Effects of thermal tides on the Venus atmospheric superrotation

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006jd007901, 2007 Effects of thermal tides on the Venus atmospheric superrotation M. Takagi 1 and Y. Matsuda 2 Received 10 August 2006; revised 9 December 2006; accepted 5 January 2007; published 9 May [1] A nonlinear dynamical model on the sphere has been numerically integrated to investigate a generation mechanism of the Venus atmospheric superrotation by the thermal tides. By using the solar heating exciting the diurnal and semidiurnal tides, the atmospheric superrotation extending from the ground to 80 km is generated. The vertical distributions of the mean zonal flow obtained in our experiments are similar to the observations. Velocity of the mean zonal wind on the equator reaches about m s 1 near the cloud top level. A linear theory suggests that the atmospheric superrotation obtained in the present study is generated and maintained by the momentum transport associated with the thermal tides. Namely, the downward transport of zonal momentum that is associated with the downward propagating semidiurnal tide excited in the cloud layer induces the mean zonal flow opposite to the Venus rotation in the lowest layer adjacent to the ground. Surface friction acting on this counter flow provides the atmosphere with the net angular momentum from the solid part of Venus. It is examined how the atmospheric superrotation depends on vertical eddy viscosity and Newtonian cooling. The result shows that magnitude of the atmospheric superrotation is not so sensitive to vertical eddy viscosity but is strongly influenced by Newtonian cooling. Citation: Takagi, M., and Y. Matsuda (2007), Effects of thermal tides on the Venus atmospheric superrotation, J. Geophys. Res., 112,, doi: /2006jd Introduction [2] The atmospheric superrotation of Venus is one of the most remarkable phenomena in the planetary meteorology. The Venus rotation is so slow that the atmospheric motion on Venus was expected to be approximately axisymmetric about a line between the subsolar and antisolar points (for stability of this axisymmetric circulation, see the works of Takagi and Matsuda [1999, 2000]). However, a number of observations show that the fast zonal flow (superrotation) is predominant in the Venus atmosphere [Schubert, 1983]. It is well known that the almost entire atmosphere of Venus rotates much faster than the Venus itself. The mean zonal wind increases monotonically from the ground and reaches about 100 m s 1 near the cloud top level. The corresponding angular velocity is about 60 times larger than that of the solid part of Venus. Although many studies have been made so far, the mechanism generating the superrotation of Venus atmosphere is not still clearly understood. [3] Fels and Lindzen [1974] and Plumb [1975] showed a possibility that the flow retrograde to the solar motion (i.e., atmospheric superrotation) can be generated by momentum transport associated with vertical propagation of the thermal 1 Department of Earth and Planetary Science, University of Tokyo, Tokyo, Japan. 2 Department of Astronomy and Earth Science, Tokyo Gakugei University, Tokyo, Japan. Copyright 2007 by the American Geophysical Union /07/2006JD tides excited in the heating layer. Covey et al. [1986] also argued that the diurnal tide behaves like a thermally direct subsolar-to-antisolar circulation in a diffusive lower Venus atmosphere and the superrotation may be generated there. In the Venus atmosphere, the thick cloud covers the whole planet at km altitudes and the solar heating is mainly absorbed there. It is likely that the thermal tides strongly excited in the cloud layer have important roles on the atmospheric circulation of Venus. The dynamical effects of the thermal tides on the Venus atmospheric superrotation have been examined further by Baker and Leovy [1987], Hou et al. [1990], and Newman and Leovy [1992]. By using a numerical model that spans km altitudes, Newman and Leovy showed that the atmospheric superrotation near the cloud top can be maintained by the momentum transport of thermal tides. However, it should be noted that increase of the net angular momentum that enables the superrotation to form at the cloud levels is produced by Rayleigh friction acting near the upper boundary in their model. Moreover, since the lower boundary is located at 30 km, the downward propagation of the thermal tides (i.e., downward momentum transport) cannot be correctly represented in their model. A vertically uniform background mean zonal flow of solid body rotation with equatorial speed of 75 m s 1 is also assumed in their study. [4] By using a Venus-like atmospheric general circulation model (GCM) with the zonally uniform solar heating, Yamamoto and Takahashi [2003a, 2003b] reproduced atmospheric superrotation faster than 100 m s 1 near 60 km altitude. In their results, a strong meridional circulation with 1of8

2 a large single cell extending from the ground to about 80 km altitude appears and seems to play an important role on the angular momentum transport. They attempt to interpret the superrotation appearing in their model by the generation mechanism proposed by Gierasch [1975] (see also the works of Matsuda [1980, 1982]). It should be noted, however, that the solar heating used in their model is too strong at the lower levels. From observational data reported by Tomasko et al. [1980], it can be estimated that the averaged solar heating rate is about K day 1 in a layer of 0 10 km altitudes (assuming that the solar flux absorbed at the ground is redistributed in this layer), whereas that used by Yamamoto and Takahashi is 0.52 K day 1 there. Hence it is possible that the meridional circulation induced in their model is overemphasized by this heating. Yamamoto and Takahashi [2004] extended these works by adopting a solar heating with diurnal variation. It is shown that the atmospheric superrotation is generated by a similar mechanism except that the angular momentum advected poleward by the meridional circulation is returned back to the lower latitudes by the thermal tides. The strong meridional circulation reproduced by the strong heating in the lower atmosphere is comparable with that of the preceding studies. Their studies are very interesting since the superrotation comparable with the observations is reproduced in the GCM by the strong meridional circulation. However, the reproduction of superrotation by the overestimated heating below the cloud layer does not necessarily demonstrate that the generating mechanism specified in their model is working in the real Venus atmosphere. Lee et al. [2005] also succeeded in reproducing a significant global atmospheric superrotation and discussed the atmospheric waves and the polar vortex which appeared in their result. It seems, however, that the generating mechanism of superrotation in their model is not fully clarified. [5] Recently, Takagi and Matsuda [2005, 2006] examined the thermal tides in the Venus atmosphere in detail by using a linear model based on the observed zonal flows. It is clearly shown that the thermal (semidiurnal) tide excited in the cloud layer propagates downward to the ground and accelerates the atmosphere in the direction opposite to the Venus rotation at altitudes of 0 10 km. They argued from these results that the surface friction acts on this counter flow, and as a result the net momentum is supplied from the solid part of Venus to maintain the atmospheric superrotation. It should be noticed here that no mean zonal flow retrograde to the Venus rotation has been observed by any of several missions. However, this fact is not necessarily contradictory to the above hypothesis (for details, see section 3.1). [6] In the present study, by extending these linear studies, we investigate whether the atmospheric superrotation of Venus can be generated by the nonlinear effect of the thermal tides, integrating a nonlinear dynamical model in spherical geometry. 2. Model [7] In order to investigate the generation mechanism of the Venus atmospheric superrotation by examining the interaction among the thermal tides, the mean zonal flows and the surface friction, a full nonlinear dynamical model on the sphere is constructed. The basic equations are primitive ones in the spherical and s coordinates [Hoskins and Simmons, 1975]. Time integration is performed using the semi-implicit method. Model performance of the dynamical core is checked by comparison with the results of Held and Suarez [1994]. Mean zonal jets and temperature distributions reproduced by the present model are very similar to those of Held and Suarez. The model atmosphere extends from the ground to 120 km, and 60 levels are taken at a regular spacing of 2 km. The horizontal resolution is T10 (triangular truncation at wave number 10). This horizontal resolution is so coarse that numerical convergence and/or truncation errors may well be questioned. It has been confirmed for a few cases, however, that the present model with T21 resolution gives similar results to those described in the following sections. The values of physical parameters for this Venus atmospheric model are as follows: the radius of planet is 6052 km, the period of planetary rotation 243 Earth days, the solar day 117 Earth days, the gravity 8.9 m s 2,the standard surface pressure Pa, and the gas constant J kg 1 K 1 for the CO 2 atmosphere. [8] In order to represent the radiative processes simply, the solar heating, Q, is prescribed in the present study. Its vertical structure is determined by the works of Tomasko et al. [1980] and Crisp [1986]. Vertical distribution of the specific heat at constant pressure, C p, is taken from the Venus international reference atmosphere (VIRA) data [Seiff et al., 1985]. Figure 1 shows the vertical profiles of C p and Q at the subsolar point. The solar flux absorbed at the ground is assumed to be redistributed equally into the lowest atmosphere with 10 km thickness just above the ground. The solar heating above 80 km is artificially attenuated in order to focus on the dynamical effects of the thermal tides excited below the cloud top level. The heating rates represented in K s 1 become extremely small below 50 km due to the dense lower atmosphere of Venus. It is assumed after the work of Crisp [1986] that the horizontal structure of the solar heating on the day side is proportional to cos 0.6 q S (cos 1.5 q S ) above (below) 71 km altitude where q S is the solar zenith angle. In the following calculations, the solar heating is decomposed into the mean zonal component, Q, and the deviation from it, Q 0 : Qðf; q; zþ ¼Qðq; zþþq 0 ðf; q; zþ; where f is longitude, q latitude, and z altitude. It is expected that the thermal tides and the mean meridional flow (Hadley circulation) are excited by Q 0 and Q, respectively. In the following, Q 0 is referred to as tidal component of the solar heating. [9] The radiative forcing in the infrared region is replaced by a linear Newtonian cooling scheme with coefficients based on the work of Crisp [1986]. The temperature field is relaxed to the prescribed horizontally uniform temperature field, T 0 (z), which is taken from the VIRA data. The thermal relaxation to a horizontally uniform temperature field is consistent with the exclusion of the mean zonal component of solar heating. The vertical profiles of T 0 and the relaxation time of Newtonian cooling are shown in Figure 2. [10] Coefficients of vertical eddy viscosity and heat diffusion are set to be , ,or m 2 s 1, ð1þ 2of8

3 Figure 1. Vertical profiles of the solar heating at the subsolar point, Q s (z) (solid line), and the specific heat at constant pressure, C p (z) (dotted line). and horizontal eddy viscosity is represented by the fourthorder hyperviscosity with relaxation time 1.0 Earth day for the maximum wave number component. In addition, we adopt molecular viscosity and heat diffusion that are dependent on temperature and density of the basic state field. Their effects are important above 90 km altitude. Rayleigh friction is not adopted in the present model except at the lowest level, where the surface friction acts on horizontal winds. The relaxation time of Rayleigh friction at the lowest level is assumed to be 1.0 Earth day. [11] The initial state for time integration is an atmosphere at rest for all experiments. It should be emphasized that the background atmospheric superrotation nor the meridional gradient of temperature is not assumed at all throughout the present study. 3. Results [12] In order to isolate specific effects of the thermal tides on the generation and maintenance of the Venus atmospheric superrotation, only the tidal component of solar heating, Q 0, is used for time integration in the present study. The model is integrated for 300 Earth years for all experiments. Parameter values chosen for five experiments conducted in the present study (cases of M1, M2, M3, W2, and S2) are summarized in Table Standard Case [13] Figure 3 shows time evolution of the mean zonal flow on the equator at 65, 45, and 5 km altitudes obtained for the case of M2 (see Table 1). In the present study, zonal velocity in the same direction as the planetary rotation is defined to be positive. Though the relaxation time of the vertical eddy viscosity is estimated to be larger than 1000 Earth years, it seems that the wind field is in a nearly equilibrium state. The zonal velocity at 65 km shows temporal variations with amplitude of a few to 10 m s 1. It is interesting to note that temporal variation has been also observed for the real atmospheric superrotation of Venus [Gierasch et al., 1997]. [14] Meridional-height distribution of the mean zonal flow and the mean temperature deviation from the prescribed equilibrium state obtained at 300 Earth years is illustrated in Figure 4. [15] The atmospheric superrotation has been generated in a wide range of the atmospheric layers below 80 km altitude. The mean zonal flow takes a maximum velocity of about m s 1 near 63 km altitude on the equator. The second local maximum of the mean zonal flow exists just below 80 km. It is likely that this profile of the mean zonal flow with two maxima results from the prescribed vertical profile of solar heating with two peaks at the corresponding altitudes, as shown in Figure 1. The mean zonal flow increases with altitude almost linearly from the ground to 63 km and decreases sharply above 75 km. Above 80 km, the mean zonal flow remains very weak in all latitudes. It is also shown in Figure 4b that there is a reversal of the latitudinal temperature gradient near 60 km. In the light of the gradient wind balance, this reversed temperature gradient is well consistent with the (negative) vertical shear of mean zonal flow. Since the mean zonal component of solar heating, Q, is excluded from our experiments, the distribution of mean temperature deviation is not forced by meridional differential heating but induced by the formation of atmospheric superrotation. [16] These features of the mean zonal flow are similar to the observational results [Schubert, 1983], though the zonal velocity produced in this experiment is slower by m s 1 than that observed in the cloud layer. Moreover, observed temperature fields indicate that midlatitude jets exist at cloud levels [Newman et al., 1984], which are not reproduced in the present result. This should be ascribed to the fact that the exclusion of the mean zonal component of the solar heating results in the absence of poleward advection of zonal momentum by the meridional circulation. [17] It is also shown in Figures 3 and 4a that the mean zonal flow retrograde to the planetary rotation (u < 0)is generated at the lowest levels in lower latitudes than 30. The time evolution of mean zonal flow at 5 km altitude Figure 2. Vertical profiles of the prescribed temperature field, T 0 (z) (solid line), and the relaxation time of Newtonian cooling, t N (z) (dotted line). 3of8

4 Table 1. Parameter Values Adopted in Five Numerical Experiments Case Vertical eddy viscosity (m 2 s 1 ) Factor of Newtonian cooling rates a M M M W /3 S a Standard values of Newtonian cooling rate are taken from the work of Crisp [1986]. shown in Figure 3 indicates that this retrograde mean zonal flow is stronger in the early stage (about Earth years) of the time integration. This distribution of the retrograde mean zonal flow seems very consistent with the numerical result and suggestion of Takagi and Matsuda [2006]. Figure 5 shows a vertical profile of vertical momentum flux, ru 0 w 0, averaged over the region equatorward of 30 degrees and Earth years. It is indicated by this profile that the mean zonal flows tend to be accelerated at about km altitudes and decelerated at about 0 10 and km. It is also noted that this result is very consistent with linear calculations for the semidiurnal tide [Takagi, 2002; Takagi and Matsuda, 2006]. These results enable us to infer that in the present model the thermal tides excited in the cloud layer propagate to the ground and the momentum transport associated with the downward propagation of the semidiurnal tide induces the mean zonal flow retrograde to the planetary rotation in the lower latitudes at 0 10 km altitudes. Since Rayleigh friction is not adopted except at the lowest level in the present model, the net angular momentum supporting the atmospheric superrotation must be provided from the solid part by the surface friction acting on the mean zonal flow adjacent to the ground. As mentioned above, this retrograde mean zonal flow appears only in the early stage of the time integration and nearly vanishes after the superrotation has reached a (quasi) steady state. This result seems consistent with the fact that no mean zonal flow retrograde to the Venus rotation has been observed yet. [18] Figure 6 depicts the time evolution of the vertical profiles of mean zonal flow on the equator at 10, 50, and 300 Earth years. It is seen from these profiles that the atmospheric superrotation is generated near 60 km first and then extends above and below. The extension of the superrotation in the vertical direction results from the effect of vertical eddy and molecular viscosity. Before 10 Earth year, the superrotation is accompanied with the counter flows above and below it; this fact is consistent with the prediction by Fels and Lindzen [1974]. However, the counter flow just below the superrotation is very weak and instead another faster counter flow is found in the lowest layer of 0 10 km altitudes as shown in Figure 6b. It should be noted that the equatorial velocity of the mean zonal flow above 80 km appears to converge at 4 ms 1, which is the zonal phase velocity of the solar heating on the equator. This result means that the critical level is formed just above 80 km and the upward propagating thermal tides are absorbed there by thermal damping due to Newtonian cooling. (Note that Figure 3. Time evolution of mean zonal flow on the equator at 65, 45, and 5 km altitudes obtained for the case of M2. Figure 4. Meridional-height distribution of (a) mean zonal flow (m s 1 ) and (b) mean temperature deviation (K) at 300 Earth years obtained for the case of M2. Contour intervals are (a) 10 m s 1 and (b) 0.3 K, respectively. Contour lines for 0 K are omitted in Figure 4b. 4of8

5 Figure 5. A vertical profile of vertical momentum flux, ru 0 w 0, averaged over the region equatorward of 30 degrees and Earth years for the M2 case. The unit is kg m 1 s 2. thermal damping due to Newtonian cooling is very weak below the cloud bottom.) As a result, the mean zonal flow is decelerated below the critical level and the vertical shear of the mean zonal flow between the cloud top and the critical level is maintained in this experiment. Since the strong solar heating above the cloud top levels, which is excluded from our experiments, would induce strong thermal tides there, this vertical profile of mean zonal flow with a critical level in this layer cannot appear in the real atmosphere of Venus Dependency on Vertical Eddy Viscosity [19] In order to examine how the atmospheric superrotation generated by the thermal tides depends on the vertical eddy viscosity, numerical experiments are conducted for the cases of small vertical eddy viscosity (M1) and large one (M3). See Table 1 for their values. [20] Figure 7 shows the vertical profiles of the mean zonal flow obtained for M1, M2, and M3. In all the cases, peaks of the mean zonal flow are located near 63 km. It is found that their maximum velocity is not so sensitive to the vertical eddy viscosity, though the velocity obtained for M3 is slightly smaller than those for M1 and M2. This result implies that the magnitude of the mean zonal flow is influenced by the mean meridional temperature gradient that is in the gradient wind balance with the zonal flow rather than the vertical eddy viscosity (see also section 3.3). It should be noted that this is not contradictory to the fact that the mean temperature deviation is induced by the formation of superrotation because the mean temperature deviation induced in this way is strongly influenced by the radiative process. [21] In the case of M1, the mean zonal flow retrograde to the Venus rotation remains in the lowest levels of 0 10 km, as shown in Figure 7. In other cases, such a retrograde flow vanishes in an early stage of the time integration due to the stronger vertical eddy viscosity. Figure 6. Vertical profiles of mean zonal flow on the equator at 10 (dotted line), 50 (dashed line), and 300 (solid line) Earth years obtained for the case of M2. Figure 6b enlarges those at 0 20 km altitudes. Figure 7. Vertical profiles of mean zonal flow on the equator obtained for M1 (solid line), M2 (dashed line), and M3 (dotted line). Note that the profiles are averaged over Earth years. 5of8

6 Figure 8. As in Figure 7 but for W2 (solid line), M2 (dashed line), and S2 (dotted line) Dependency on Newtonian Cooling [22] In this subsection, in order to examine how Newtonian cooling influences the generation of atmospheric superrotation, numerical experiments are conducted for the cases with coefficients of Newtonian cooling multiplied by factors of 1/3 (W2) and 3 (S2). The adopted value of vertical eddy viscosity is the same as M2. [23] Figure 8 shows the vertical profiles of mean zonal flow on the equator obtained for the cases of W2, M2, and S2. The mean zonal flow is more sensitive to Newtonian cooling than to the vertical eddy viscosity. Velocities of the mean zonal flow obtained in the three cases are considerably different in a layer of km altitudes. The maximum velocity of mean zonal flow increases (decreases) to about 95 (60) m s 1 for weak (strong) Newtonian cooling. It is also found from time series of the mean zonal flow that the maximum velocity fluctuates between about 80 and 110 m s 1 for the W2 case (not shown). In the case of S2, the mean zonal flow decreases sharply with altitude above 63 km. This is because the thermal tides are damped there by strong Newtonian cooling. The corresponding meridional distributions of zonal mean temperature deviation at altitudes of km obtained for W2, M2, and S2 are shown in Figure 9. It is understood that the larger (smaller) vertical shear of mean zonal flow is associated with the larger (smaller) meridional temperature gradient in the weak (strong) Newtonian cooling case. The magnitude of the atmospheric superrotation is strongly influenced by Newtonian cooling in the present model. 4. Discussion 4.1. Pumping Mechanism of Momentum [24] Though the solar heating used in the present study does not involve its zonal mean component, the present results shown in section 3 suggest that the atmospheric superrotation of Venus can be generated and maintained by the dynamical effects of the thermal tides. As suggested by Takagi and Matsuda [2006], the surface friction acting on the mean zonal flow in the lowest layer, which is created by the downward transport of the zonal momentum associated with the semidiurnal tide excited in the cloud layer, can provide the atmosphere with the net angular momentum required for the maintenance of the global superrotation. It might be speculated, however, that this pumping mechanism of the momentum is inconsistent with the work of Fels and Lindzen [1974]. They predicted that the critical levels were formed just above and below the heating layer and the thermal tides could not propagate across these critical levels. Since the angular momentum cannot be transported across these levels, the generation of the strong superrotation should be prevented. However, only the critical level above the cloud layer is formed in the present experiments. As shown by Takagi and Matsuda [2006], the thermal tides propagating downward from the cloud layer are not necessarily damped below the cloud layer, but reach the ground. This is because Newtonian cooling is much weaker in the lower atmosphere. [25] Figure 10 is a schematic illustration of acceleration mechanism of the mean zonal flow induced by the thermal tides in the work of Fels and Lindzen [1974] and the present one. Since the critical level below the cloud layer is not formed in the present experiments, the angular momentum associated with the downward propagating thermal tides is transported from the cloud layer to the lowest layer adjacent to the ground. This view is also supported by the vertical momentum flux shown in Figure 5. [26] It should be noted here that Hou and Farrel [1987] examined the effect of critical levels in the Venus atmosphere. They proposed that the superrotation may be induced by the critical level absorption of the upward propagating gravity waves excited in the lower atmosphere. This mechanism requires gravity waves with zonal phase velocities much faster than the mean zonal flow at which the waves are excited. It is difficult, however, to suppose such waves in the real atmosphere. Figure 9. Meridional distributions of zonal mean temperature deviation at altitudes of km obtained for W2 (solid line), M2 (dashed line), and S2 (dotted line). 6of8

7 Figure 10. Schematic illustration of acceleration mechanism of mean zonal flow by the thermal tides (a) in the work of Fels and Lindzen [1974] and (b) in the present model. The dashed lines denote zonal phase velocity of the solar heating. The short arrow under the ground represents the surface friction force exerted on the mean flow adjacent to the surface Initial Development of Mean Zonal Flow [27] Since the basic state used in the linear calculation of Takagi and Matsuda [2006] is a mean zonal flow based on the observations, their result cannot be applied directly to the initial stages of our time integration, which is started from a resting atmosphere. It is confirmed by linear calculations with a basic atmosphere at rest that both the diurnal and semidiurnal tides excited in the cloud layer cannot propagate to the ground (not shown), as expected from the dispersion relation of the internal gravity wave. This result implies that the initial development of the mean zonal flow must be caused by other processes except the thermal tides, which are stationary observed from the sun. [28] Figure 11 shows time height distributions of the temperature deviations and the mean zonal flow on the equator in the initial evolution obtained in the case of M2. It is seen that two wave packets propagate downward from 50 km altitude to the ground in the period of Earth days. As a result, the mean zonal flow retrograde to the planetary rotation is induced at altitudes of 0 5 km at about 100 Earth days and the net angular momentum held by the atmosphere increases by the action of surface friction. After 100 Earth days, wave packets propagate to the ground one after another and the mean zonal flow retrograde to the planetary rotation is reinforced at altitudes of 0 10 km. This result indicates that the downward propagating transient waves have important roles on the generation of the mean zonal flow in the initial stage. 5. Conclusion and Remarks [29] A full nonlinear dynamical model on the sphere is constructed to investigate the generation and maintenance of the Venus atmospheric superrotation by the thermal tides. In order to focus on the generation mechanism proposed by Takagi and Matsuda [2006], numerical experiments are conducted by using the solar heating without the mean zonal component. The results show that the atmospheric superrotation similar to the observations is reproduced at altitudes of 0 80 km. The superrotation is generated and maintained by the mechanism summarized as follows. The thermal tides excited in the cloud layer propagate downward to the ground. The momentum transport associated with the downward propagating thermal tides induces the mean zonal flow retrograde to the planetary rotation at altitudes of 0 10 km, on which the surface friction acts. As a result, the net momentum required for the generation of the superrotation is pumped up from the solid part to the atmosphere. It is confirmed that the theory proposed by Takagi and Matsuda [2006] may work and the atmospheric superrotation is generated in the nonlinear model. It should be emphasized that this mechanism does not require effects of mean meridional circulation at all. Above the cloud layer, the vertical shear of the mean zonal flow is maintained by the decelerating effect of the thermal tides which are damped by Newtonian cooling. [30] The vertical structure of the atmospheric superrotation generated by the thermal tides is not so sensitive to the vertical eddy viscosity. The maximum velocity in the equatorial cloud layer is about m s 1 for the cases of standard Newtonian cooling. It is also confirmed that velocity of the mean zonal flow at about km altitudes is strongly influenced by Newtonian cooling. In the weak (strong) Newtonian cooling case, the faster (slower) mean zonal flow about (50 60) m s 1 is produced in the equatorial cloud layer. These results may be ascribed to the following points: (1) mean meridional temperature gradient is reduced by stronger Newtonian Figure 11. Time height distributions of (a) temperature deviations (K) at 0 50 km and (b) mean zonal flow (m s 1 ) at 0 10 km on the equator. Contour intervals are 1 K and 0.05 m s 1, respectively. The period is Earth days of the initial stage. 7of8

8 cooling, and (2) stronger Newtonian cooling tends to inhibit the vertical propagation of thermal tides, as shown by Takagi and Matsuda [2005]. [31] The zonal mean component of solar heating is excluded in the present study. In order to demonstrate that the mechanism proposed in this study can work to generate the superrotation in the real Venus atmosphere, the present work should be extended to include the zonal mean component of the solar heating and the mean meridional circulation excited by it. It should be also noted that the radiative process in the Venus atmosphere with enormous optical depth cannot be correctly represented by a linear Newtonian cooling scheme. In order to simulate and understand the Venus atmospheric superrotation better, it is necessary to incorporate a radiation scheme suitable for the Venus atmosphere into the present model in future. [32] Acknowledgment. Figures were produced by GrADS, GNUPLOT, Tgif, and GFD-DENNOU Library. References Baker, N., and C. B. 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Takahashi (2003b), Superrotation and equatorial waves in a T21 Venus-like AGCM, Geophys. Res. Lett., 30(9), 1449, doi: /2003gl Yamamoto, M., and M. Takahashi (2004), Dynamics of Venus superrotation: The eddy momentum transport processes newly found in a GCM, Geophys. Res. Lett., 31, L09701, doi: /2004gl Y. Matsuda, Department of Astronomy and Earth Science, Tokyo Gakugei University, Nukuikita-machi, Koganei, Tokyo , Japan. (ymatsuda@u-gakugei.ac.jp) M. Takagi, Department of Earth and Planetary Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo , Japan. (takagi@eps. s.u-tokyo.ac.jp) 8of8