The Fully Developed Superrotation Simulated by a General Circulation Model of a Venus-like Atmosphere

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1 1FEBRUARY 2003 YAMAMOTO AND TAKAHASHI 561 The Fully Developed Superrotation Simulated by a General Circulation Model of a Venus-like Atmosphere MASARU YAMAMOTO Faculty of Education, Wakayama University, Wakayama, Japan MASAAKI TAKAHASHI Center for Climate System Research, University of Tokyo, Tokyo, Japan (Manuscript received 6 September 2001, in final form 19 April 2002) ABSTRACT Formation and maintenance of the fully developed superrotation in the Venus atmosphere are investigated by using a Center for Climate System Research/National Institute for Environmental Study (CCSR/NIES) Venuslike atmospheric general circulation model. Under the condition that zonally uniform solar heating is used, the meridional circulation is dominated by a single cell in a whole atmosphere, and the superrotation with velocities faster than 100 m s 1 is formed near 60-km altitude. The meridional circulation effectively pumps up angular momentum from the lower to the middle atmosphere. Then the angular momentum is transported by poleward flows of the meridional circulation, and a part of the transported momentum is returned back to the low-latitudinal regions by waves. As a result, the simulated superrotation is formed by the Gierasch mechanism. Equatorward angular momentum flux required in the Gierasch mechanism is caused by not only barotropic waves but also various waves. Rossby, mixed Rossby gravity, and gravity waves transport the angular momentum equatorward. Although vertically propagating gravity waves decelerate the superrotation above 70 km, the fully developed superrotation can be maintained in the cloud layer (45 70 km). 1. Introduction On the surface of Venus, a temperature of 730 K is maintained by a greenhouse effect of thick CO 2 gas of 90 atm (e.g., Matsuda and Matsuno 1978; Bullock and Grinspoon 2001). The atmospheric stability is low near the surface. The intermediate stable layer is located at a height of between 30 and 50 km. Near 55-km altitude, the low-stability layer with 5-km thickness is sandwiched between stable layers. Sulfuric acid clouds cover the whole planet range in height from 48 to 70 km and absorb solar radiative fluxes. As a result, diabatic heating is forced in the optically thick cloud. These thermal structures influence the general circulation of Venus s atmosphere. According to UV and near-infrared (NIR) cloud trackings (e.g., Rossow et al. 1990; Belton et al. 1991), probe Doppler measurements (Counselman et al. 1980), and data analysis using the thermal wind relation (Newman et al. 1984), atmospheric superrotation is maintained in a great part of the Venus atmosphere. The zonal wind increases with height below and in the cloud layer. The Corresponding author address: M. Yamamoto, Faculty of Education, Wakayama University, 930 Sakaedani, Wakayama Japan. yamakatu@center.wakayama-u.ac.jp strongest superrotational flow with a velocity of about 100ms 1 exists at the cloud top (65 70 km). In UV detection (Rossow et al. 1990), the cloud-top mean zonal wind with a constant velocity of more than 90 m s 1 is found within 40 latitude, together with mean poleward flow of 1 10 m s 1. Data analysis could indicate the existence of a Hadley circulation (e.g., Rossow et al. 1990; Smith and Gierasch 1996). In upper regions above the cloud top, the zonal wind decreases with height. Maxima of mean zonal wind are located near the cloud top. On the other hand, a maximum of angular momentum density is located near 20 km (Schubert et al. 1980). This results from large atmospheric density in the lower atmosphere. The cloud-top superrotation with a 60 times shorter period than the solid surface rotation period (243 days) is the so-called 4-day circulation. Some basic theories of superrotation have been proposed in previous studies. Atmospheric angular momentum per unit mass a cos ( a cos u) is supplied from the planetary sur- face (a is the planetary radius, is the angular velocity of the planetary rotation, is latitude, u is longitudi- nally averaged zonal flow). The angular momentum is conserved along a trajectory for axisymmetric advection without nonaxisymmetric motion. Hide (1969) pointed out that some nonaxisymmetric motion is required in 2003 American Meteorological Society

2 562 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 60 FIG. 1. (a) The vertical profile of global mean solar heating rate Q 0 (K day 1 ), (b) the latitude height cross section of Q Q 0 ( Q: the zonal mean heating rate). Dashed curve indicates negative value. order for an equatorial flow to rotate with much faster angular velocity than that of the planetary rotation under the existence of axisymmetric circulation. Gierasch (1975) and Matsuda (1980, 1982) introduced eddy diffusion (the parameterization of the nonaxisymmetric motion) in their models, and indicated that Venus s superrotation is maintained by meridional circulation and large horizontal eddy diffusion. Rossow and Williams (1979) and Iga and Matsuda (1999) studied roles of twodimensional barotropic eddies in the horizontal momentum transport process of Venus. Some researchers proposed the superrotation theory without considering meridional circulation. Moving flame experiments (e.g., Schubert and Whitehead 1969), longitudinally tilting convections (e.g., Thompson 1970), and vertically propagating thermal tides (e.g., Fels and Lindzen 1974) lead to the formation and maintenance of the superrotation. In addition, planetary-scale waves (e.g., Covey and Schubert 1981; 1982; Smith et al. 1992, 1993; Yamamoto 2001) and small-scale gravity waves (e.g., Hou and Farrell 1987; Leroy and Ingersoll 1995; Baker et al. 2000) probably redistribute angular momentum vertically in Venus s superrotation. Recently, these mechanisms were investigated under realistic conditions in simple mechanistic models (e.g., Newman and Leovy 1992; Yamamoto and Tanaka 1997). However, the real mechanism of Venus s superrotation is still unclear because of the lack of meteorological observations. On the other hand, GCMs have been used in order to investigate dynamics of atmospheric superrotation in a slowly rotating planet like Venus and a moon like Titan. Most of Venus-like GCMs (e.g., Rossow 1983; Del Genio et al. 1993; Del Genio and Zhou 1996) support the Gierasch Rossow Williams (GRW) mechanism (Gierasch 1975; Rossow and Williams 1979). In the GRW mechanism, the Hadley circulation and quasi-barotropic eddies drive a superrotational flow. However, they did not reproduce a realistic wind of about 100 m s 1 in these Venus-like GCMs (Rossow 1983; Del Genio et al. 1993; Del Genio and Zhou 1996). Although Young and Pollack (1977) produced Venus s superrotation of about 100 m s 1, the diffusion parameterization of vertical momentum introduces spurious forces in their model (Rossow et al. 1980). On the condition that the planetary rotation period T is set at 243 days and the surface pressure P S is set at 90 atm, there is no Venus GCM in which a realistic wind of about 100 m s 1 is reproduced without such assumptions as spurious force, imposed background rotation, additional wave forcing, and large horizontal eddy diffusion. In Titan (Saturn s moon) and Titan-like GCMs (e.g., Hourdin et al. 1995; Del Genio et al. 1993), the superrotations of more than 100 m s 1 are produced on the condition of T 16 days (K243 days on Venus). Titan s superrotation mechanism is also the same as the GRW mechanism. Dynamics of fully developed superrotation in the Venus atmosphere (with the 60 times faster angular velocity than that of the solid surface) is still unclear. In the present study, we try to reproduce the fully developed superrotation in the simplified GCM under the condition that the planetary rotation period of 243 days and the surface pressure of hpa are set. In order to examine how atmospheric waves maintain the superrotation, we analyze the structures of atmospheric waves and general circulation in detail. 2. Model The model used is the version 5.4 of GCM developed at the Center for Climate System Research/National Institute for Environmental Study (Numaguti et al. 1995). The horizontal resolution is T10 and the vertical domain between 0 and 90 km has 50 layers. Numbers of grid points for the calculation of physical processes are 32 and 16 in zonal and meridional directions, respectively. A sigma coordinate is applied in the vertical direction. Layer thickness is approximately 1 km below 10-km altitude, and 2 km at heights from 10 to 80 km. Physical parameters in the Earth s GCM are changed to Venus s values. The planetary rotation period is 243 days (the Earth day), the radius is 6050 km, the gravity acceleration is 8.87 m s 2, and the standard surface pressure is hpa. For the CO 2 atmosphere, a specific heat of Jkg 1 K 1 at constant pressure and gas constant of J kg 1 K 1 are used. Species other than CO 2 are not included. In the Venus atmosphere, it takes more than 10 4 days for dynamical and thermal phenomena to reach equilibrium. Complex radiative processes, which consume significant CPU resources for long-term time integration, are simplified in our Venus-like GCM. A simple radiative process of zonally uniform solar heating and Newtonian cooling is assumed in the Venus-like GCM, since radiative properties are still unknown in the Venus atmosphere. Figure 1 shows the vertical profile of global

3 1FEBRUARY 2003 YAMAMOTO AND TAKAHASHI 563 FIG. 2. Vertical profiles of reference temperature (solid curve) and time constant of Newtonian cooling (dashed curve). mean solar heating rate Q 0 (K day 1 ) and the latitude height cross section of Q Q 0 ( Q is the zonal mean heating rate). The value Q is set as the zonally uniform solar heating rate in our model. The global mean heating has a maximum of 5.2 K day 1 in the cloud layer. Below 35 km, the heating has a rate of 0.52 K day 1. The altitude of the maximum heating rate is lower than that of the cloud-top heating maximum (Tomasko et al. 1985) by about 10 km. The solar heating due to CO 2 above 70 km and the radiative processes on the surface are not included in the present study. Although the vertical heating profile is somewhat different from those of previous studies, the heating in Fig. 1 is incorporated as the Venus-like solar heating. The infrared cooling rate (K day 1 ) is written as Q0 (T T 0)/ N, where T is temperature, T 0 is a reference temperature, and N is a time constant of Newtonian cooling. The Newtonian cooling relaxes the deviation from the reference temperature. Figure 2 shows the reference temperature and the time constant of the Newtonian cooling, based on Seiff et al. (1980) and Hou and Farrell (1987), respectively. In Venus s GCM, the parameterizations of subgridscale physics on Venus are not established. Accordingly, the following physical processes are simplified. Horizontal flow is dissipated by Rayleigh friction of 30 days near the top layer. In addition, eddy components of horizontal flow are dissipated at the same time constant as the Newtonian cooling one in the model atmosphere. In the lowermost layer, the surface frictional drags are incorporated as u/ t u/ drag, / t /, drag / t ( )/, 0 drag where is potential temperature, and 0 is a reference potential temperature at the standard surface pressure. The variable drag has a time constant of 30 days in this model. A fourth-order horizontal diffusion of the e-folding time of 40 days at the maximum wavenumber and the vertical diffusion of K Z 0.15 m 2 s 1 are applied in order to prevent numerical instability (K Z is the vertical eddy diffusion coefficient). At the top and bottom boundaries, the vertical atmospheric eddy diffusion fluxes F vdf are set as zero. Thus, 0 vdf F ( ) d F vdf (0) F vdf (1) 0, 1 where P/P S and P is pressure. The parameterization of the atmospheric diffusion never supplies the angular momentum from the surface to the model atmosphere. In the Earth s GCMs, the surface angular momentum is supplied to the atmosphere through the boundary momentum fluxes depending on the surface condition and turbulence. However, these parameterizations introducing the Earth s empirical constants are not applied in our Venus-like GCM since the validity of the Earth s constants is not clear in the Venusian simulation. The surface momentum is supplied through the simple frictional form of drag in the present study. Although the unknown physical processes are simplified, we can discuss dynamical properties of the fully developed superrotation, if the superrotation can be reproduced in our Venus-like GCM, as was discussed in previous Venus-like GCMs. 3. Results a. Zonal mean fields Time integration was started from a motionless state and was continued until equilibrium was reached. Time variations of longitudinally averaged zonal flow at 5.5 latitude and at 21- and 61-km altitudes are shown in Fig. 3. The result shows almost equilibrium after day (Earth day). An equilibrium state on day is examined. Figure 4 shows the latitude height distributions of longitudinal averages of zonal flow u and total angular momentum density 0 (u acos )a cos ( 0 is mean atmospheric density). The fully developed superrotation is reproduced in this study. The zonal flow increases with height in the lower atmosphere, while it decreases with height in the upper atmosphere. The mean zonal flow has high velocity of about 100 m s 1 near 60 km within 60 latitude. This is consistent with UV cloud

4 564 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 60 FIG. 3. Time variations of zonal mean flows (m s 1 ) at 61- and 21- km levels and at 5.5 lat. tracking observation (Rossow et al. 1990). At the equatorial 21-km level, the mean zonal flow of 35 m s 1 is seen in Fig. 4a, and the total angular momentum density of kg m 1 s 1 is seen in Fig. 4b. The superrotation is fully developed in the lower atmosphere. The simulated angular momentum density is similar to that of the Pioneer Venus observations (Schubert et al. 1980). Figure 5 shows the latitude height cross sections of zonal mean meridional circulation. The strong poleward flow over 10 m s 1 is seen in the upper shear regions where the zonal flow steeply decreases with height. The upward flow of 1 cm s 1 at the equator and the downward flow over 1.5 cm s 1 at the poles are seen in the region between 60 and 75 km. The vertical flow is formed continuously in the height range from the surface to 75 km, though there are noisy structures in the lower atmosphere. The meridional circulation of a single cell is predominant in the model atmosphere. The angular momentum is effectively transported from the lower to the middle atmosphere by the zonal mean upward flow in the equatorial region, where a maximum of the angular momentum is located. Figure 6 shows the latitude height distributions of zonal mean temperature T and buoyancy frequency squared N 2. In the region where the vertical shear of the mean zonal flow u/ z is large, the latitudinal gra- dient of the zonal mean temperature is also large. The zonal mean temperature increases as latitude is higher near 70 km, while it decreases as latitude is higher near 50 km. The zonal mean buoyancy frequency of N s 2 is located near 60 km. The altitude of this low-stability layer is higher than the observed level by about 5 km. The intermediate stable layer appears near 50 km, and the low-stability region of N s 2 is located below 40 km. This thermal structure is qualitatively similar to the Pioneer Venus observation (e.g., Seiff et al. 1980). FIG. 4. Latitude height cross sections of longitudinal average of (a) zonal flow (m s 1 ) and (b) angular momentum density (kg m 1 s 1 ), averaged over 117 days (one Venus day) on day b. Predominant waves The structures of waves with a wide range of phase velocities were investigated for a period of wave analysis over 4096 h from day The data were sampled with 2-h intervals. The time series f(t, ) were transformed to Fourier coefficient F(, s) for the quantities of u,, w,t,and h (t is time, is longitude, is frequency, s is zonal wavenumber, and h is geopotential height). The wave amplitude and the momentum flux obtained from Fourier coefficient F(,s) were sort-

5 1FEBRUARY 2003 YAMAMOTO AND TAKAHASHI 565 FIG. 5. Latitude height cross sections of (a) zonal mean meridional flow (m s 1 ) and (b) zonal mean vertical flow (m s 1 ), averaged over 117 days on day Dashed curve indicates negative value. FIG. 6. Latitude height cross sections of (a) zonal mean temperature (K) and (b) zonal mean buoyancy frequency squared (s 2 ), averaged over 117 days on day ed in order of large value. We picked up more than 20 of the large modes and investigated their wave structures. From the horizontal structure of horizontal flow and geopotential height, the picked-up mode was identified. In this subsection, predominant waves with large amplitudes of h (, s) are discussed. Zonal wavenumber-1 component is most predominant in midlatitudes. At 60 latitude, these waves have large amplitudes in the height range between 40 and 60 km. Figure 7 shows the largest h (, s) of two-type horizontal structures, together with u and. The planetaryscale wave similar to mixed Rossby gravity (MRG) wave is seen in Fig. 7a. This wave has the largest h (, s) in MRG-wave modes at 55-km level and 60 lati-

6 566 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 60 FIG. 7. Horizontal structures of (a) a quasi-stationary MRG-like wave with a zonal wavenumber 1 and (b) a 7.1-day Rossby wave with a zonal wavenumber 1 at 55-km altitude. For this figure and Figs , contours and arrows show the geopotential height (m) and the horizontal flow (m s 1 ), respectively. Dashed curve indicates negative value. Zonal and meridional magnitudes of a reference wind vector are shown by XUNIT and YUNIT, respectively. Superrotational zonal wind flows from left to right. tude. Most of MRG-like waves have phase velocities of 0 10ms 1 at 60 latitude, where the maximum amplitudes are located. Since it is difficult for the MRGlike wave with large intrinsic phase velocity c u ( 90 m s 1 ) to be trapped in the equatorial region, the equatorially trapped width of the MRG-like wave becomes much wider than that of the Earth s MRG wave. The horizontal structure of a 7.1-day Rossby wave is shown in Fig. 7b. This wave has the largest h (, s) in Rossby wave modes at 55-km level and 60 latitude. Vortical winds flowing along contours are predominant. Rossby waves have phase velocities of m s 1 at 60 latitude. Since the sign of the latitudinal gradient of zonal mean potential vorticity averaged for an analysis period (4096 h) is not changed near the region where maximum amplitudes of the predominant waves are located, the waves are not directly generated by barotropic or baroclinic instability. These zonal wavenumber-1 waves may be resonant waves in the intermediate stable layer (40 55 km). As zonal wavenumber becomes higher, h is confined in lower latitudes. Gravity waves with higher wavenumber emitted from the lower atmosphere (below 40 km) are seen in the middle atmosphere. In the equatorial low-stability layer ( 60 km), the zonal wavenumber- 10 waves have almost the same velocity as mean zonal wind. According to UV detection (Rossow et al. 1990; Del Genio and Rossow 1990), the equatorial 4-day and midlatitude 5-day waves with zonal wavenumber 1 are observed. The planetary-scale 4- and 5-day waves are identified with Kelvin and Rossby waves, respectively. The midlatitude 5-day wave in UV detection is reproduced as the zonal wavenumber-1 Rossby wave with periods of 5 7 days in the present study. The simulated Rossby waves have maximum amplitudes of 1/2 h in the intermediate stable layer. On the other hand, the wavenumber-10 gravity waves of 110ms 1 like the Kelvin wave are seen in our experiment, instead of the planetary-scale 4-day wave of 110 m s 1. Accordingly, some formation mechanism of the planetary-scale 4-day wave is required. For example, a nonlinear cascade from high wavenumbers to planetary-scale 4-day wave or other wave forcings (Covey and Schubert 1981, 1982; Smith et al. 1992, 1993) may be worked in the real Venus atmosphere. Although the previous wave analysis shows the structures of predominant waves with large amplitude of h (, s), we do not know whether all of these predominant waves contribute to the formation of the superrotation, or not. In the following subsections, we examine what kinds of waves contribute to the fully developed superrotation. c. Horizontal transport of eddy momentum Figure 8a shows the latitude height distribution of zonal mean horizontal eddy momentum flux u. Equa-

7 1FEBRUARY 2003 YAMAMOTO AND TAKAHASHI 567 FIG. 8. Latitude height cross sections of (a) u (m 2 s 2 ) and (b) 0 a cos u (kg s 2 ), averaged over a sampling period of 4096 h from day Dashed curve indicates negative value. torward momentum fluxes caused by waves are predominant in the height range between 40 and 75 km. Figure 8b shows the latitude height distribution of zonal mean horizontal fluxes of eddy angular momentum density 0 a cos u. Waves transport the angular mo- mentum density equatorward near 10 km. In the height range from the surface to 75 km, waves transport the momentum equatorward. Here we investigate the momentum transport mechanisms at 71, 65, 53, and 11 km. As shown in Fig. 9a, the horizontal momentum is transported by the waves with velocities slower than that of mean flow at 71 km. Although both equatorward and poleward momentum fluxes exist in Fig. 9a, the total eddy momentum flux integrated over all the waves is equatorward at 71 km in Fig. 8a. The equatorward momentum fluxes are mainly caused by vertically propagating gravity waves with zonal wavenumbers of 4 7. Figure 10 shows the horizontal structure of the vertically propagating gravity wave with the equatorward momentum flux (phase velocity c 22.3 m s 1 at 38.2 latitude and zonal wavenumber s 7). The horizontal winds blow from high to low pressure in the height region where the Newtonian cooling is strong. At 71 km, the occupying ratio of gravity wave mode (percentage of number of gravity wave modes in the picked-up modes) is 90% in 33 large equatorward u modes. There are few Rossby and MRG-like wave modes with equatorward momentum fluxes. Figure 9b shows the phase velocity latitude distribution of u at 65 km. Equatorward eddy momentum fluxes are caused by the faster waves of c 80 m s 1 and the slower waves of c 0 40 m s 1. In this region, Rossby and gravity waves contribute to the equatorward momentum transport. Figure 11 shows the horizontal structure of a Rossby wave with equatorward momentum flux (c m s 1 at 27.2 lat and s 2). The phase tilting and the divergence of Rossby waves are seen in midlatitudes. In addition, zonal wavenumber-1 MRG-like wave having maximum amplitude at 50 latitude contributes to the equatorward momentum transport. The latitudinal gradient of zonal mean absolute vorticity averaged over 10 days sometimes becomes negative in low latitudes. Thus, some of the Rossby waves may be associated with barotropic instability. However, all of the waves with equatorward momentum fluxes are not generated by barotropic instability. Divergent winds blowing from high to low pressure also produce the equatorward momentum flux. The eddy divergent winds with phase velocities of 0 40 m s 1 are caused by vertically propagating gravity waves with zonal wavenumbers of 3 7. At 65 km, although the largest u mode is Rossby wave, the occupying ratio of gravity wave mode is 60% in 33 large equatorward u modes. At the 53-km level, equatorward momentum fluxes are caused by planetary-scale MRG-like and Rossby waves, together with gravity waves. The occupying ratio of gravity wave mode is 50% in 33 large equatorward u modes. Although equatorward eddy momentum fluxes of the phase velocities of m s 1 are predominant, the largest u mode is an MRG-like wave

8 568 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 60 FIG. 9. Phase velocity latitude cross sections of spectrum of u at (a) 71 and (b) 65 km, averaged over a sampling period of 4096 h from day of c 0ms 1. The u of the MRG-like wave is 4 times larger than the largest u in gravity wave modes. At 11-km level, the planetary-scale MRG-like wave of c 0ms 1 contributes to equatorward eddy momentum flux. Figure 12 shows the horizontal structure of the MRG-like wave at 11 km. Arrows of the equatorward and poleward flows tilt in the latitudinal region within 60. The tilting of the horizontal flow leads to

9 1FEBRUARY 2003 YAMAMOTO AND TAKAHASHI 569 FIG. 10. Horizontal structure of a zonal wavenumber-7 gravity wave with a phase velocity of 22.3 m s 1 at 38.2 lat and 71-km level. Magnitude of reference wind vector is 6.25 m s 1. See Fig. 7 for more details. FIG. 11. Horizontal structure of a zonal wavenumber-2 Rossby wave with a phase velocity of m s 1 at 27.2 lat and 65-km level. Magnitude of reference wind vector is 3.33 m s 1. See Fig. 7 for more details. the equatorward momentum flux. This planetary-scale MRG-like wave mostly contributes to the equatorial su perrotation in the lower atmosphere. The u of the MRG-like wave is 24 times larger than that of the second predominant mode (Rossby wave). The total u of various waves leads to the equa- torward eddy momentum transport. The equatorward eddy momentum flux is caused by different type waves at the different levels. The Rossby wave modes with large equatorward u mostly have wavenumbers of 1 and 2, while the gravity wave modes mostly have higher wavenumbers. Below 30 km, MRG-like wave transports the momentum equatorward. In the midlatitudinal regions ranging in height from 40 to 65 km, the equatorward momentum fluxes are caused by Rossby, MRGlike, and gravity waves. At 65 and 71 km, vertically propagating gravity waves with phase velocities slower than that of mean flow produce the equatorward momentum fluxes. Since the occupying rate of the gravity wave mode with large equatorward u is high near the critical levels (about 90% at 71 km), some of the vertically propagating gravity waves of c 0 40 m s 1 play an important role as the equatorward momentum transporter near the critical levels. d. Vertical transport of eddy momentum Figure 13 shows the phase velocity height distribu tions of eddy vertical momentum flux u w at 5.5 and 38.2 latitudes. At 5.5 latitude, zonal mean eddy momentum fluxes of c 0 50 m s 1 are negative (u w 0m 2 s 2 in Fig. 13a), since the waves with phase velocities slower than u propagate from the lower to the middle atmosphere. These waves are identified with gravity waves with zonal wavenumbers higher than 4. Since the momentum fluxes of the slower gravity waves (0 50 m s 1 ) are absorbed by mean flow in the vicinity of the critical levels, the weak zonal wind of about 20 ms 1 is formed near 75 km. As shown in Fig. 13a, eddies with velocities of about 105ms 1 also contribute to the vertical eddy momentum transport at 5.5 latitude. The fast-traveling eddies have negative values of zonal mean momentum fluxes near 62 km (blue area near 105 m s 1 in Fig. 13a), while they have positive values above 65 km (red area in Fig. 13a). The momentum fluxes of u w 0m 2 s 2 near 62 km are caused by zonal wavenumber-10 eddies with phase velocities of about 105 m s 1 in the equatorial low-stability layer. These small-scale waves are transiently generated by local convective instability in the low-stability region where global thermal structure is a little stable. The wavenumber-10 eddies of u w 0 m 2 s 2 are similar to longitudinally tilting convection in the equatorial longitude height plane, and confined in the height region between 55 and 65 km. On the other hand, the momentum fluxes of u w 0m 2 s 2 above FIG. 12. Horizontal structures of a zonal wavenumber-1 quasistationary MRG-like wave at 11 km. See Fig. 7 for more details.

10 570 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 60 FIG. 13. Phase velocity height cross sections of spectrum of u w at (a) 5.5 and (b) 38.2, averaged over a sampling period of 4096 h from day

11 1FEBRUARY 2003 YAMAMOTO AND TAKAHASHI km are caused by vertically propagating gravity waves, which are generated in the low-stability layer. These gravity waves are confined in the equatorial region. The vertically propagating waves with fast phase velocities accelerate the equatorial jet at 90 km. This suggests that the fast equatorial waves above the cloud top supply the angular momentum to the superrotating thermosphere. The vertical propagations of the gravity waves are influenced by basic zonal flow and static stability. In the 1979 observation, the maximum of zonal flow is located above the low-stability layer. The vertically propagating waves emitted from the low-stability layer are unlikely to contribute to the thermospheric superrotation, since the waves probably have phase velocities slower than the velocity of basic flow. According to Rossow et al. (1990), the mean cloud-top zonal flow is changed for the period of If the maximum of an equatorial jet is located near the low-stability layer as simulated in our model, the gravity waves emitted from the equatorial jet contribute to the thermospheric superrotation. At 38.2 latitude, the momentum flux of u w 0 m 2 s 2 in Fig. 13b is caused by vertically propagating gravity waves with velocities ranging from 0 to 50 m s 1. These gravity waves are absorbed by mean flow near 75 km, and braking of the superrotation occurs there. Then the deceleration by gravity waves leads to the enhancement of meridional flow near 75 km (e.g., McIntyre 1989; Imamura 1997). e. Horizontal and vertical eddy diffusions The effects of horizontal diffusions are trivial in our low-truncation model of T10. In the equatorial 65-km region where the superrotation is fully developed, the acceleration caused by the fourth-order horizontal diffusion ( 0.02 m s 1 day 1 ) is much smaller than the acceleration caused by u ( 0.4ms 1 day 1 ). The mean zonal flow acceleration caused by the horizontal diffusion is about 0.06 m s 1 day 1 in the weak wind region of u 20ms 1 near 80 km (where waves are strongly dissipated by Newtonian cooling) and in the polar region near 45 km (where the horizontal shear of mean zonal flow is large). In other regions, the acceleration by the horizontal diffusion is smaller than 0.02 ms 1 day 1. The fourth-order horizontal diffusion is not important in the maintenance of the superrotation. A vertical eddy diffusion of K Z 0.15 m 2 s 1 has an e-folding diffusion time of 7700 days, when a scale height of 10 km is considered. The vertical eddy diffusion cannot be ignored below 10-km altitude, since the diffusion has a timescale shorter than that of Newtonian cooling. The zonal mean diffusion flux 0 a cos K z u/ z has a maximum value of about kg s 2 at the equatorial 16-km level. At 60 latitude near the surface ( 0.936), there are submaxima of about kg s 2. In these regions, the vertical eddy diffusion fluxes are nearly equal to the downward angular momentum flux caused by the gravity waves ( kg s 2 ). Although 0 a cos K z u/ z is trivial above 25 km, the vertical eddy diffusion of K z 0.15 m 2 s 1 also contributes to the downward angular momentum flux below 25 km. 4. Formation and maintenance mechanism of Venus s superrotation Based on the results of our Venus-like GCM, a possible mechanism of Venus s superrotation is discussed in this section. Figure 14 shows the latitude height distributions of zonal mean vertical angular momentum fluxes caused by zonal mean flow and eddy at day Zonal mean upward flow pumps up large angular momentum in low latitudes, while angular momentum fluxes transported by zonal mean downward flow are small in high latitudes. This indicates that the Hadley circulation effectively transports the angular momentum upward. On the other hand, the downward angular momentum flux of waves is much smaller than the upward flux of the Hadley circulation, as shown in Fig. 14. Thus, the pumped-up angular momentum is accumulated in the cloud layer. In the present study, formation and maintenance of the superrotation are caused by the Gierasch mechanism (Gierasch 1975; Matsuda 1980, 1982) under the condition that meridional circulation of a single cell is predominant. In the layers where mean zonal flow has almost constant velocity in the latitudinal region within 60, the mean equatorial upward flow effectively pumps up large angular momentum from the lower to the middle atmosphere, while the mean polar downward flow does not effectively transport the angular momentum since the polar angular momentum is much smaller than the equatorial one. Thus the net angular momentum fluxes integrated over whole latitudes are upward. Accordingly, the angular momentum in the lower atmosphere is pumped up by the Hadley circulation. In the upper branch of the meridional circulation, the mean poleward flows transport the angular momentum to high latitudes. A part of the transported momentum is returned back to the low-latitudinal regions by waves before the momentum is removed by the downward flow in high latitudes. Thus the angular momentum is accumulated in the upper branch. In the Gierasch mechanism, large horizontal and small vertical eddy diffusions are required. The present study indicates that various kinds of waves contribute to the horizontal transport of angular momentum, instead of the large eddy horizontal diffusions assumed by Gierasch (1975) and Matsuda (1980, 1982). Equatorward angular momentum fluxes due to Rossby, MRG-like, and gravity waves correspond to the large horizontal eddy diffusion in the Gierasch mechanism. Although barotropic waves are emphasized in the GRW mechanism, various waves produce equatorward angular momentum fluxes, leading to

12 572 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 60 vertically propagating gravity waves of 0 40 m s 1 produce equatorward momentum fluxes. Although we usually discuss eddy vertical momentum flux as a role of vertically propagating gravity waves in atmospheric general circulation, the equatorward momentum flux due to gravity waves must be also considered in the Venus atmosphere. The eddy downward angular momentum fluxes, which correspond to the small vertical eddy diffusion in the Gierasch mechanism, are caused by vertically propagating gravity waves. The zonal-flow deceleration by the gravity waves leads to the enhancement of polar downward flows (e.g., McIntyre 1989; Imamura 1997). As a result, a single Hadley cell spread over a whole atmosphere is enhanced. The single Hadley cell is formed by the assumed heating profile and enhanced by the vertically propagating gravity waves. A large-scale one-loop Hadley circulation is seen on the condition of stable stratification in laboratory experiments (e.g., Koschmieder and Lewis 1986). Thus the circulation simulated in our model may prefer a single cell since the zonal mean atmospheric structure is stable (N 2 0) in the whole model domain. However, we cannot conclude whether the single Hadley cell is formed in the real atmosphere, or not, since a neutrally stable layer with a thickness of 5 km is observed near 55 km on Venus. If the vertical flow of the meridional circulation penetrates into the thin neutral layer of Venus, a single Hadley cell could be formed in the real atmosphere. In the case of the layered Hadley cells (e.g., Schubert et al. 1980), since the vertical flow (also vertical angular momentum flux) is not continuously upward in the equatorial regions between the surface and the cloud top, the layered Hadley cells cannot efficiently transport the angular momentum upward. Accordingly, some upward angular momentum fluxes caused by vertically propagating waves are needed in the case of the layered Hadley cells, as emphasized in Yamamoto and Tanaka (1997). FIG. 14. Latitude height cross sections of (a) 0 a cos ( u a cos ) w (kg s 2 ) and (b) 0 a cos u w (kg s 2 ), averaged over a sampling period of 4096 hours from day Dashed curve indicates negative value. the equatorial acceleration. In the cloud layer and the lower atmosphere, the planetary-scale Rossby and MRG-like waves produce equatorward momentum fluxes. On the other hand, gravity waves also contribute to equatorward momentum transport. At 65 and 71 km, 5. Conclusions When zonally uniform solar heating is forced in our Venus-like GCM, the Hadley circulation and various waves can drive the fully developed superrotation. The strong superrotation is simulated without such assumptions as imposed background rotation, additional wave forcing, and large horizontal diffusion. The results support the Gierasch mechanism, as was simulated in previous Venus-like GCMs (e.g., Rossow 1983; Del Genio et al. 1993; Del Genio and Zhou 1996). Although quasibarotropic waves are emphasized in the previous GCM studies supporting the GRW mechanism, various waves play important roles in the formation and maintenance of the superrotation in the present study. The dynamical process simulated by our Venus-like GCM is one of the possible mechanisms of Venus s superrotation. Meridional circulation is dominated by a single cell,

13 1FEBRUARY 2003 YAMAMOTO AND TAKAHASHI 573 when the zonally uniform solar heating in Fig. 1 is used. Superrotation with the 60 times shorter period than the planetary rotation is formed near the cloud top, and a maximum of angular momentum density is located near 20 km. The low-stability regions are formed near 60 and below 40 km. The simulated atmospheric structures are similar to the observational ones. The formation and maintenance of the superrotation are explained as follows. The Hadley circulation pumps up angular momentum to the cloud layer. In the upper branch of the Hadley circulation, the pumped-up angular momentum is transported by the poleward flows, and a part of the transported momentum is returned back to low latitudes by various waves. As a result, the angular momentum is accumulated in Venus s cloud layer. The zonal mean flows of about 100 m s 1 are reproduced in latitudes within 60. Our numerical experiment shows what causes the large horizontal eddy diffusion in the Gierasch mechanism. Not only barotropic waves but also various other waves contribute to the superrotation. The equatorward momentum fluxes by Rossby, MRG-like, and gravity waves correspond to the large horizontal diffusion in the Gierasch mechanism. Both a single Hadley cell and these waves lead to the fully developed superrotation in the model. On the other hand, vertically propagating gravity waves decelerate the superrotation above the cloud top, and enhance the meridional circulation. Downward angular momentum fluxes of the gravity waves correspond to the small vertical diffusion in the Gierasch mechanism above 25 km. Although the gravity waves decelerate mean zonal flow above the cloud top, the fully developed superrotation (the 4-day circulation) is formed in the cloud layer. Acknowledgments. The authors would like to thank Drs. H. Tanaka, Y. Matsuda, M. D. Yamanaka, T. Imamura, T. 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