Icarus 366 (2021) 114400

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Research Paper

Venus’ upper atmosphere revealed by a GCM: I. Structure and variability of
the circulation
Thomas Navarro a,b ,∗, Gabriella Gilli c,d , Gerald Schubert a , Sébastien Lebonnois e ,Franck Lefèvre f , Diogo Quirino c,da

Department of Earth, Planetary and Space Sciences, University of California, Los Angeles, CA, USA

b McGill Space Institute, McGill University, Montreal, Canadac Instituto de Astrofisica e Ciências do Espaço (IA), OAL, Tapada da Ajuda, PT1349-018 Lisboa, Portugal
d Faculdade de Ciências, Campo Grande, PT1749-016 Lisboa, PortugalefLaboratoire de Météorologie Dynamique (LMD) Paris, France
IPSL/LATMOS, Paris, France

ARTICLEINFO

Keywords:
Venus
GCM
Upper atmosphere
Atmospheric circulation
Airglow
Kelvin wave
Singlet oxygen

ABSTRACTA numerical simulation of the upper atmosphere of Venus is carried out with an improved version of the Institut
Pierre-Simon Laplace (IPSL) full-physics Venus General Circulation Model (GCM). This simulation reveals theorganization of the atmospheric circulation at an altitude above 80 km in unprecedented detail. Converging
flow towards the antisolar point results in supersonic wind speeds and generates a shock-like feature past
the terminator at altitudes above 110 km. This shock-like feature greatly decreases nightside thermosphericwind speeds, favoring atmospheric variability on a hourly timescale in the nightside of the thermosphere.
A ∼5-day period Kelvin wave originating in the cloud deck is found to substantially impact the Venusian
upper atmosphere circulation. As the Kelvin wave impacts the nightside, the poleward meridional circulationis enhanced. Consequently, recombined molecular oxygen is periodically ejected to high latitudes, explaining
the characteristics of the various observations of oxygen nightglow at 1.27 μm. An analysis of the simulated
1.27 μm oxygen nightglow shows that it is not necessarily a good tracer of the upper atmospheric dynamics,
since contributions from chemical processes and vertical transport often prevail over horizontal transport.
Moreover, dayside atomic oxygen abundances also vary periodically as the Kelvin wave momentarily decreases
horizontal wind speeds and enhances atomic oxygen abundances, explaining the observations of EUV oxygen
dayglow. Despite the nitrogen chemistry not being currently included in the IPSL Venus GCM, the apparent
maximum NO nightglow shifted towards the morning terminator might be explained by the simulated structureof winds.

1. Introduction
The circulation of the Venusian atmosphere is dominated by the
westward retrograde zonal superrotation (RZS) of the cloud deck at
altitudes up to 70 km. Higher up in the thermosphere, the strong
day-to-night thermal gradient induces a Subsolar to Antisolar (SS–AS)
circulation, with air flowing from the dayside to the nightside (Bougher
et al., 1997; Schubert et al., 2007). Between approximately 90 and 120
km of altitude, the circulation changes from RZS to SS–AS, forming atransition region between the two circulations.
Understanding in detail the mechanisms at stake in the upper atmosphere is crucial for many key questions arising for Venus, and forslowly rotating, highly irradiated exoplanets in general. The cause andmaintenance of the RZS remains one the largest Venusian mysteries.

The transition region is where the RZS ends and may shed light onsuch a mystery by assessing the angular momentum exchanges between
the upper and lower atmospheres. The upper atmosphere is criticalfor atmospheric escape, as it is the location where light elements areformed, transported, and interact with the solar wind. It is also a crucial
region for the stability of carbon dioxide as the main constituent of theVenusian atmosphere. Carbon dioxide is photochemically dissociatedand recombined in the upper atmosphere, but there is no consensus
on why it is orders of magnitude more abundant than e.g. carbon
monoxide or dioxygen, despite being recycled continuously (Marcq
et al., 2018). Airglow emissions that are present in the transition region
due to excited chemical species from recombination (such as O2 andNO) in the transition region have been proposed as a possible medium∗ Corresponding author at: Department of Earth, Planetary and Space Sciences, University of California, Los Angeles, CA, USA.

E-mail address: tnavarro@epss.ucla.edu (T. Navarro).
https://doi.org/10.1016/j.icarus.2021.114400
Received 18 September 2020; Received in revised form 19 February 2021; Accepted 22 February 2021
Available online 6 March 2021
0019-1035/© 2021 The Authors.
Published by Elsevier Inc.
This is an open access(http://creativecommons.org/licenses/by-nc-nd/4.0/).

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T. Navarro et al.

atmosphere. Such models reproduce the SS–AS circulation (Bougher
et al., 1988a), and include a photochemical package (Brecht et al.,2011; Brecht and Bougher, 2012; Gilli et al., 2017), a parameterizationof unresolved gravity waves (Zhang et al., 1996; Zalucha et al., 2013;
Hoshino et al., 2013; Gilli et al., 2017). The inclusion of planetary-scale
waves generated in the lower atmosphere shows that a Kelvin wave can
impact the upper atmosphere dynamics and the O2 nightglow (Hoshino
et al., 2012; Nakagawa et al., 2013; Brecht et al., 2021).
In this article, we build on the work by Gilli et al. (2017) andinvestigate in detail the nightside circulation from the cloud top, and up
to 150 km, with the IPSL Venus GCM, while a companion article (Gilli
et al., 2021) addresses a fine-tuning in the non-LTE parameterization,
which improves the representation of thermal structure above 90 km,
and provides data-model validation with a comprehensive selection oftemperature and density measurements from VEx and ground-based
telescopes. Specifics of the simulation done for this work are describedin Section 2. Section 3 details the structure of the nightside circulation,and Section 4 addresses its variability. Section 5 shows the impact of
the Kelvin wave on the whole upper atmosphere. Section 6 presents
the impact of the circulation on the O2 and EUV oxygen airglows, thenSection 7 discusses the use of O2 nightglow as a tracer of dynamics.
Finally, Section 8 discusses the findings and limitations of such asimulation, and a conclusion is given in Section 9.

for detecting seismic waves from remote observations and assess if
Venus is geologically active in the present day (Didion et al., 2018).
Many unresolved questions pertaining to the observations of Venus’
upper atmospheric circulation still prevail after the space mission Venus
Express (VEx) era (Drossart et al., 2007; Svedhem et al., 2007; Gérard
et al., 2017). Among them is the cause of the variability and spatial
patterns of horizontal wind speeds and O2 and NO nightglows. In orderto close the large-scale circulation between the RZS and the SS–AS
circulations, an upward flow must exist on the dayside and a downward
flow on the nightside. The downward vertical motion on the nightside
is the location of the recombination of chemical species that createa variety of nightglows (O2 , NO, OH). For instance, singlet oxygenO2 (1 𝛥𝑔 ), the end product of the recombination of atomic oxygen,creates a nightglow at 1.27 μm and observed statistically to be evenly
distributed around the Anti-Solar (AS) point (Soret et al., 2012). Suchan observation suggests that the AS point is, on the average, where
the SS–AS converges. However, rapid changes on a daily timescale ofindividual patches or large scale elongated structures of O2 nightglow
at low and high latitudes (Crisp et al., 1996; Lellouch et al., 1997;
Hueso et al., 2008; Gérard et al., 2014; Soret et al., 2014) do not matchwith the simple view of a steady, fixed downward flux centered at the
AS point. Moreover, NO nightglow is produced by the reaction between
atomic nitrogen and oxygen, at an altitude of 115 km, and located on
average towards the morning terminator (Stewart et al., 1980; Stiepen
et al., 2013). The interpretation of this observation is challenging, since
the O2 nightglow happens at an altitude of 95 km, thus suggesting an
unknown mechanism produces a westward shift towards the morningterminator at 115 km, but not at 95 km. Another class of airglow is
the Extreme Ultra-Violet (EUV) dayglow due to photon emission at
135 nm by excited atomic oxygen on the dayside upper atmosphere,
above 130 km. Periodic variations of this dayglow, notably 3-day and 4day ones, have been observed by the Hisaki space telescope (Masunaga
et al., 2015), mostly on the morning side (Masunaga et al., 2017).
Simultaneous observations with winds retrieved from tracking cloudtop features by the Akatsuki orbiter (Nakamura et al., 2016) and Hisaki
suggest a coupling between the RZS and the SS–AS circulations by thermospheric gravity waves excited by a cloud-level Kelvin wave (Naraet al., 2020).
Another kind of unexplained observation is the atmospheric variability of the upper atmosphere observed from both the ground andthe Venusian orbit. Clancy et al. (2008) observed daily fluctuations of
CO volume mixing ratio of 30%–50% and temperature of 5–20 K on theevening terminator above 95 km from Doppler shift of sub-mm and mm
CO lines. Clancy et al. (2012) observed a sizeable nighttime variabilityof 50%–70% of horizontal wind speeds at an altitude of 110 km fromhourly to interannual timescales, with a complex superimposition of
SS–AS and RZS winds, as confirmed by Clancy et al. (2015). Sornig
et al. (2008), Sornig et al. (2012) also observed a large variabilityof wind speeds at 110 km on the dayside, from heterodyne non-LTE(Local Thermal Equilibrium) infrared CO2 emission at 10 μm, and did
not detect superrotation at the equator at 110 km, but at a latitude of33◦ . Sornig et al. (2013) then detected wind variability and interpreted
the location of the converging point of the SS–AS circulation to varyfrom the west or east of the midnight meridian in less than a month.
Temperature measurements by VEX also showed a spatial variability of
the nightside temperature (Piccialli et al., 2015). Krause et al. (2018)measured terminator temperature at 110 km with a ground-based
spectrometer, showing that temperature variability is the same orderon long (6 years) and on short timescales (< 10 days).
Numerical models are tools of choice for interpreting observations
and exploring the mechanisms at stake in the upper atmosphere circulations, where direct wind measurements are usually very scarce. As amatter of fact, the SS–AS circulation was first hypothesized from a twodimensional numerical model (altitude vs. solar zenith angle) (Dickinson and Ridley, 1972). Later on, three-dimensional General Circulation
Models (GCM) revealed the details of the circulation of the upper

2. GCM simulation
The GCM used for this study is the Institut Pierre-Simon Laplace(IPSL) Venus GCM, a full-physics, ground-to-thermosphere model(Lebonnois et al., 2010; Gilli et al., 2017) able to simulate the RZS
circulation reasonably well to observed values (Lebonnois et al., 2016;
Garate-Lopez and Lebonnois, 2018). It notably includes a radiativetransfer with solar heating rates (Crisp, 1986) and infrared net exchanges rates (Eymet et al., 2009), Magellan topography, a Mellor–
Yamada level 2.5 scheme for the boundary layer (Mellor and Yamada,1982), a temperature-dependent heat capacity to reflect deviation of
the deep atmosphere from the assumption of an ideal gas. This model
has been extended to the thermosphere (Gilli et al., 2017), up to
3 × 10−6 Pa (approximately 150 km), with the inclusion of non-LTE
processes, near-IR heating, CO2 thermal cooling at 15 μm, molecular
diffusion, and thermal conduction. It also includes a cloud and photochemical model for 34 chemical species relevant to the carbon, oxygen,chlorine, and sulfur chemistry, and are dynamically transported by the
GCM (Stolzenbach, 2016).
The present setup with the inclusion of the upper atmosphere has
been improved since its first development presented in Gilli et al.
(2017). First, the non-LTE parameterization, detailed in the companion
paper Gilli et al. (2021), was fine-tuned to temperature observationsof VEx, resulting in reduced (factor 2) heating/cooling peaks at 0.5
Pa (about 100 km) at daytime and reduced heating rates (factor 3) atmorning/evening terminators around 0.1 Pa, compared to Gilli et al.
(2017). At nightime, radiative tendencies are affected by changes in
the non-LTE parameterization mostly in the thermosphere, above 110
km approximately, suggesting that the region below is dominated bydynamical tendencies. Second, the present simulation now employs
the same heating rates as in Garate-Lopez and Lebonnois (2018), witha latitude-dependent cloud top altitude (Haus et al., 2015) and theradiative effects of a sub-cloud haze, which resulted in increased zonal
wind values from 15 to 45 m s−1 below the cloud deck at 45 km,
in better agreement with values of 60 m s−1 measured in-situ by
Pioneer Venus (Schubert, 1983). Third, we increased the horizontal resolution of the Laboratoire de Météorologie Dynamique Zoom (LMDZ)
longitude–latitude grid dynamical core (Hourdin et al., 2006) from theone employed by Gilli et al. (2017), from 7.5◦ × 5.625◦ (48 × 32 grid
points) to 3.75◦ × 1.875◦ (96 × 96). While this increased resolution
is not a novelty for the lower atmosphere of Venus with the IPSL
Venus GCM (Lebonnois et al., 2016; Garate-Lopez and Lebonnois, 2018;2

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Fig. 1. (top) Vertical, (middle) absolute zonal wind speeds, and (bottom) temperature
at the equator averaged for one Vd. Streamlines show the circulation in the altitude vs.
local time plan constructed from the average wind field shown in the top and middle
panels. Thick solid line indicates where zonal wind values are zero.

Fig. 2. Same as Fig. 1, but for absolute meridional wind speeds along thenoon-midnight meridians averaged for one Vd.

CO2 , CO, O, and N2 species above 90 km (Hedin et al., 1983). We thus
obtained an initial state stable for the full interactive photochemical
package, suggesting that the numerical instabilities may arise fromfeedback loops between the upper atmosphere heating rates, dynamic
chemical species, and the non-converged circulation of the downward
moving flow near the AS point. We then obtained, after 29 Vd, aconverged simulation with constant 1 Vd-averaged SS–AS wind speeds,
without prescribed chemical species.
Additionally, the IPSL Venus GCM uses a stochastic parameterization of non-orographic gravity waves (Lott et al., 2012). Gravity waves
are assumed to be generated at the top of the convective cells, locatedat about 55 km on Venus, propagate upwards, and break in the upper
atmosphere. These waves were found to impact the circulation of theupper atmosphere (Zalucha et al., 2013; Gilli et al., 2017). To correctly
implement this parameterization with the increased resolution, we
corrected the minimal horizontal wavenumber 𝑘𝑚𝑖𝑛 of individual waves:𝜋𝑘∗𝑚𝑖𝑛 = 𝑚𝑎𝑥(𝑘𝑚𝑖𝑛 , )(1)𝐴
with 𝐴 the surface area of the grid cell.

Navarro et al., 2018) or other GCMs at a higher (Ando et al., 2016;
Takagi et al., 2018) or much higher (Kashimura et al., 2019) resolution,
it is the highest resolution ever used for the upper atmosphere of Venus,
compared for instance to 5◦ × 5◦ in Brecht and Bougher (2012),
Brecht et al. (2021), or T21 (11.25◦ × 2.8125◦ ) in Hoshino et al.
(2012, 2013) and Nakagawa et al. (2013). Sugimoto et al. (2014)
studied waves with the AFES GCM at a T63 (192 × 96) resolution
and a model top at 120 km. However, their setup did not include
any parameterization of upper atmospheric processes and they implemented a sponge layer starting at 80 km, thus efficiently damping
atmospheric circulation in the upper atmosphere. Brecht and Bougher(2012) deemed necessary an increased resolution in order to resolve
the sharp horizontal temperature gradients near the terminators, andindeed resulted in substantial changes in our simulations, as will be
detailed below. The major hurdle in implementing such an increased
resolution is the high numerical instability of the simulations, withinstabilities leading to unrealistic temperatures within a few tens ofhours near the AS point in the upper atmosphere. To overcome thisissue, we first ran the IPSL Venus GCM during one solar Venus day(Vd) from a converged initial state of the lower atmosphere obtained
after 300 Vd in Garate-Lopez and Lebonnois (2018), and simplified
prescribed altitude and solar zenith angle dependent distributions for

3. Average structure of the nightside circulation
3.1. Horizontal wind
Atmospheric fields above 70 km and averaged for 1 Vd are shown
as a function of local time in Fig. 1, of latitude in Fig. 2, and as maps
3

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simulated by Dickinson and Ridley (1975, 1977) with a 2D altitudesolar zenith angle model, or Bougher et al. (1986) with a 3D GCM.
The tongue-like shape is apparent in the vertical, horizontal winds andtemperature fields in Figs. 1 and 2, with the structure moving awayfrom the terminator towards the AS point as it gets lower in altitude.
According to Dickinson and Ridley (1975), the cause of the hot ring is
adiabatic heating from the downward motion caused by the decrease
in altitude of isobars past the terminator.
However, there is a major difference between our simulation andthese past works. In our simulation, the horizontal wind speed is higher,
with values greater than 300 m s−1 at an altitude of 130 km, compared
to 250 m s−1 in Dickinson and Ridley (1975, 1977), and 200 m s−1
in Bougher et al. (1986). Our result is in agreement with more recent
ground-based measurements of Doppler winds as high as 348 m s−1 on
the morning terminator (Clancy et al., 2015). Therefore, the simulated
winds are supersonic, with Mach numbers attaining a value of 2 at
130 km (Fig. 3), with the Mach number defined√ as 𝑀 = 𝑣∕𝑐𝑠 with𝑣 the wind speed, the speed of sound 𝑐𝑠 =𝛾𝑅𝑇 ∕, 𝛾 the heat
capacity ratio, 𝑇 the temperature, 𝑅 the ideal gas constant, and  themolar mass. Given the Mach number is well above unity in our simulation, followed by a sharp wind decrease and temperature increaseat altitudes above 120 km (Fig. 4), it is reasonable to investigate thepresence of a supersonic shock wave as a possible cause of the structurein the vicinity of the terminator. Atmospheric supersonic shocks havebeen studied in the context of hot, highly irradiated, giant exoplanets(e.g. Rauscher and Menou, 2010; Heng, 2012), but quite rarely for the
Venusian upper atmosphere. By considering the air densities measured
by Pioneer Venus, Seiff (1982) briefly discussed the possibility of ashock in the Venusian upper atmosphere as a dissipation mechanism toslow down the SS–AS flow. Moreover, Clancy et al. (2015) estimateda Mach number 1.5 from their observations, and Hoshino et al. (2012)
simulated supersonic winds, but neither mentioned a shock.
The primitive equations of the IPSL dynamical core are based on
the hydrostatic equilibrium. Therefore, vertically propagating soundwaves are filtered out, leaving horizontally propagating sound waves,also known as Lamb waves (Vallis, 2006, Chapter 2). Although the IPSL
dynamical core can simulate Lamb waves because it is a compressible
core, a standing Lamb wave steepening into a shock may not beproperly simulated because of the large grid resolution (> 100 km)
compared to the rapid changes of atmospheric variables over a small
distance, typical of a shock.
The limitation of this GCM configuration does not preclude investigating the possibility of a shock in the Venusian upper atmosphere.
With a hydrostatic dynamical core having the same limitations, Showman et al. (2009) reported a structure of strong convergence andtemperature increase on a narrow region for a hot Jupiter at 1 mbar,
while Rauscher and Menou (2010) discussed the nature of a similarfeature and concluded it may be a Lamb wave. Drawing on this result, Fromang et al. (2016) performed simulations using a dynamicalcore with a proper treatment for shocks, eventually showing that hot
Jupiter were prone to shocks. This useful result is pertinent for our case,as it proves that features such as Lamb waves with a limited dynamicalcore can be the first clue that shocks may be simulated, and actuallyexist, in the Venusian upper atmosphere. Future dedicated studies
may be tackled with a more suitable numerical code, for instance a
finite-volume one, with a higher resolution near the terminator.
One way to detect shock-like features in a numerical code is to𝛥𝑥∇ ⋅ 𝐯consider the variable 𝜂 = −, with 𝛥𝑥 the horizontal grid spac𝑐𝑠
ing. Zhu et al. (2013) and Fromang et al. (2016) empirically identified
shocks wherever 𝜂 has values greater than 0.2. In our simulation, we
find 𝜂 to be smaller than 0.2 in the upper atmosphere, except at the
hot ring location, with values of 𝜂 between 0.5 and 1. This fact alonestrongly suggests a shock-like mechanism.
Another indication of a possible shock-like feature is the dependenceof the SS–AS flow results on the horizontal resolution. Fig. 4 provides

at different altitudes in Fig. 3. The circulation is dominated by the SS–
AS circulation above 100 km of altitude, with winds converging fromthe SS point to the AS point, and wind speed exceeding 300 m s−1 atthe terminator. The RZS circulation is dominant below 85 km (Fig. 1),
with values around 100 m s−1 at the cloud top (∼ 70 km). Between
90 and 105 km approximately lies a transition region consisting of areversal of the zonal wind from retrograde (westwards) to prograde(eastwards) values between local times 0 h and 12 h (Fig. 1). Figs. 1
and 3 also show an asymmetry of the SS–AS zonal flow between themorning and evening branches and between 120 and 130 km due tothe breaking of non-orographic gravity waves at those altitudes (seecompanion paper). The wind is slightly more westwards on the average,
with convergence shifted away between midnight and 2 h between
about 100 and 130 km, as apparent in the zero zonal wind contourof Fig. 1. Conversely, the SS–AS meridional flow is symmetric between
the Northern and Southern hemispheres (Fig. 2), as the non-orographic
gravity waves’ drag is weaker on the meridional direction comparedto the zonal one. Because of this structure, a point with null windspeed (both zonal and vertical) exists at the equator at local time
6 h, and between altitudes 95 to 100 km (see average equatorial windstreamlines in Fig. 1).
3.2. Temperature
Temperature decreases with altitude until the transition region,
where local maxima of 240 K are centered near the Sub-Solar (SS) andAS point (bottom panels of Figs. 1 and 2). The warming at the SS point
between altitudes 100 and 110 km is due to near-IR heating produced
by CO2 molecules non-LTE absorption of solar radiation, as pointed out
by Gilli et al. (2017) and Brecht and Bougher (2012) and observed by
the VIRTIS instrument on board VEx (Gilli et al., 2015). The warming
near the AS point has also been observed with VEx (Bertaux et al.,2007; Piccialli et al., 2015) and is due to the downward flow of day-tonight air by adiabatic compression and advection from the dayside, as
shown by Gilli et al. (2017) and Brecht and Bougher (2012). Abovethese warm layers, temperature decreases anew with altitude, until
EUV heating warms the dayside above 140 km. The cold nightside
temperatures above 120 km and below 140 km observed by Pioneer
Venus (Schubert et al., 1980) are due to CO2 cooling at 15 μm (Gilli
et al., 2017). The terminators are cooler than other local times ataltitudes 95 to 115 km as shown in Figs. 1, 2, and 3. This result is
not in agreement with Piccialli et al. (2017), probably because theyused a-priori CO profiles from Clancy et al. (2012) up to 100 km, anda constant value above, whereas our model predicts instead CO volume
mixing ratio decreasing above that altitude (see companion paper Gilli
et al., 2021). A more detailed comparison of the temperature structureof this simulation is given in Gilli et al. (2021).
3.3. Shock-like feature and downward motion near the terminator
These results are in general agreement with previously published
GCM studies and observations, and the mechanisms at stake understoodto a large extent. However, our simulations reveal a particular structure
consisting of downward vertical speeds maximal near the terminator on
the nightside, with larger values near the morning terminator than theevening terminator, reaching 100 cm s−1 above 120 km (see top panelin Fig. 1). This downward motion is associated with sharp horizontal
gradients of horizontal winds (Figs. 1, 2, and 3), with a decrease
reaching up to 200 m s−1 over a distance of 500 km and less. A local
increase of temperature of up to 40 K is also associated with thisdownward motion (Figs. 1, 2, 3 and 4), producing a nightside ‘‘hot ring’’feature above 120 km, well visible in the time-averaged field at 130 km
in Fig. 3, or in the instantaneous field at 120 km in Fig. 8.
The nature of this structure is not straightforward. It is reminiscent of the ‘‘tongue’’ of downward vertical motion and local heating4

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Fig. 3. Maps of Mach number, winds and temperature averaged for one Vd at 5 different altitudes. Black contour can indicate Mach number unity (left column) and zero verticalwind speed (middle column). Positive values of vertical speeds indicate downward winds.

an example of equatorial Mach number and temperature at 130 km for
two resolutions: high (the present study) and low (the same employedin Gilli et al., 2017). While horizontal supersonic speeds (𝑀 >1) are
obtained for both resolutions, the decrease of 𝑀 below unity happens rather abruptly for the high resolution, over just two grid points
past the morning and evening terminators. In contrast, the transition
from supersonic to subsonic flow occurs smoothly over thousands ofkilometers with the low resolution. Moreover, temperature increases
just after the decrease of 𝑀 for the high resolution, forming the ‘‘hotring’’ feature described above, whereas no such local maximum of
temperature happens for the low resolution simulation. This behaviorof Mach number and temperature is in line with a shock-like feature:a decrease of 𝑀 past the feature, and an increase of temperature.
Shocks, including Lamb waves, happen when regions of lower density(e.g. generated by a wave) acoustically propagate faster than regions ofhigher density, possibly converging together if the flow is supersonic,
and forming a shock. The formation and location of the shock thus
depends on the profile of density perturbations and the flow’s speed,
temperature, and pressure along a streamline. Therefore, it makes sensethat an increase in resolution is more suited to resolve the convergenceof density perturbations and that a shock is eventually simulated as theresolution increases, as noted by Fromang et al. (2016) in the context
of hot Jupiters.
In order to test the hypothesis of a shock-like feature against simulated values of temperatures and Mach number, we use the classic
relation between temperature and Mach number of normal shock equations from one-dimensional gas dynamics theory (e.g. Liepmann andRoshko, 2001):()()
2𝛾𝑀12 − (𝛾 − 1) (𝛾 − 1)𝑀12 + 2
𝑇2
=
(2)
𝑇1
(𝛾 + 1)2 𝑀12of temperature is a non-isentropic, irreversible, process caused by adecrease of wind speed. Alternatively, if the temperature increase werecaused by adiabatic heating of descending air as found by Dickinson
and Ridley (1975, 1977), the temperature ratio would be given by theisentropic relation:
𝑇2
=
𝑇1

(

𝑃2
𝑃1

)𝛾 − 1𝛾(3)with 𝑃 the pressure. Fig. 5 compares the temperature ratio of the hotring to Eqs. (2) and (3). At altitudes of 120 and 130 km, the generaltrend of the temperature increase in the hot ring is in broad agreementwith a shock-like feature as given by Eq. (2). At an altitude of 140 km,
the temperature increase is, in general, systematically smaller by 20%
than the one expected for a shock. Isentropic compression alone does
not seem to account for the simulated increase in temperature, especially at a high pressure ratio. The standard deviation between expected
and simulated temperatures is smaller at 120 and 130 km for the caseof a normal shock than for an isentropic compression (Fig. 5).
All in all, these results suggest that a strong (i.e. with 𝑀 > 1
upstream and 𝑀 < 1 downstream), normal, shock-like feature in theform a of standing Lamb wave, is present in our simulations above
120 km and is the main reason for the hot ring and strong wind
deceleration. The enhanced downward motion must also play a role
and will inevitably warm the descending air by adiabatic compression,
but it is not the chief reason for the hot ring and wind deceleration
above 120 km. Between 110 km and 120 km, where wind speeds are
subsonic, adiabatic warming would then be the main reason for thepersisting hot ring at those lower altitudes. Other processes also play arole, such as near-IR heating that may be responsible for slightly higher
than expected temperature ratios at 120 km, and thermal conduction,
possibly responsible for the lower than expected ones at 140 km.
Moreover, and as pointed out by Seiff (1982), the air needs to bewith subscripts 1 and 2 denoting the quantities upstream and downstream of the shock-like feature, respectively. In this case, the increase5

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Fig. 4. Equatorial Mach number and temperature at an altitude of 130 km for high (96 × 96) and low (48 × 32) resolutions. The atmospheric flow is directed towards the AS
point at local time 0 h. Dots indicate the horizontal spacing for each model resolution.

diabatically cooled to avoid high unrealistic nightside temperatures
regardless of the cause of the hot ring.

4. Variability of the nightside dynamics

It results that there is a normal shock-like feature, dissipating kinetic
energy, resulting in downstream increased temperature, pressure, anddensity. The shock-like feature is the strongest at an altitude of 130 km,
with 𝑀 ∼ 2 (Fig. 3). The horizontal wind speed upstream of the shocklike feature increases roughly from 200 m s−1 at 110 km to 300 m s−1
at 130 km (Figs. 1 and 2), while the upstream temperature roughly
decreases from 200 K at 110 km to 100 K at 130 km, and then increases‖𝐯‖
to 200 K at 140 km in the thermosphere. Therefore, as 𝑀 ∝ √ , the𝑇largest impact on the Mach number upstream of the shock-like featureis the local minimum of temperature with altitude, located at 130 km.

The time-averaged view of atmospheric fields in Section 3 does notshow a crucial point of the GCM results: the strong variability of thenightside, in stark contrast to the quiet dayside, as seen in Figs. 6, 7, and
8. The SS–AS circulation on the dayside is very simply described as atime-independent increase of horizontal winds with solar zenith angle,
modest temperature changes of less than 10 K at any location, andan almost constant atmospheric composition of 96% CO2 . Meanwhile,the nightside is subject to abrupt changes of atmospheric composition,
horizontal wind velocity, vertical wind speed, and temperature on atimescale of tens of hours.
As SS–AS horizontal winds are decreased due to non-orographic
gravity waves, a shock-like feature, and downward motion at the terminator, converging air flows form multiple local subsiding ∼ 1000 km
size eddies that vary in strength and location in a seemingly unstructured way. This behavior is apparent in the local maxima and minima
of wind vorticity (e.g. at 130 km in Fig. 7), with those eddies on
the nightside forming and disappearing in a matter of a few hours.
The changes of horizontal wind speed induce a change in atmosphericcomposition. Indeed, CO2 is photodissociated into O and CO on thedayside, and air depleted in CO2 piles up wherever horizontal windgets slower. CO2 concentration thus varies in both local time andlatitude (Fig. 6). Moreover, individual species start to diffuse separately
according to their masses above the homopause due to molecular
diffusion, leading to the prevalence of the lightest species, such as
CO and O. Therefore, air composition is a tracer of dynamics on theThis structure consisting of a shock-like feature above ∼ 120 km,
and adiabatic heating below, would be apparent in the temperature anddensity structures of horizontal profiles, but so far no such observation
seems to exist. The nightside temperature maps measured by SPICAV
on board VEx (Piccialli et al., 2015) are scattered, and their coverage isquite limited at the local times of the terminator structure, at 18–20 hand 4–6 h. Piccialli et al. (2015, figure 7) show a 15 K bump centered at
19 h at 115 km, but is much less than the variability of the nightside, as
explained in the next section. Moreover, Clancy et al. (2015) retrieved
supersonic cross-terminator zonal winds at 100 to 125 km, with fasterwinds in the evening than in the morning side, which is the case in our
simulation at altitudes 130 km and above (Fig. 1).
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Fig. 5. Top: ‘‘Hot ring’’ temperature ratio as a function of upstream Mach number and pressure ratio. Black solid lines indicate the analytical 1-D normal shock equation given
by Eq. (2) or the isentropic compression by Eq. (3). Dots indicate GCM values, and dashed color lines indicate the best fit to those values. Bottom: standard deviation between
the GCM simulated temperature and Eqs. (2) and (3) for each case. The downstream (upstream) values are obtained for 10 Earth days from the locations of the local maximum(minimum) of temperature after (before) 𝑀 − 1 become negative along the SS–AS lines. (For interpretation of the references to color in this figure legend, the reader is referredto the web version of this article.)nightside, with air composition and wind speed well correlated inFig. 6. The varying vertical wind speed is well correlated locally withnightside temperatures, as the descending air is warmed by adiabatic
compression in the region between the AS point and the hot ring causedby the shock-like feature (Fig. 8).
Such behavior of highly time-variable planetary scale structureson the nightside is not seen in simulations at lower resolution withthe same GCM (Gilli et al., 2017), and was not reported with other
GCMs (Brecht et al., 2011; Hoshino et al., 2012; Nakagawa et al.,2013), all having a lower resolution than the GCM simulation presented
here. Fig. 9 compares the time-integrated eddy enstrophy 𝑞 on thedaysides and nightsides of simulations at low (7.5◦ × 5.625◦ ) and high(3.75◦ × 1.875◦ ) resolution with:
𝑞(𝑧) =∫𝐷|∇ × 𝐔|2 𝑑𝑆

The difference between dayside and nightside eddy enstrophy increases
to a factor 10 at 100 km for both resolutions, with a smaller spread,because the circulation of the dayside flow is direct and less variable
than on the nightside. Above 110 km, the nightside enstrophy at highresolution does not vary much with altitude, whereas the low resolution
one decreases by a factor around 3 between 110 and 130 km. The
reason for such a difference between the two different resolutions is thepresence of the shock-like feature above 110 km in the high-resolution
case only, which reduces horizontal wind speeds and increases thenumber of large-scale eddies downstream of this shock-like feature. It
is worth noting that eddy enstrophy is nearly constant with altitude
above 100 km, so potential vorticity is not conserved, indicating a sinkor source of potential vorticity from diabatic heating in the upper atmosphere, unlike the polar vortex at the cloud deck level (Garate-Lopez
and Lebonnois, 2018).
Fig. 10 presents the periodograms of equatorial wind speed as afunction of altitude and local time. There is a dominant 5.7 Earth days
period at all altitudes above 40 km due to a Kelvin wave, as further
explained in Section 5. Another period at 2.9 Earth days is also present
at all those altitudes. The periodicity does not depend on local timein the lower atmosphere, in contrast with the transition and SS–AS
regions. At 90 km, in the transition region, the atmospheric flow is morevariable from midnight to noon, that is to say downstream to the AS(4)with z the altitude and D the considered domain (e.g nightside or
dayside). Eddy enstrophy is a useful quantity to assess eddy activity
and the transience of the atmospheric flow. It gives a global metric of
the wind vorticity and the associated energy per mass. The difference ofeddy enstrophy by a factor 5 in Fig. 9 at altitudes 70 to 85 km between
the two GCM resolutions is simply due to increased resolution that
resolves more eddies. For the high resolution, eddy enstrophy above
90 km is seven times higher on the nightside than on the dayside.
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Fig. 6. Snapshots 24 h apart each of (colors) CO2 in volume mixing ratio and (contour) wind speed in m s−1 at an altitude of 130 km for the (top) nightside and (bottom) daysideof Venus. The position of the subsolar point is indicated by a light gray star and the antisolar point by a dark gray star. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

Fig. 7. Same as Fig. 6 with (colors) wind vorticity and wind streamlines at an altitude of 130 km for the (top) nightside and (bottom) dayside of Venus. (For interpretation of
the references to color in this figure legend, the reader is referred to the web version of this article.)

5. Impact of the Kelvin wave

point and below the inversion of zonal wind at the morning terminator(Figs. 1 and 3), than from noon to midnight, upstream of the AS point.
Above 100 km, the local times for which the wind variability is greater
are found between 0 h and 6 h. At 130 km, the whole nightside isvariable, in contrast to a quieter dayside. The impact of the shock-likefeature on wind variability is obvious at 130 km, with higher nightside
variability clearly delimited at the location of the shock-like featurenear the terminators. The 5.7-day period caused by the Kelvin wave isa major periodicity for all the atmospheric layers, but we could notassess if smaller frequencies would exist without it. In other words,
it is not clear if the strong variability of the equatorial horizontal
wind at high altitudes, and by extension of the upper atmosphere in
general, requires this 5.7-day period from the lower atmosphere, or if
it is an inherent characteristic of the nightside dynamics caused by theshock-like feature and downward motion.

Kelvin waves in the Venusian atmosphere have been observed(e.g. Belton et al. (1976), Covey and Schubert (1982), del Genioand Rossow (1990)) and modeled (e.g. Yamamoto, 2019) on multiple
occasions. Our simulation produces a westward propagating Kelvinwave excited in the middle and upper cloud deck, between 60 and
65 km. This Kelvin wave appears when a sufficiently strong zonal windproduces a Coriolis force for the local atmospheric flow (Peralta et al.,2015). The Kelvin wave may be linked to the meridional discontinuity
observed in the lower cloud (Peralta et al., 2020). The detailed characteristics of this wave in the lower atmosphere are beyond the scopeof this paper, but we can nevertheless briefly mention its main points.
This wave also enters in resonance with a Rossby mode at mid-latitudes,
forming a Kelvin–Rossby instability (Wang and Mitchell, 2014). Note8

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Fig. 8. Same as Fig. 6 with (colors) temperature and (contours) vertical wind speed (cm/s, downward positive) at an altitude of 120 km for the (top) nightside and (bottom)
dayside of Venus. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)wave has an average zonal wind amplitude of 5 m s−1 at 70 km and15 m s−1 at 80 km (Fig. 11), and its latitudinal extent is 60◦ S to 60◦ N.
The period of this wave is 5.7 Earth days (Fig. 10) and depends onthe zonal wind speed below the cloud deck. At the cloud top, this wave
propagates slower than the mean zonal wind, while recent Akatsuki UV
observations suggest that the Kelvin wave propagates faster (Imai et al.,2020). As our GCM underestimates the zonal wind speed at altitudes 30
to 40 km (Garate-Lopez and Lebonnois, 2018, Fig. 5), we would expect
the period of the wave to be actually lower (Peralta et al., 2020). All
in all, our simulated Kelvin wave’s period and amplitude are in generalagreement with observations of the cloud top (Imai et al., 2016; Imaiet al., 2020), even if its period is too large, and if the morphology of
the Y-feature is not apparent in the simulated zonal wind field at a
fixed altitude or pressure. The absence of this feature could be due tothe lack of a transported UV absorber in the GCM, that reveals such aspatial pattern in the observations (Peralta et al., 2015).
5.1. Impact on the upper atmosphere
The Kelvin wave has a considerable impact on both the transition
region and the SS–AS circulation. The phase and amplitude structureof the equatorial zonal wind perturbed by the Kelvin wave is shown in
Fig. 11. The wave has a wavenumber-1 structure up to roughly 95 km,
and perturbs the wind field above and excites wind fluctuations thatare seen with high amplitude on the nightside, but much less on thedayside (though they are still present). These fluctuations are excitedby the wavenumber-1 Kelvin wave below 95 km, but do not keep thiswavenumber-1 structure as they do not propagate upward the sameway in the night and in the day. These perturbations are certainly
secondary waves, excited by the Kelvin equatorial wave.
Therefore, the Kelvin wave is able to impact the SS–AS circulation
except for local times close to noon. This result is contrary to theconclusion of analytical models, using idealized zonal wind verticalprofiles of decreasing speed above the cloud top (Kouyama et al., 2015;
Nara et al., 2020), that a Kelvin wave is attenuated below 80 km.
Indeed, the structure of the zonal wind simulated by the IPSL VGCM
is different, with speeds higher than 100 m s−1 on average in thetransition region at the vicinity of the evening terminator (Fig. 1).
Brecht et al. (2021) prescribed Kelvin and Rossby waves-like perturbations in an upper atmosphere GCM with a lower boundary at
70 km, and found that the Kelvin wave propagate up to 110 km

Fig. 9. Eddy enstrophy as a function of altitude averaged over 1 Vd and latitude lower
than 75◦ , on the day and night sides, at high (96 × 96) and low (48 × 32) resolutions.
The envelopes show the minima and maxima for 1 Vd.

that under Venusian conditions, and as it spans more than 100 km in
altitude, the true nature of the wave we simulate is not straightforward,
and may be a Kelvin-like, a Kelvin–Rossby type, or else. Therefore, we
simply refer to it as a ‘‘Kelvin wave‘‘ and leave those considerations forfurther studies. When it reaches the cloud top, we note that the Kelvin9Icarus 366 (2021) 114400

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Fig. 10. Periodograms of equatorial (10◦ S-10◦ N) horizontal wind speed at different altitudes.

Fig. 11. Spectral decomposition of equatorial (10◦ S-10◦ N) zonal wind at frequency 2𝜋/T, with T = 5.7 Earth days, showing the westwards propagation and impact of the Kelvinwave for half of its period. The cloud bottom and top altitudes are indicated at 48 and 70 km. Thick solid line indicates where zonal wind values are zero on average. Upper andlower limits of the cloud deck are represented by two horizontal gray lines. The time zero is chosen as the cloud top maximum at local time 12 h.

only, due to differences with their vertical wind profile and amplitude
and wavelength of their wave forcing, compared to the Kelvin wave
naturally simulated in the IPSL GCM.
As a consequence of the resulting vertical profiles of horizontal
wind, the zonal wind field impacted by the Kelvin wave in Fig. 11 is acomplex structure, and is not straightforward to interpret. The vertical
wavelength is 15 km in the lower and middle cloud deck, with anamplitude of 10 m s−1 (Peralta et al., 2020). In the upper cloud deck,
the vertical wavelength dramatically changes, and is equal to 50 km,
comparable to Hoshino et al. (2012). Downstream of the shock-likefeature and downward motion on the nightside terminator, the zonal
wind is 180◦ out-of-phase with the upstream side. This makes sense
because in case of a shock, the faster a supersonic flow is, the slower
the downstream subsonic flow is (c.f. Liepmann and Roshko, 2001).
Another contribution to the out-of-phase structure on the nightside is
the retrograde zonal flow entering from the transition region inside
the region delimited by the shock-like feature, creating a temporary
reversal of the SS–AS flow at 110 km with a delay of a few tens ofhours. This reversal can be seen in the meridional wind structure of
Fig. 12.

creating a retrograde imbalance of the flow towards the morning
side. As westwards wind rushes into the nightside from the evening
terminator, two 2000 km large-scale transient vortices are formed in
the transition region between local times midnight and 3 h, one ineach hemisphere, as also seen in Fig. 15. As a consequence, a strong
poleward transport attaining 150 m s−1 is present for approximately
100 h in both hemispheres, up to 60◦ latitude and 130 km of altitude.
This causes the periodic transport of atomic oxygen to high latitudes
after its downward transport. The location of the recombination ofoxygen into O2 (1 𝛥) thus happens at all latitudes from the equator to 60◦
in the transition region, with periodic episodes of high latitude 1.27 μm
oxygen nightglow (Fig. 14).
5.3. Impact on the dayside SS-AS circulation
Similarly, Fig. 13 shows the impact of the Kelvin wave on the circulation and O species at 130 km of altitude. At this altitude, the Kelvinwave has a negligible impact on the zonal wind between local times
6 h and 15 h. Between 15 h and 18 h, the Kelvin wave creates a local
maximum (minimum) of horizontal wind lasting approximately 100 hwhen the Kelvin wave cloud top zonal wind is minimum (maximum).
This is shown in the panel at times 0 and 3T/8 of Fig. 11, with zonal
wind maximum on the nightside in the RZS circulation, ducting into
the dayside of the SS–AS circulation from the evening terminator. Then,the whole nightside is impacted by the Kelvin wave perturbation on the
SS–AS evening branch, even if the Kelvin wave does not propagate into
in the SS–AS morning branch between local times midnight to noon due
to the zonal wind inversion at altitude 95 km. Since the cloud top zonal

5.2. Impact on the nightside transition region
Fig. 12 shows the impact of the Kelvin wave on the meridional
wind and oxygen species as the wave passes through the night. In theabsence of a Kelvin wave, the SS–AS winds at 110 km are balanced
in all directions, creating a convergence at the AS point. The Kelvinwave perturbs the zonal wind in the transition region below 95 km,
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Fig. 12. Four consecutive snapshots, from left to right, of: (1) map of cloud top zonal wind, (2) map of meridional wind at 110 km, (3) latitude vs. altitude volume mixing ratioof O2 (1 𝛥𝑔 ) (colors) and O (contours), (4) O2 nightglow at 1.27 μm, with the AS point indicated by a gray star. (For interpretation of the references to color in this figure legend,
the reader is referred to the web version of this article.)

Fig. 13. Left: Equatorial zonal wind at 70 km (black contours) and 130 km (colors). Right: Column density of atomic oxygen for altitudes above 130 km (colors). Gray shaded
areas indicate where the vertical wind is greater than 17 cm s−1 upwards at an altitude of 130 km. (For interpretation of the references to color in this figure legend, the reader
is referred to the web version of this article.)

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Fig. 14. Time series of noon cloud top zonal wind speed, dayside O column abundance above 130 km as a proxy for OI 135.6 nm dayglow, and O2 nightglow at 1.27 μm at midlatitudes.

states. This fraction is quite uncertain and may lie between 0.6 and 1.
In his detailed discussion, Krasnopolsky (2011) recommended a valueof 0.7. We adopted 𝜖 = 0.75 for consistency with Gérard et al. (2009)
and Soret et al. (2012). In this paper we present the nightside column
integrated O2 (1 𝛥) nightglow (Figs. 12, 15, and Appendix A), as it would
be observed from nadir (Crisp et al., 1996; Lellouch et al., 1997; Hueso
et al., 2008; Soret et al., 2012, 2014; Gorinov et al., 2018). On average,
the nightglow is centered on the AS point. Still, the strong variability,
detailed previously in Sections 4 and 5, creates a varied morphology ofthe nightglow’s spatial structure. Nightglow intensity varies up to 12
MR in the vicinity of the AS point. Elongated structures up to 8 MR at
mid-latitudes (30◦ to 60◦ ) seen by Crisp et al. (1996) and Soret et al.
(2014) are large-scale fronts created by the periodic poleward transport
in the transition region triggered by the Kelvin wave, and associatedwith a 2000 km size vortex that varies on a daily timescale, as seen
by Gérard et al. (2014). At lower latitudes, below 30◦ , highly variablebright spots are caused by eddies of subsiding flow whose location andintensity vary on a 10 h timescale.

wind is maximum, the dayside SS–AS circulation is weakened, and thus
the dayside upwards vertical wind is decreased (Fig. 13). Conversely,
the upwards vertical wind is increased when the cloud top zonal windis minimum. As can be seen in the right panel of Fig. 13, this increase of
upwards motion, associated with a decrease of horizontal wind between
15 h and 18 h, favors a decrease of CO2 abundance above 130 km, andan increase of O and CO abundances. Indeed, as explained in Section 3,
the air composition at altitudes where CO2 is being photodissociateddepends on the local wind speeds. For instance, the vertically integrated
column of O above 130 km, shown in Fig. 13, increases from 20 to
25 moles km−2 . All in all, CO2 varies by 2000 ppm on the dayside dueto the Kelvin wave, much less than the difference between the daysideand the nightside.
6. Oxygen airglows
The structure of the upper atmosphere and the impact of the Kelvinwave help us to understand the observations of two airglows: the emission of O2 (1 𝛥) at 1.27 μm, and OI at 135.6 nm. We focus on these two
airglows because they notably reveal the circulation at different local
times and altitudes. Our GCM simulation provides new insights into
the existing observations of these airglows. Other emissions have been
observed, such as the nitric oxide UV nightglow (Stewart et al., 1980;
Stiepen et al., 2013), OII 83.4 nm and OI 130.4 nm dayglows (Masunaga et al., 2015, 2017). However, the IPSL GCM does not yet include
the nitrogen chemistry, and the OI emission at 130.4 nm is opticallythick, making it difficult to interpret the O abundance (Masunaga et al.,2015).

6.2. OI 135.6 nm dayglow
OI 135.6 nm emission dayglow is produced by photoelectron impact
in the upper atmosphere and is nearly proportional to O column density
above 130 km (Masunaga et al., 2015; Nakamura et al., 2016). As
explained in Section 5, the amount of atomic oxygen on the daysideis periodic and in phase with the cloud top noon zonal wind. Fig. 14
shows the time series of zonal wind and O dayside column as aproxy for the OI 135.6 nm dayglow. The total amount of dayside O isapproximately 35 × 1028 moles above 130 km, with variations ranging
from 2 × 1028 to 3 × 1028 moles, giving a variation of ∼6 to ∼8%. Thisvalue compares well to the ∼4% variation of dayglow reported by Naraet al. (2020). The difference in observed and simulated variations
may be explained by the fact that these observations were restricted
to the morning side, and that the proportionality between O densityand dayglow is sensitive to UV solar intensity. At the same time, we
integrate the whole dayside with an average solar intensity in the
GCM. Nara et al. (2020) reported a 3.6-day periodicity in both the
dayglow and the cloud top zonal wind and Masunaga et al. (2015)
a 4-day periodicity, while our model simulates a 5.7-day periodicity.
This discrepancy stems from the atmospheric dynamics in the deep
atmosphere in the cloud deck, since the Kelvin wave originates, as
explained in Section 5. Artificially imposing more realistic faster winds
in this region in the GCM results in a faster phase speed of the Kelvinwave (Peralta et al., 2020), as the Kelvin wave phase velocity depends
on the zonal wind vertical profile (Peralta et al., 2015).

6.1. O2 (1 𝛥) nightglow
While O, O2 , and CO2 are dynamical tracers computed online in
the IPSL Venus GCM, the O2 (1 𝛥) nightglow at 1.27 μm can be entirely
calculated offline from the simulated GCM atmospheric fields. We
employ the reaction rate coefficient 𝑘1 of the trimolecular reaction
O + O + CO2 → O2 (1 𝛥) + CO2 given by Campbell and Gray (1973):()
485
𝑘1 = 2.5 × 9.4610−34 exp(5)𝑇with 𝑇 the temperature. The volume emission rate VER(in photons.cm−3 s−1 = 10−4 kR km−1 ) is calculated as:
VER = 𝜖𝑘1

𝑛𝑐𝑜2 𝑛2𝑜
1 + 𝜏𝑞𝑛𝑐𝑜2(6)with 𝑛𝑐𝑜2 and 𝑛𝑜 the concentration of CO2 and O species inmolecules.cm−3 , 𝜏 = 4470 s the Einstein coefficient, a quenchingcoefficient 𝑞 = 0.5 × 10−20 cm3 molecule−1 s−1 , and 𝜖 the fraction ofmolecules produced in the O2 (1 𝛥) state, rather than in higher excited
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Fig. 15. 1.27 μm oxygen nightglow with wind arrows at 95 km. The black contours indicate the cloud top zonal retrograde wind at 100 m s−1 to show how the wind field isperturbed by the Kelvin wave underneath. See Appendix A for an animated version of this figure. (For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)

6.3. Airglow intensities and cloud deck dynamics

inaccurate modeled background wind and temperature fields affecting
the vertical propagation and impact of the Kelvin wave.

Nara et al. (2020) reported and modeled a phase lag of 4 ± 2 h
between the noon cloud top and the O dayglow intensity, and explained
it as the sum of the times of vertical propagation of waves and diffusionof O. The mechanism revealed by our simulation does not let us
determine on a phase lag. The complex pattern of wave propagationin the thermosphere (Fig. 11) is not entirely understood, while theanalysis of simulated time series of zonal wind and O density suggest
the absence of a phase lag between the noon cloud top and the O
dayglow intensity (Fig. 14). The phase lag in the observations could
be an artifact caused by uncertainties to the sensing altitude at thecloud top, and noise and sampling. Alternatively, the IPSL Venus GCM
in its present form could inaccurately estimate a zero phase lag, due toInterestingly, the same periodicity is also clearly visible in the O2nightglow emission at mid-latitudes, lagging behind the noon cloud
top zonal maximum by approximately one-fourth of the Kelvin wave
period, i.e. ∼1.4 days. This phase lag is due to the phase lag of the
Kelvin wave structure between the cloud top at the SS point, andthe transition region at the AS point and the transport of O enriched
air to high latitudes from the equator to mid-latitudes. The former isapproximately one-eighth of the Kelvin wave period, as can be seenin the panel T/8 of Fig. 11, i.e. ∼0.7 days. The latter corresponds tothe transport of oxygen over from 30◦ to 50◦ latitude at ∼80 m s−1(Fig. 12), i.e. ∼0.3 days. To our knowledge, no periodic behavior in
the observations of the O2 (1 𝛥) nightglow has ever been reported.
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Fig. 16. Relative contributions of horizontal transport, vertical transport, and chemical reactions in the apparent motion of O2 nightglow. AG stands for AirGlow column emission.

7. Interpreting nightglow’s apparent motions(2008), who pointed out the importance of local strong downward
flows on the O2 nightglow. Therefore, how, when, and where the O2

Hueso et al. (2008), Soret et al. (2014), and Gorinov et al. (2018)
tracked the observed O2 nightglow emission and derived its apparent
horizontal motions. Variations of O2 nightglow can be caused by horizontal transport, vertical transport, chemical reactions, or local change
in temperature or density. Thus, the apparent motion is not necessarilyequal to actual horizontal wind speeds, as hinted by Ohtsuki et al.

nightglow apparent motion is a good tracer of the atmospheric flow isa legitimate question. Since we benefit from a GCM able to simulate
reasonably well the O2 nightglow emission, the first model capable ofreproducing the variability and high latitude events of observations, we
aim to address this question.
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A first look at Fig. 15 and associated animation (see Appendix A)
reveals that large scale eddies play an important role in the nightglow
apparent motion. O2 (1 𝛥)-enriched air is trapped inside downwellingeddies, and is every so often ejected from the eddy as it is disrupted
or merges with other eddies. Those eddies are produced by the highlyvariable motion of flow past the shock-like feature in the thermosphere,
and are subject to intense vertical downwards motion (Fig. 7), directlytransporting atomic oxygen from higher altitudes, and eventually beinga favored location of O2 (1 𝛥) production. This could explain the brightemission patches observed by Ohtsuki et al. (2008), and seen andtracked in Soret et al. (2014), implying that their apparent motions
reflect the eddy motion, rather than horizontal winds. Emission at highlatitudes are caused by the poleward transport of O. Since this transport
stops after a few tens of hours, the apparent motion at the front of theelongated structure is caused by the progressive lack of O available forrecombination. This may have been observed by Gorinov et al. (2018),
with elongated structures at high latitudes subject to a decrease of
intensity at the end of the Kelvin wave cycle.
To quantify these behaviors, we computed the respective contributions from three terms responsible for the nightglow apparent motion:
namely horizontal transport, vertical transport, and chemical reactions.
Other terms, such as diffusion, are orders of magnitude smaller thanthese three terms. The apparent motion is related to the local changeof the volume emission rate VER computed in Eq. (6):These results show that horizontal motions cannot alone explain
the apparent motion of the fast changing nightglow in the complex
circulation of the transition region, unlike clouds that act as mostly
passive tracers, usually in quieter atmospheric flow. It does not meanthat existing observations of nightglow apparent motion are necessarily
poorly correlated with horizontal wind speeds. It rather means thatapparent motion should be analyzed with caution, especially if suchan analysis spans wide ranges of latitudes, local times, total emissions,morphology patterns, and Kelvin wave phases. For instance, manual
tracking (Gorinov et al., 2018) discards features that are deformed
or disappeared over short timescales, ensuring a crude, pragmatic,
filtering that might select horizontal transport over vertical transportand chemical variations.
Interpreting nightglow apparent motion can greatly benefit from theoutputs of such a GCM. Data assimilation would be an ideal technique
for this feat, as it would optimally combine both the information given
by observations and a GCM. It would be an interesting application
to the emerging field of Venusian data assimilation (Sugimoto et al.,2017). Moreover, it could serve for the identification of possible GCM
biases in the transition region, which is sensitive to both upper andlower atmosphere processes.

𝜕VER ||𝑑VER=+ 𝐔 ⋅ ∇VER𝑑t
𝜕t ||chem

Though we provided clues to long-standing scientific questions pertaining to Venus upper atmospheric circulation, some open questions
remain nevertheless. These questions may be answered with further
GCM studies with an emphasis on comparison between models, including data assimilation, as well as the analysis of existing observations
and the planning of future ones:

8. Discussion(7)

with 𝐔 the Eulerian wind. The chemical contribution is obtained
from the recombination of atomic oxygen with rate coefficient 𝑘1
from Eq. (5) for the source term, with inverse lifetime of k2 = 1/𝜏 =1/4470 s−1 (Lafferty et al., 1998) for the sink term:𝜕VER ||= 𝜖𝑘1 𝑛𝑐𝑜2 𝑛2𝑜 − 𝑘2 𝑛𝑜2 (1 𝛥) − 𝑞𝑛𝑜2 (1 𝛥) 𝑛𝑐𝑜2
𝜕t ||chem
Thus, the horizontal, vertical, and chemical contributions torespectively noted h, v, and c, are computed as:

8.1. Is there a supersonic shock in the Venusian upper atmosphere?

(8)

We provided evidence that the ‘‘hot ring’’ may indicate a shock,but the limitations of the dynamical core of the IPSL GCM currently
only hints, but does not prove, that a shock may develop in the flow of
the SS–AS circulation. The fact that the vertical component of soundwaves are filtered out by the hydrostatic dynamical core probably
hinders the modelling of the three dimensional structure of the shocklike feature. For instance, Fromang et al. (2016) found that vertical
shear instabilities were leading to weak shocks in hot Jupiters. A shockresolving code, applied to Venus, will answer the question of if and how
a shock can actually form in its upper atmosphere.
One piece of the puzzle might be the measurements of crossterminator supersonic winds by Clancy et al. (2015), showing a major
unexplained characteristic: their high temporal variability, more than
100 m s−1 over an hourly timescale, with a fine limb resolution of∼0.2 h in local time, but a large horizontal resolution of 3000 km.
They concluded that an unknown large-scale forcing mechanism must
be invoked to account for these changes. Such a mechanism could
be a moving shock, as it is a process that reduces wind speeds.
Our simulations predict the Kelvin wave makes the shock-like feature
position oscillate by ∼0.5 h in local time on the evening, and ∼0.2 h
on the morning (left panel of Fig. 13). Thus, the measurements may
have caught a shock passing through the limb, efficiently reducing windvelocity upstream.

𝑑VER
,
𝑑t

ℎ = |𝑈𝑥 𝑑𝑥 VER + 𝑈𝑦 𝑑𝑦 VER|

(9)𝑣 = |𝑈𝑧 𝑑𝑧 VER|

(10)𝑐 = |𝜖𝑘1 𝑛𝑐𝑜2 𝑛2𝑜 − 𝑘2 𝑛𝑜2 (1 𝛥) − 𝑞𝑛𝑐𝑜2 𝑛𝑜2 |(11)

with 𝑑𝑥, 𝑑𝑦, and 𝑑𝑧 the derivatives with respect to the x, y, and z
directions.
𝑣
𝑐
ℎ
,
, and
, vertically weighted
The ratiosℎ+𝑣+𝑐 ℎ+𝑣+𝑐ℎ+𝑣+𝑐
by VER, and averaged for four classes of total column intensity, areshown as maps in Fig. 16. On average, it is rare that one single
contribution accounts for more than two-thirds of the total nightglow
variation, meaning that, generally speaking, each of the three terms
has comparable values. The vertical profiles for each contribution in
Fig. 16 show that where the VER peaks near 95 km, the chemical
contribution accounts for 50% of the VER variation, the horizontaltransport for 30%, and the vertical one for 20%. Indeed, this altitudein the transition region is the major location of O2 (1 𝛥) production andloss, while the nightside circulation is mostly horizontal. The verticaltransport dominates the horizontal one above 100 km, with downward
motion of the SS–AS circulation, and a peak of the relative abundance(volume mixing ratio) of O2 (1 𝛥) in Fig. 12 near 110 km, higher thanthe VER peak at 95 km.
For nightglow emission < 1 MR, vertical transport dominates between local times 0 h and 22 h. At higher nightglow emissions, horizontal transport plays a dominant role. For nightglow emissions > 2 MR
and more, the chemical contribution dominates at latitudes greaterthan 30◦ , as it corresponds to episodes of strong changes driven by
the sudden influx or lack or atomic oxygen, such as the bright patches
confined in eddies, or the high latitude episodes triggered by the Kelvinwave.

8.2. What are the parameters controlling the characteristics of the Kelvinwave and the possible shock in the upper atmosphere?
The complex circulation modeled by the GCM creates waves thatplay a key role in atmospheric physical processes. However, under thecomplexity of the modeled waves (for instance the patterns of Fig. 11)
and because of the lack of sufficient observational constraints, it notclear what controls some of their important characteristics, such as
their amplitude, the location of the shock-like feature, the propagation
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T. Navarro et al.

and hundreds of kilometers length-scale. For instance, the assumptionsof spherical homogeneous layers (a.k.a. the onion-peeling technique)made for stellar (Piccialli et al., 2015) and solar (Vandaele et al.,2008; Mahieux et al., 2015) occultations may result in larger error
bars than initially thought in the upper atmosphere. Moreover, thedependence of SOIR/SPICAV profiles based on an initial guess of CO2
mixing ratio from the VTS3 semi-empirical model (Hedin et al., 1983)
above 100 km, may not be correct and that it should be reflected inlarger uncertainties in the region 100–140 km, where the VTS3 results
are extrapolated. Once again, data assimilation may prove useful for the
retrievals of observations made sufficiently frequent and consecutive toconverge to an estimate of the true state of the atmosphere.

of secondary waves excited by the Kelvin wave at very high altitudes.
This question shall be addressed by sensitivity analysis of the GCM anddedicated studies of the nonlinear theory applied to these waves in the
Venusian context.
8.3. Can observations confirm that the O2 nightglow spatially changing
structure is linked to the Kelvin wave?
Although neither Crisp et al. (1996), Soret et al. (2014), nor Gorinov
et al. (2018) reported any periodic behavior in the O2 nightglow
despite their long baselines, existing observations may prove sufficient
to answer that question. A detailed analysis of VEx observations would
confirm or disprove if the nightglow events seen by the VIRTIS-M
imaging spectrometer are correlated with the Kelvin wave seen by the
Venus Monitoring Camera (VMC) (Nara et al., 2019). This question is
crucial, as it would put an observational constraint on the Kelvin wave
structure in the upper atmosphere by observing at the same time thecloud top and the nightside transition region and providing a phase lag
between the cloud top wind speed and the nightglow pulsation, if that
pulsation were to actually exist.

8.7. Can the different locations of He, and NO and O2 nightglows bereconciled?
The shift of nitric oxide (NO) nightglow emission at 115 km towards
the morning terminator formed by the reaction of atomic nitrogenand oxygen (Stewart et al., 1980; Stiepen et al., 2013) is difficult tointerpret in terms of circulation because the peak of O2 nightglow
happens at midnight around 95 km. One essential difference between
these nightglows is that the lifetime of N is at least one order ofmagnitude shorter than the one of O above 105 km (Collet et al.,2010). Elaborating on this fact, Collet et al. (2010) demonstrated thatthe peak emission of NO should happen ∼10 h after injection of N
and O, whereas the O2 peak happens ∼48 h after, thus suggesting that
the NO nightglow is a better tracer of the dynamics than the O2 one.
Stewart et al. (1980), Bougher et al. (1990), Royer et al. (2010) andStiepen et al. (2013) reported observations of variable NO nightglow
in brightness and location, sharing the same characteristics as the O2nightglow, suggesting that both nightglows are subject to the complex
variable dynamics of the transition region.
The IPSL Venus GCM does not include a nitrogen chemistry yet, so itcannot simulate the NO species. However, some general considerations
can be made from the simulation results. Even though the average zonal
wind is zero, the asymmetry in the circulation seen in Fig. 1 could
perhaps explain the NO maximum at 110 km, since the circulation on
the morning terminator could trap species at an altitude of ∼100 km.
Between about 100 and 130 km, the zonal wind convergence is shifted
westward from the AS-point, between midnight and 2 h. One possible
source of O and N in the NO production could be their photodissociation on the dayside between 100 and 120 km, and transported to thenightside downwards, west of the AS point. This would be in contrast
to the source of O for the creation of O2 , with O coming mainly fromphotodissociation above 130 km and transported downwards to the AS
point. These two different source locations and transport paths would
favor faster chemical processes in the first case with NO, and longer
ones in the second case with O2 .
Regarding the He nightglow, although the maximum of this emission is located at 165 km, above the top of our model, our current
simulations cannot interpret the emission shift towards the morningterminator (Brinton et al., 1980) as an effect of superrotation. Instead,
we suggest it might be caused by the indirect impact of the Kelvinwave on the nightside, periodically transporting helium westward, oran external effect such as an asymmetry of the solar wind in the Venus
frame of Lundin et al. (2011). Thus, the nightside westward shift ofboth nitric oxide and helium at different altitudes does not necessarily
point to a common mechanism, and future development of the IPSLVGCM (inclusion of the chemistry of nitrogen and vertical extension
up to the ionosphere) may shed light on this topic.

8.4. What is the actual role of the non-orographic gravity waves on thenightside dynamics?
Many assumptions are made concerning this parameterization.
Venus upper atmosphere GCMs that take into account non-orographic
gravity waves suppose a uniform emission from the cloud top (Zalucha
et al., 2013; Hoshino et al., 2012; Gilli et al., 2017), but our study shows
how an increase of resolution is able to reveal the impact of structures
nonexistent at a lower resolution. To explore this aspect, the use of ahigh-resolution mesoscale model (Lefèvre et al., 2020) or Large-Eddy
Simulations (Imamura et al., 2014; Lefèvre et al., 2018) is poised to
guide future GCM developments, as it did on Mars (e.g. Wang et al.,2018) and Earth.
8.5. What is the role of the planetary-scale mountain waves on the upper
atmosphere?
The Akatsuki spacecraft found reoccurring planetary-scale mountain waves in the afternoon at five locations (Fukuhara et al., 2017;
Kouyama et al., 2017). Our simulation did not include the mountainwaves parameterization developed in Navarro et al. (2018) because
it triggered a loss of angular momentum of nonphysical origin in the
dynamical core on a 10 Vd timescale that would bring confusion in theanalysis of the complex mechanisms at stake in the upper atmosphericcirculation beyond the scope of this study. However, these mountainwaves happen between noon and 18 h local time, and should extend
into the SS–AS circulation in the absence of vertical shear. Thus,
they may impact the evening terminator and how the Kelvin wave
interacts with the shock-like feature, and in turn the nightside dynamics. However, Gorinov et al. (2018) claims a correlation between the
structure of O2 nightglow and its apparent motion with the underlying
topography, which could perhaps be explained by a mechanism linked
to mountain waves, as they are the only known manifestation of the
topography on the cloud deck and above. Unexplained observations ofsmall-scale fixed structures seen in the upper cloud deck’s nightside andcorrelated with topography (Peralta et al., 2017), and large-scale cloud
top varying speed (Bertaux et al., 2016) also exist.
8.6. What assumptions are valid for atmospheric retrievals?

9. Conclusion

In the light of the strong variability of atmospheric fields such as
density, and temperature (Figs. 6 and 8), it may appear that assumptions made for existing observation retrievals are not always correct.
We think that observations should be carefully retrieved, as air temperature and composition vary so much on a tens of hours timescale

Our simulation of the ground-to-thermosphere Venusian circulation
with the IPSL Venus GCM reveals unexpected features, such as a shocklike feature in the SS–AS circulation near the terminator (manifested
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T. Navarro et al.

Fig. 17. Principal mechanisms of the upper atmospheric circulation from the IPSL VGCM. Supersonic wind speeds create a shock and downward motion at the terminator, with
reduced speed and CO2 depleted air downstream. The Kelvin wave periodically transports O2 and CO poleward in the nightside transition region, and enhances dayside O and CO
abundances.

by a Lamb wave due to the hydrostatic dynamic core), and a direct
intrusion of a sub-cloud Kelvin wave to the upper atmosphere. Our
proposed mechanism, summed up in Fig. 17, invokes these mechanisms
to explain the variability the nightside upper atmosphere and thecharacteristics of the IR O2 and EUV O airglows observations. Note that
CO is also periodically transported to high latitudes in the transition
region as O2 is, and enhanced on the dayside of the thermosphere as O
is.
This simulation gives new insights on processes occurring in theupper atmosphere of Venus. However, it remains a pure modeling study
that comes with limitations, known and unknown. We can identify
some possible limitations to the realism of the simulation:

Eddy Simulations (LES) for both the cloud deck (Lefèvre et al.,2018, 2020) and the upper atmosphere. This is important because
it impacts the strength of the SS–AS circulation, and in turn thelocation of the shock wave near the terminator. For instance,enhanced winds would push the shock closer to the AS point andreduce the horizontal extent of the region with variable dynamics
on the nightside. This is what we notice when we turn off thisparameterization. A weakened shock would let more westwards
flow enter the nightside, triggering a more vigorous subsidence
and poleward transport. This is also what we noted during thefirst few Venus solar days of simulation before convergence, with
O2 nightglow reaching the pole during Kelvin wave events, while
it is limited to 60◦ once the circulation is established.
• Mountain waves described in Fukuhara et al. (2017), Kouyama
et al. (2017) and Navarro et al. (2018) are not included in thesimulation presented here. One reason is that they destroy thesuperrotation through nonphysical non-conservation of angularmomentum in the dynamical core as explained in Lebonnois et al.
(2012) and Navarro et al. (2018). They would reduce zonal winds
below and inside the cloud deck, drastically changing the Kelvinwave over the course of tens of Venus days that are necessary toreach a steady circulation in the upper atmosphere. As mountainwaves occur between noon and 18 h, they may impact the circulation at the evening terminator, and in turn the whole nightside
dynamics.
• There is a clear gap in the results by changing the resolution from46 × 32 to 96 × 96. For that matter, we recommend that any
Venus upper atmospheric GCM should test if there is a threshold in resolution that creates a shock-like structure, i.e a sharp
decrease of horizontal winds followed by sudden warming and increase in pressure and density. However, other similar behaviors
with threshold in resolution may exist when increasing further the
resolution, by resolving smaller scale waves that would alter the
structure of the nightside dynamics.

• The accuracy of the upward propagation of the Kelvin wave andits secondary waves impacting the upper atmosphere is a criticalcomponent of the model and for the results presented here. The
wave’s vertical propagation strongly depends on the simulated
wind and temperature fields. The Kelvin wave is naturally occurring by the IPSL GCM, unlike forced waves above the clouddeck in GCMs that do not include the lower atmosphere (Hoshino
et al., 2012; Brecht et al., 2021). On one hand, this capability
is an asset of our GCM, since it creates a wave forcing thought
to be as realistic as possible. On the other hand, this could
also be seen as a limitation because assessment of the upper
atmosphere’s sensitivity to wave characteristics is made difficult,requiring sophisticated changes in the simulated global wind andtemperature fields.
• The non-orographic gravity wave drag parameterization assumes
a homogeneous source of small scale gravity waves from the topof convective cells (∼55 km). The source may actually vary withtime and latitude. Other unresolved gravity waves from the low
stability regions on the day and night sides of the upper atmosphere (Fig. 1) may also play a role in the circulation. This would
require a combination of high resolution mesoscale and Large
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• The UV solar flux assumes a mean solar condition for the eight
years of the VEx mission, from 2006 to 2014 (Gilli et al., 2017).
Therefore, the simulation is not sensitive to the 11-year solar
cycle. The bigger impact is on the EUV heating on the dayside
above 130 km, responsible for higher dayside temperatures, anda driver of the SS–AS circulation. An increase of this forcing may
result in a change in SS–AS wind speeds near the terminator,
and in turn the location of the shock and downward flow on
the nightside. Interestingly, Soret and Gérard (2015) found noevidence of correlation between O2 nightglow emission and solar
activity during the VEx mission. Simulations with a different levelof solar activity have not been conducted yet and are a topic offuture research.

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Finally, this work is part of a growing list of evidences that the deep
atmospheric dynamics directly impacts the whole atmosphere up to
the thermosphere, with numerous observables exhibiting periodicities
associated with superrotation. Since Venus is a laboratory for terrestrial
exoplanets with slow rotation and strong insolation gradient leading toa vigorous day-to-night circulation (Kane et al., 2019), typically planets
orbiting M-dwarfs, this result may prove of interest to the interpretationof observations of exoplanetary atmospheres.
Acknowledgments
TN and GS acknowledge NASA Akatsuki Participating Scientist Program under grant NNX16AC84G. GG was supported by the European
Union’s Horizon2020 research and innovation programme under theMarie Sklodowska-Curie grant agreement No 796923 and by Fundação
para a Ciência e a Tecnologia (FCT) through the research grants
UIDB/04434/2020, UIDP/04434/2020, P-TUGA PTDC/FIS-AST/
29942/2017. SL acknowledges the support of the Centre Nationald’Études Spatiales (CNES). This work used computational and storage
services associated with the Hoffman2 Shared Cluster provided by
UCLA Institute for Digital Research and Education’s Research Technology Group, as well as the High-Performance Computing (HPC)
resources of Centre Informatique National de l’Enseignement Suérieur(CINES) under the allocations A0060110391 and A0080110391 madeby Grand Equipment National de Calcul Intensif (GENCI).
Appendix A. Supplementary data
Supplementary material related to this article can be found online
at https://doi.org/10.1016/j.icarus.2021.114400.
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