuda, 2007). To clarify if these waves play a role in the superrotation mechanism, future studies must find observational evidence of the waves and their zonal-wind acceleration/deceleration in the lower atmosphere, theoretically clarify the wave generation processes, and evaluate the wave amplitudes required to produce the superrotation below and in the cloud layer. Furthermore, dynamical linkages between the upper atmosphere and the cloud layer are very interesting in Venus’s thermosphere general circulation. The importance of small-scale gravity waves and planetary-scale waves propagating upward from the middle atmosphere has been discussed in Venus thermosphere dynamics (Alexander, 1992; Brecht & Bougher, 2012; Gilli et al., 2017; Hoshino, Fujiwara, Takagi, & Kasaba, 2013; Hoshino, Fujiwara, Takagi, Takahashi, & Kasaba, 2012; Zhang, Bougher, & Alexander, 1996). Dynamics of wave propagation and forcing in the region below 100 km altitude is essential for understanding the dynamical linkage between the upper atmosphere and the cloud layer.

As seen in Figure 2c, small-scale eddies are apparent in the Venus cloud layer. The small-scale gravity waves could contribute to the acceleration/deceleration of superrotation via Reynolds stress, which influences the meridional circulation and the temperature structure. In general, because it is difficult to simulate small eddies and their related convection in GCMs applying the hydrostatic assumption, future studies need to directly simulate these eddies in high-resolution nonhydrostatic regional models and to develop gravity-wave parameterizations. In addition, the subgrid-scale diffusions used to parameterize turbulent eddies and prevent numerical instabilities may also influence the general circulation during long-term GCM simulations. Thus the coefficients need to be improved and the validity of these simulations should be fully discussed (Izakov, 2012, 2016).

### Conclusion

Although Venus is almost the same size as the earth, the atmospheric circulation is very different. The slowly rotating planet has a thick CO2 atmosphere (~9.2 MPa and 735 K at the surface) and is covered with clouds (49–70 km altitude). Atmospheric superrotation fully develops in the upper cloud layer, where thermal tides and planetary-scale 3- to 8-day waves are predominant. The zonal circulation with wind speeds of ~100 m/s at around 70 km altitude is much faster than the solid surface rotation. Impressive fast-rotating Y-shaped wave structures, stationary bow-shaped waves, and complex polar vortices are observed in the cloud layer. Dynamics of the atmospheric circulation and waves have been inferred from observations and simulations based on theories of geophysical fluid dynamics and meteorology. To investigate the three-dimensional atmospheric structure and its temporal variation, GCMs along with data analyses of the observational data are useful. Most of the GCM experiments show that the equator-to-pole Hadley circulation and thermal tides are induced in the cloud layer. The simulated global superrotation is driven by angular momentum transport caused by the zonal-mean Hadley circulation and eddies with equatorward momentum fluxes (the Gierasch–Rossow–Williams mechanism). The equatorial superrotation is driven by thermal tides, Kelvin wave, Rossby waves, and gravity waves in the previously proposed mechanisms. The wave producing the equatorial superrotation differs at different levels of elevation. Toward deep understanding of the atmospheric circulation and climate on Venus, the GCMs including the radiative and gravity wave parameterizations will be further developed in future works. Based on the realistic GCM simulations, the momentum and energy analyses of the atmospheric circulation should be conducted to elucidate how the superrotation is formed and maintained.

Venusian meteorological data accumulation and their theoretical interpretations have provided information on the dynamical and thermodynamic constraints on the atmospheric circulation. With help from data assimilation techniques, we expect to elucidate a realistic view of the wind and thermal structures in and above the cloud layer, of which the meteorological data have been stored. However, because the meteorological data are insufficient to investigate the dynamics and thermodynamics in the lower atmosphere, it is difficult to understand the global atmospheric circulation. Thus the radiative and dynamical processes under high pressure and temperature conditions on the slowly rotating planet should be further examined, along with future observations of the deep atmosphere below the clouds. In addition, the following two processes should be examined by future observations and modeling: (a) the dynamical effects of the topography and surface process on the atmospheric circulation and (b) the dynamical linkages among the lower, middle, and upper atmospheres via vertically propagating waves.

### Acknowledgments

This article was supported by the Japan Society for the Promotion of Science/Ministry of Education, Culture, Sports, Science, and Technology Grant-in-Aid for Scientific Research (KAKENHI Grant Number JP17H02960).

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