Toward high resolution simulation for the atmosphere on Venusby AFES (Atmospheric GCM For the Earth Simulator)
Norihiko Sugimoto 1, Masahiro Takagi 2, Yoshihisa Matsuda 3, Yoshiyuki O. Takahashi 4,Masaki Ishiwatari 5, and Yoshi-Yuki Hayashi 4
1

1

Research and Education Center for Natural Sciences, Department of Physics, Keio University
2
Faculty of Science, Kyoto Sangyo University
3
Department of Astronomy and Earth Science, Tokyo Gakugei University
4
Department of Earth and Planetary Sciences, Kobe University,
5
Department of Cosmosciences, Hokkaido University

Introduction

Super-rotation in the atmosphere on Venus is one of themost interesting topics in the planetary science. While Venus issimilar to Earth in its radius, mass, and gravity acceleration, theatmosphere on Venus is quite different from that on Earth.
Venus has a thick CO2 atmosphere, with surface pressure of 92
bar. Its surface temperature is about 730 K owing to the large
greenhouse effect of massive CO2. In addition, there are
optically thick clouds of sulfuric acid droplets, where solar
heating is one of the energy sources to drive atmosphericcirculation. While the solid part of Venus rotates at extremely
slow rate with the period of 243 Earth days, the atmosphere atcloud-top level (about 70 km) rotates about 60 times faster inthe same direction, which is called as “super-rotation”.
In order to elucidate the mechanism of super-rotation,
several mechanisms, such as the Gierasch mechanism [1]through meridional circulation and the thermal tides mechanism[2] through wave mean flow interaction, have been proposed.
Although simulations using Venus-like atmospheric generalcirculation model (GCM) [3,4] suggested that both mechanism
can work to generate super-rotation, these simulations use only
coarse resolutions and involve simple physical processes.
Therefore, in the present study we modify AFES [5](Atmospheric general circulation model For the EarthSimulator) to simulate the Venus atmospheric dynamics withrealistic physical process and high resolution. AFES is highly
optimized for the Earth simulator which is one of the world's
largest vector super-computers provided by Japan Agency for
Marine-Earth Science and Technology (JAMSTEC). Although
our final goal is to understand the fundamental mechanism of
the super-rotation, we have to check the numerical model before
performing long time simulation. As a first step we investigate
unstable modes initiated from the state of super-rotation by thenonlinear numerical simulation.
2Experimental settings

A full nonlinear dynamical model for the atmosphere on
Venus is constructed on the basis of AFES. The basic equations
are primitive ones in sigma coordinates on the sphere. Values ofphysical parameters are chosen for Venus. Physical processes
for the atmosphere on Earth have been replaced by thesimplified version for the atmosphere on Venus. Experimental
settings are basically based on the previous linear stability
analysis [6]. The resolution is now T42L60 (medium), 128 and64 grids are in the longitudinal and meridional direction,respectively. Vertical domain extends from the ground 0 toabout 120 km with almost the constant grid spacing of 2 km.
The model includes vertical and horizontal diffusions. Rayleighfriction (or sponge layer) is not used in the present model except

at the lowest level, where the surface friction acts on horizontal
winds. In addition, the dry convective adjustment scheme isused to restore the temperature lapse rate to the neutral one
when an atmospheric layer becomes statically unstable. Thespecific heat is fixed to constant value.
The solar heating is excluded in the present study forsimplicity, but scheme of the solar heating based on the previous
works is also prepared. Vertical distribution of the specific heatat constant pressure can also be taken from the Venus
international reference atmosphere (VIRA) data. The radiative
forcing in the infrared region is simplified by Newtonian
cooling. The coefficients are based on the previous study. The
temperature field is relaxed to the prescribed zonally uniform
but meridionally gradient field. It is also possible to taketemperature profile from the VIRA data, for future improvement.
We also develop scheme of realistic radiative forcing for future
investigation.
The realistic but idealized static stability based on theobservations is set. The lower atmosphere near the ground ofVenus is weakly stable. In the cloud layer, there is a layer (from55 to 60 km) with almost neutral stability due to the solar
heating. Stable layer is at the bottom of the cloud layer, and thestability has a maximum value at around 45 km. The atmosphereabove the cloud layer (from 70 km) is strongly stratified, as in
the stratosphere on Earth. It is expected that unstable modes willappear in the cloud layer, because low static stability ispreferred for the appearance of unstable barocilinic modes.
The initial state is an idealized super-rotation. The flow
linearly increases with height from ground to 70 km. Its
maximum is 100 m/s at 70 km at the equator and above there it
is constant. Meridional distribution is solid body rotation.
Temperature is in balance with the zonally uniform flow,
namely, gradient wind balance. Meridional temperature
difference from equator to pole is about 5 K at the top of cloudlayer. Initiated from this idealized basic state of super-rotation,
we perform nonlinear numerical simulation of AFES for aperiod of 5 Earth years. The leap frog method is used for thetime integrations with an increment of 600 s. Computationalmodes are excluded by the Asselin filter.
3Results

In the results of numerical simulation, super-rotation is
gradually decreasing in the cloud layer (50 to 70 km) from midlatitude to the pole owing to unstable modes of growing vortices.
Figure 1 shows snapshot of horizontal cross section of vorticity
disturbance at 54 km. Clearly vortices of wavenumber 3 and 4grow at the mid latitude. These growing vortices decrease superrotation where they evolve.

Figure 2 shows height – longitude cross sections of
meridional flow (a) and temperature deviation (b) at the sectionof 40 ˚N where unstable modes grow. The phases of these
disturbances are tilted from down-east to up-west. In addition,
they are out of phase. Namely, cold air flows downward andsouthward, while warm air flows upward and northward. This is
the typical structure of baroclinic instability. It is almost
consistent with the results of previous linear stability analysis[6], although basic zonal flow changed in the time evolution of
nonlinear simulation. Since stable layer exists below the cloudlayer and atmospheric density is large in the lower layer,
unstable modes do not vertically extend to the lower layer. We
also estimate growth rate of these unstable modes by the time
evolution of kinetic energy for each wavenumber. After around240 days, there is a linear growth of energy disturbances forwavenumber 3 and 4. Its e-folding time is about 50 days, which
is longer than the estimates of the previous study [6]. This isbecause of slowing down of super-rotation by 20 – 30 m/s.
We investigate momentum and heat transport of growing
vortices. In the initial stage of baroclinic instability, zonal-mean
zonal flow is accelerated by unstable modes using available
potential energy. Thus, momentum flux converges to thelatitudes where baroclinic modes develop. Heat flux is negativeon the northern hemisphere, that is, heat is transported fromequator to pole. However, after baroclinic vortices havedeveloped, trains of cyclone and anticyclone vortex appear andthey turn into barotropic vortices. While these vortices transport
momentum to equatorial region where they develop, theytransport heat pole ward.
In order to check the dependence of the results on theresolution we also perform simulation with T21L60 resolution,
which has 64 and 32 grids for the longitudinal and latitudinal
direction, respectively. Although we used the same condition
except for the resolution (and therefore the horizontal diffusion),
the flow field is quite different from that of T42L60. Only large
scale vortices appear and there is no filament structure of vortex
due to lack of the resolution. In addition, it takes more time forunstable mode to develop in T21L60 simulation than in T42L60
simulation. Although further analysis is needed to elucidate thedependence on the resolution, we have to use higher resolution
than T21L60, as is done in the present study, in order toinvestigate these disturbances quantitatively.

4Summary and discussion

We investigated unstable modes growing in the idealized
super-rotation using AFES with medium resolution. Baroclinic
instability occurred at the mid latitude in the cloud layer wheresuper-rotation is fast and meridional temperature gradient islarge. They transported momentum from equator and pole to theregion where they evolved, and accelerated super-rotation using
available potential energy. After baroclinic vortices developed
to finite amplitude, they turned into vortices of barotropic type.
They transported significant momentum from pole to equator
while they transport heat from equator to pole. Since basic zonal
flow was changed in the time evolution of nonlinear simulation,
the results of the linear stability analysis [6] could not apply toall stages of the evolution. Especially, vortices of barotropic
type appeared at the later stage, which was not anticipated in thelinear stability analysis.
So far, there are no observations of baroclinic instability on
Venus, though this instability is considered to have very
important roles. This study suggests barocilinic modes could
exist in the cloud layer with small static stability. The conditionof baroclinic instability will be satisfied by the solar heating. Itis also expected that baroclinic modes have a significant impact
on the general circulation on Venus through momentum andheat transportation.
Finally, this study treated only an initial growth ofbaroclinic instability. For future work, we plan to include
realistic solar heating in the model to maintain meridionaltemperature gradient. It is expected that the solar heating willkeep strong super-rotation in the cloud layer. As is frequently
discussed on Gierasch mechanism, several unstable modes arecandidates to transport momentum from pole to equator [7].
Long time numerical simulation initiated from super-rotation [8]would be one of the promising ways to investigate roles ofdisturbances, including baroclinic modes, on super-rotation.
Further study with high resolution simulations and realistic
radiative process will reveal generation and maintenancemechanism of super-rotation on Venus.
Acknowledgements
This study was conducted under the joint research project of theEarth Simulator Center with title "Simulations of Atmospheric
General Circulations of Earth-like Planets by AFES''.
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Fig. 1. Snapshot of horizontal cross section of vorticity
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Fig. 2. Height – longitude cross sections at 40 degrees northof meridional flow disturbance (a) and temperature
disturbance (b) at 300 days.

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